From b8473a3dc8747b6e553cde806768445459b61b07 Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 10 Apr 2019 17:02:44 +0200 Subject: [PATCH 001/121] [eli] improve on FFT impl WIP - The eliashberg_product_fft now uses indices instead of interpolation. But this comes with the cost of giving a Gamma with the correct wmesh. The sum over omega for the constant part was substituted by already known Fourier transformation. Also fixed 10. - We now use semi-randomized inputs for the eigenvalue solver to get rid of the tail fit problems. --- c++/triqs_tprf/lattice/eliashberg.cpp | 28 ++- test/python/eliashberg.py | 2 +- test/python/eliashberg_fft.py | 31 ++- test/python/eliashberg_impl_comparison.py | 246 ++++++++++++++++++++++ 4 files changed, 291 insertions(+), 16 deletions(-) create mode 100644 test/python/eliashberg_impl_comparison.py diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index e40316882..efc064c72 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -108,37 +108,45 @@ std::tuple dynamic_and_constant_to_tr(chi_wk_vt Gamma_pp_dy gk_iw_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const_r, gk_iw_vt g_wk, gk_iw_vt delta_wk) { + auto _ = all_t{}; + auto F_wk = eliashberg_g_delta_g_product(g_wk, delta_wk); - // FIXME - // Warning at this point if Matsubara space is too small, also dependent on input delta. - // Seems to be that there is some random fluctuation if this is used in combination with scipy. - // Does not greatly change the results but should be kept in mind. Also ugly print outs. auto F_tr = make_gf_from_fourier<0, 1>(F_wk); - auto F_wr = make_gf_from_fourier<1>(F_wk); // Dynamic part auto delta_tr_out = make_gf(F_tr.mesh(), delta_wk.target()); delta_tr_out *= 0.; + auto [tmesh, rmesh] = delta_tr_out.mesh(); + auto gamma_tmesh = std::get<0>(Gamma_pp_dyn_tr.mesh()); + + // Test if the tau meshs of delta and gamma are compatible. If not raise an error, because + // it would lead to wrong results. + if (tmesh.size() != gamma_tmesh.size()) + TRIQS_RUNTIME_ERROR << "The size of the imaginary time mesh of Gamma" + " (" << gamma_tmesh.size() << ") must be the size of the mesh of Delta (" << + tmesh.size() << ")."; + for (const auto [t, r] : delta_tr_out.mesh()) { for (auto [A, a, B, b] : Gamma_pp_dyn_tr.target_indices()) - delta_tr_out[t, r](a, b) += -Gamma_pp_dyn_tr(t, r)(A, a, B, b) * F_tr(t, r)(A, B); + delta_tr_out[t, r](a, b) += -Gamma_pp_dyn_tr[t, r](A, a, B, b) * F_tr[t, r](A, B); } + // FIXME + // This raises warnings when used with random delta input, e.g. eigenvalue finder auto delta_wk_out = make_gf_from_fourier<0, 1>(delta_tr_out); // Constant part auto delta_r_out = make_gf(std::get<1>(F_tr.mesh()), delta_wk.target()); delta_r_out *= 0.; - for (const auto [w, r] : F_wr.mesh()) { + for (const auto r : rmesh) { + auto F_t = F_tr[_, r]; for (auto [A, a, B, b] : Gamma_pp_dyn_tr.target_indices()) - delta_r_out[r](a, b) += -Gamma_pp_const_r(r)(A, a, B, b) * F_wr(w, r)(A, B); + delta_r_out[r](a, b) += -Gamma_pp_const_r[r](A, a, B, b) * F_t(0)(A, B); } auto delta_k_out = make_gf_from_fourier<0>(delta_r_out); - auto beta = std::get<0>(delta_wk.mesh()).domain().beta; - delta_k_out *= 1. / beta; // Combine dynamic and constant part for (const auto [w , k]: delta_wk_out.mesh()) diff --git a/test/python/eliashberg.py b/test/python/eliashberg.py index 9aa28afe1..caf280eb0 100644 --- a/test/python/eliashberg.py +++ b/test/python/eliashberg.py @@ -120,7 +120,7 @@ print('\nThe benchmark data was obtained with %s.'%show_version_info(p_benchmark.version_info)) np.testing.assert_allclose(p_benchmark.gamma.data, p.gamma.data) -np.testing.assert_allclose(p_benchmark.next_delta.data, p.next_delta.data, atol=1e-7) +np.testing.assert_allclose(p_benchmark.next_delta.data, p.next_delta.data) np.testing.assert_allclose(p_benchmark.E, p.E) try: np.testing.assert_allclose(p_benchmark.eigen_mode.data, p.eigen_mode.data, atol=1e-6) diff --git a/test/python/eliashberg_fft.py b/test/python/eliashberg_fft.py index f90fd86da..6326c9f56 100644 --- a/test/python/eliashberg_fft.py +++ b/test/python/eliashberg_fft.py @@ -68,29 +68,50 @@ g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh) g0_wk_big = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh_big) +chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw) chi0_wk_big = imtime_bubble_chi0_wk(g0_wk_big, nw=int(big_factor*p.nw)+1) U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norbs, p.U, 0, 0, 0) +chi_s = solve_rpa_PH(chi0_wk, U_s) +chi_c = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation chi_s_big = solve_rpa_PH(chi0_wk_big, U_s) chi_c_big = solve_rpa_PH(chi0_wk_big, -U_c) # Minus for correct charge rpa equation +gamma = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) gamma_big = gamma_PP_singlet(chi_c_big, chi_s_big, U_c, U_s) +print(gamma.mesh[0]) +print(gamma.mesh[0].first_index()) +print(gamma.mesh[0].last_index()) +print(gamma_big.mesh[0].first_index()) +print(gamma_big.mesh[0].last_index()) +print(g0_wk.mesh[0].first_index()) +print(g0_wk.mesh[0].last_index()) + # -- Preprocess gamma for the FFT implementation -gamma_dyn_wk, gamma_const_k = split_into_dynamic_wk_and_constant_k(gamma_big) +gamma_dyn_wk, gamma_const_k = split_into_dynamic_wk_and_constant_k(gamma) gamma_dyn_tr, gamma_const_r = dynamic_and_constant_to_tr(gamma_dyn_wk, gamma_const_k) + +print(len(list(gamma_dyn_tr.mesh[0].values()))) + + # -- Test the Eliashberg equation -next_delta = eliashberg_product(gamma_big, g0_wk, g0_wk) -next_delta_fft = eliashberg_product_fft(gamma_dyn_tr, gamma_const_r, g0_wk, g0_wk) +v0 = g0_wk.copy() +#v0.data[:] = v0.data[:] +1.0 +#v0.data[:] = np.random.random(g0_wk.data.shape) + +next_delta = eliashberg_product(gamma_big, g0_wk, v0) +next_delta_fft = eliashberg_product_fft(gamma_dyn_tr, gamma_const_r, g0_wk, v0) + +#np.testing.assert_allclose(next_delta.data, next_delta_fft.data, atol=1e-7) -np.testing.assert_allclose(next_delta.data, next_delta_fft.data, atol=1e-7) Es, eigen_modes = solve_eliashberg(gamma_big, g0_wk) -Es_fft, eigen_modes_fft = solve_eliashberg_fft(gamma_big, g0_wk) +Es_fft, eigen_modes_fft = solve_eliashberg_fft(gamma, g0_wk) E = Es[0] eigen_mode = eigen_modes[0] diff --git a/test/python/eliashberg_impl_comparison.py b/test/python/eliashberg_impl_comparison.py new file mode 100644 index 000000000..6aca8f1dd --- /dev/null +++ b/test/python/eliashberg_impl_comparison.py @@ -0,0 +1,246 @@ +# ---------------------------------------------------------------------- + +""" Compare the naive implementation of the linearized Eliashberg product +and the one using Fourier transformations. +This test is quite computational intensive, because of the inefficiency of +the naive implementations. In the future the Fourier transformation +implementation will subsitute the naive one. +""" + +# ---------------------------------------------------------------------- + +import itertools + +# ---------------------------------------------------------------------- + +import numpy as np + +# ---------------------------------------------------------------------- + +from triqs_tprf.ParameterCollection import ParameterCollection +from pytriqs.gf import Gf, MeshImFreq, Idx + +from triqs_tprf.tight_binding import TBLattice + +from triqs_tprf.lattice import lattice_dyson_g0_wk, solve_rpa_PH +from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk +from triqs_tprf.lattice import gamma_PP_singlet +from triqs_tprf.lattice import eliashberg_product +from triqs_tprf.lattice import eliashberg_product_fft, eliashberg_product_fft_v2 +from triqs_tprf.lattice import split_into_dynamic_wk_and_constant_k, dynamic_and_constant_to_tr +from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors + +# ---------------------------------------------------------------------- + +def compare_deltas(deltas_1, deltas_2=None, static=False): + + if not deltas_2: + deltas_2 = deltas_1 + + if static: + deltas_1 = [ele[Idx(0), :] for ele in deltas_1] + deltas_2 = [ele[Idx(0), :] for ele in deltas_2] + + diff = np.zeros(shape=(len(deltas_1), len(deltas_2))) + + for i, delta_1 in enumerate(deltas_1): + for j, delta_2 in enumerate(deltas_2): + + diff[i,j] = np.max(np.abs(delta_1.data - delta_2.data)) + + return diff + +def print_diff(diff): + + i_max, j_max = diff.shape + + s = "" + + for i in range(i_max): + + for j in range(j_max): + + s += np.format_float_scientific(diff[i,j], precision=2, pad_left=3) + s += "\t" + + s += "\n" + print(s) + + + + + + +def compare_next_delta(p): + +# -- Setup model, RPA susceptibilities and spin/charge interaction + + full_units = [(1, 0, 0), (0, 1, 0), (0, 0, 1)] + all_nn_hoppings = list(itertools.product([-1, 0, 1], repeat=p.dim)) + non_diagonal_hoppings = [ele for ele in all_nn_hoppings if sum(np.abs(ele)) == 1] + + t = -p.t * np.eye(p.norbs) + + H = TBLattice( + units = full_units[:p.dim], + hopping = {hop : t for hop in non_diagonal_hoppings}, + orbital_positions = [(0,0,0)]*p.norbs, + ) + + e_k = H.on_mesh_brillouin_zone(n_k=[p.nk]*p.dim + [1]*(3-p.dim)) + +# A bigger w-mesh is needed to construct a Gamma with a twice as big w-mesh than GF + + wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nw) + wmesh_small = MeshImFreq(beta=p.beta, S='Fermion', n_max=int(p.small_factor*p.nw)+1) + wmesh_big = MeshImFreq(beta=p.beta, S='Fermion', n_max=int(p.big_factor*p.nw)+1) + + g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh) + g0_wk_small = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh_small) + g0_wk_big = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh_big) + + chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw) + chi0_wk_small = imtime_bubble_chi0_wk(g0_wk_big, nw=int(p.small_factor*p.nw)+1) + chi0_wk_big = imtime_bubble_chi0_wk(g0_wk_big, nw=int(p.big_factor*p.nw)+1) + + U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norbs, p.U, 0, 0, 0) + + chi_s = solve_rpa_PH(chi0_wk, U_s) + chi_c = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation + chi_s_small = solve_rpa_PH(chi0_wk_small, U_s) + chi_c_small = solve_rpa_PH(chi0_wk_small, -U_c) # Minus for correct charge rpa equation + chi_s_big = solve_rpa_PH(chi0_wk_big, U_s) + chi_c_big = solve_rpa_PH(chi0_wk_big, -U_c) # Minus for correct charge rpa equation + + gamma = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) + gamma_small = gamma_PP_singlet(chi_c_small, chi_s_small, U_c, U_s) + gamma_big = gamma_PP_singlet(chi_c_big, chi_s_big, U_c, U_s) + +# -- Preprocess gamma for the FFT implementations + + gamma_dyn_wk, gamma_const_k = split_into_dynamic_wk_and_constant_k(gamma) + gamma_dyn_wk_small, gamma_const_k_small = split_into_dynamic_wk_and_constant_k(gamma_small) + gamma_dyn_wk_big, gamma_const_k_big = split_into_dynamic_wk_and_constant_k(gamma_big) + + if not p.const: + + gamma.data[:] = gamma.data - p.U + gamma_small.data[:] = gamma_small.data - p.U + gamma_big.data[:] = gamma_big.data - p.U + + gamma_dyn_wk.data[:] = gamma.data + gamma_dyn_wk_small.data[:] = gamma_small.data + gamma_dyn_wk_big.data[:] = gamma_big.data + + gamma_const_k.data[:] = 0.0 + gamma_const_k_small.data[:] = 0.0 + gamma_const_k_big.data[:] = 0.0 + + if not p.fit_const: + + gamma_dyn_wk.data[:] = gamma.data - p.U + gamma_dyn_wk_small.data[:] = gamma_small.data - p.U + gamma_dyn_wk_big.data[:] = gamma_big.data - p.U + + gamma_const_k.data[:] = p.U + gamma_const_k_small.data[:] = p.U + gamma_const_k_big.data[:] = p.U + + gamma_dyn_tr, gamma_const_r = dynamic_and_constant_to_tr(gamma_dyn_wk, gamma_const_k) + gamma_dyn_tr_small, gamma_const_r_small = dynamic_and_constant_to_tr(gamma_dyn_wk_small, + gamma_const_k_small) + gamma_dyn_tr_big, gamma_const_r_big = dynamic_and_constant_to_tr(gamma_dyn_wk_big, + gamma_const_k_big) + + # -- Creating Semi-Random input Delta + + np.random.seed(1337) + + v0 = g0_wk.copy() + v0.data[:] = v0.data.real + random_data = np.random.random(v0.data.shape[1:]) + freq_data = np.mean(np.abs(v0.data), axis=tuple(range(len(v0.data.shape))[1:])) + not_randomized = 40 + start, stop = not_randomized, v0.data.shape[0]-not_randomized + freq_data[start:stop] *= np.random.random(stop-start) + + v0.data[:] = np.tensordot(freq_data, random_data, axes=0) + + + p.v0 = v0 + +# -- Test the Eliashberg equation + + print('summation') + next_delta = eliashberg_product(gamma_big, g0_wk, p.v0) + print('fft') + next_delta_fft = eliashberg_product_fft(gamma_dyn_tr, gamma_const_r, g0_wk, p.v0) + print('fft_small') + next_delta_fft_small = eliashberg_product_fft(gamma_dyn_tr_small, gamma_const_r_small, g0_wk, p.v0) + print('fft_big') + next_delta_fft_big = eliashberg_product_fft(gamma_dyn_tr_big, gamma_const_r_big, g0_wk, p.v0) + print('fft_v2') + next_delta_fft_v2 = eliashberg_product_fft(gamma_dyn_tr, gamma_const_r, g0_wk, p.v0) + + + from pytriqs.plot.mpl_interface import oplot, plt + subp = [2, 6, 1] + fig = plt.figure(figsize=(18, 15)) + + deltas = [v0, next_delta, next_delta_fft, next_delta_fft_small, next_delta_fft_big, next_delta_fft_v2] + titles = ['input', 'summation', 'fft', 'fft_small', 'fft_big', 'fft_v2'] + + for k_point in [Idx(0,0,0), Idx(1,0,0)]: + + + for delta, title in zip(deltas, titles): + + ax = plt.subplot(*subp); subp[-1] += 1 + oplot(delta[:, k_point]) + plt.title(title) + + ax.legend_ = None + + + plt.show() + + diff = compare_deltas(deltas[1:]) + + print_diff(diff) + + return deltas + + + + +# ---------------------------------------------------------------------- + +p = ParameterCollection( + dim = 1, + norbs = 1, + t = 2.0, + mu = 0.0, + beta = 5, + U = 1.0, + nk = 4, + nw = 200, + const = True, + fit_const = False, + big_factor = 2, + small_factor = 1.0, + ) + +deltas_1 = compare_next_delta(p) + +exit() + +p.nw = 100 + + +deltas_2 = compare_next_delta(p) + +diff = compare_deltas(deltas_1[1:], deltas_2[1:], static=True) + +print_diff(diff) + + From 5ab7c65257e7d2713659d613d9b6807bf1ea1fbf Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 12 Apr 2019 15:28:36 +0200 Subject: [PATCH 002/121] [eli] generalize solving methods - Restructure the eliashberg module to be more flexible - Add power method - Test eliashberg_product and the eigenvalue solver individually in seperate tests. - Add documentation --- doc/reference/eliashberg.rst | 12 + python/triqs_tprf/eliashberg.py | 309 ++++++++++++++---- test/python/CMakeLists.txt | 4 +- test/python/eliashberg/eigenvalue_solver.py | 118 +++++++ .../eliashberg_benchmark.tar.gz | Bin .../previous_implementation.py} | 2 +- .../eliashberg/product_summation_vs_fft.py | 219 +++++++++++++ test/python/eliashberg_fft.py | 128 -------- test/python/eliashberg_impl_comparison.py | 246 -------------- 9 files changed, 593 insertions(+), 445 deletions(-) create mode 100644 doc/reference/eliashberg.rst create mode 100644 test/python/eliashberg/eigenvalue_solver.py rename test/python/{ => eliashberg}/eliashberg_benchmark.tar.gz (100%) rename test/python/{eliashberg.py => eliashberg/previous_implementation.py} (98%) create mode 100644 test/python/eliashberg/product_summation_vs_fft.py delete mode 100644 test/python/eliashberg_fft.py delete mode 100644 test/python/eliashberg_impl_comparison.py diff --git a/doc/reference/eliashberg.rst b/doc/reference/eliashberg.rst new file mode 100644 index 000000000..a1dc194d1 --- /dev/null +++ b/doc/reference/eliashberg.rst @@ -0,0 +1,12 @@ +.. highlight:: python + +.. _eliashberg_functions: + +Eliashberg +========== + +.. autofunction:: triqs_tprf.eliashberg.solve_eliashberg +.. autofunction:: triqs_tprf.eliashberg.semi_random_initial_delta +.. autofunction:: triqs_tprf.eliashberg.power_method_LR +.. autofunction:: triqs_tprf.eliashberg.implicitly_restarted_arnoldi_method +.. autofunction:: triqs_tprf.eliashberg.preprocess_gamma_for_fft diff --git a/python/triqs_tprf/eliashberg.py b/python/triqs_tprf/eliashberg.py index 115450250..fa0317995 100644 --- a/python/triqs_tprf/eliashberg.py +++ b/python/triqs_tprf/eliashberg.py @@ -28,47 +28,101 @@ # ---------------------------------------------------------------------- +from pytriqs.gf import Gf from lattice import eliashberg_product from lattice import eliashberg_product_fft from lattice import split_into_dynamic_wk_and_constant_k, dynamic_and_constant_to_tr # ---------------------------------------------------------------------- -def solve_eliashberg(Gamma_pp, g_wk, tol=1e-10): - """ Solve the linearized Eliashberg equation using - iterative eigenvalue algorithms from scipy """ - - def from_x_to_wk(delta_x): - delta_wk = g_wk.copy() - delta_wk.data[:] = delta_x.reshape(delta_wk.data.shape) - return delta_wk +def semi_random_initial_delta(g_wk, nr_factor=0.5, seed=None): - def from_wk_to_x(delta_wk): - delta_x = delta_wk.data.copy().flatten() - return delta_x - - def matvec(delta_x): - delta_wk = from_x_to_wk(delta_x) - delta_out_wk = eliashberg_product(Gamma_pp, g_wk, delta_wk) - delta_out_x = from_wk_to_x(delta_out_wk) - return delta_out_x - - x = from_wk_to_x(g_wk) - N = x.shape[0] - linop = LinearOperator(matvec=matvec, dtype=np.complex, shape=(N, N)) + r"""Create a delta based on the GF with random elements - np.random.seed(1337) - v0 = np.random.random(N) - E, U = eigs(linop, which='LR', tol=tol, v0=v0) + Returns an anomalous self-energy that can be used as an inital input for the iterative + solvers. The momentum space is random, while the Matsubara space is only partialy + randomized to ensure working tail fits for the Fourier transformations. - eigen_modes = [] - for idx in xrange(U.shape[-1]): - delta_wk = from_x_to_wk(U[:, idx]) - eigen_modes.append(delta_wk) + Parameters + ---------- + g_wk : Gf, + Green's function :math:`G(i\nu_n, \mathbf{k})`. The mesh attribute of the Gf must + be a MeshProduct with the components (MeshImFreq, MeshBrillouinZone). + nr_factor : float, optional + Percentage of :math:`\omega` points which shall not be randomized. This is needed + to assure a working tail fit for the Fourier transformations. The default is 0.5, + meaning that 50% of the :math:`\omega` points will not be randomized. + seed : int, optional + Set a np.random.seed to enforce predictable results. - return E, eigen_modes - -def solve_eliashberg_fft(Gamma_pp_wk, g_wk, Gamma_pp_const_k=None, tol=1e-10): + Returns + ------- + delta : Gf, + An inital anomalous self-energy :math:`\Delta(i\nu_n, \mathbf{k})` to start + a iterative solver, given as a Gf with MeshProduct with the components + (MeshImFreq, MeshBrillouinZone). + """ + + np.random.seed(seed) + + delta = g_wk.copy() + shape = delta.data.shape + delta.data[:] = delta.data.real # Pure real delta is sufficient w/o magnetic field + random_data = np.random.random(shape[1:]) + freq_data = np.mean(np.abs(delta.data), axis=tuple(range(len(shape))[1:])) + not_randomized = int(nr_factor*shape[0] / 2.) + start, stop = not_randomized, shape[0]-not_randomized + freq_data[start:stop] *= np.random.random(stop-start) + + delta.data[:] = np.tensordot(freq_data, random_data, axes=0) + + return delta + +def preprocess_gamma_for_fft(Gamma_pp_wk, Gamma_pp_const_k): + r""" Prepare Gamma to be used with the FFT implementation + + Parameters + ---------- + Gamma_pp_wk : Gf, + Pairing vertex :math:`\Gamma(i\omega_n, \mathbf{k})`. The mesh attribute of + the Gf must be a MeshProduct with the components (MeshImFreq, MeshBrillouinZone). + Gamma_pp_const_k : float or np.ndarray or Gf + Part of the pairing vertex that is constant in Matsubara frequency space + :math:`\Gamma(\mathbf{k})`. If given as a Gf its mesh attribute needs to + be a MeshBrillouinZone. + + Returns + ------- + Gamma_pp_dyn_tr : Gf, + The dynamic part of Gamma, which converges to zero for + :math:`\omega_n \rightarrow \infty`, but now in :math:`\tau`-space. + Its mesh attribute is MeshProduct with the components + (MeshImTime, MeshCyclicLattice). + Gamma_pp_const_r : Gf, + The constant part of Gamma with mesh attribute MeshCyclicLattice. + """ + + # -- Determine the dynamic and constant part via a tail fit + # -- (This is done even if the constant term is given to get the specific Gf types) + Gamma_pp_dyn_wk_fit, Gamma_pp_const_k_fit = split_into_dynamic_wk_and_constant_k(Gamma_pp_wk) + + # -- Use a constant term if explicitly given + const_type = type(Gamma_pp_const_k) + if (const_type == float) or (const_type == np.ndarray): + Gamma_pp_const_k_fit.data[:] = Gamma_pp_const_k + Gamma_pp_dyn_wk_fit.data[:] = Gamma_pp_wk.data - Gamma_pp_const_k + elif (const_type == Gf): + Gamma_pp_const_k_fit[:] = Gamma_pp_const_k.data + Gamma_pp_dyn_wk_fit.data[:] = Gamma_pp_wk.data - Gamma_pp_const_k.data + + # -- FFT dynamic and constant term to (tau, real) or (real) + Gamma_pp_dyn_tr, Gamma_pp_const_r = dynamic_and_constant_to_tr(Gamma_pp_dyn_wk_fit, + Gamma_pp_const_k_fit) + + return Gamma_pp_dyn_tr, Gamma_pp_const_r + +def solve_eliashberg(Gamma_pp_wk, g_wk, Gamma_pp_const_k=None, tol=1e-10, + product='FFT', solver='PM', nr_factor=0.5, seed=None): r""" Solve the linearized Eliashberg equation @@ -90,6 +144,28 @@ def solve_eliashberg_fft(Gamma_pp_wk, g_wk, Gamma_pp_const_k=None, tol=1e-10): be a MeshBrillouinZone. tol : float, optional Relative accuracy for eigenvalues (stopping criterion). + product : str, ['FFT', 'SUM'], optional + Which function of the Eliashberg product shall be used: + + 'FFT' : triqs_tprf.lattice.eliashberg_product_fft, + which uses Fourier transformation for optimal computational efficiency. + Restrictions : + 'SUM' : triqs_tprf.lattice.eliashberg_product, uses the explicit sum. + Restrictions : wmesh of Gamma_pp_wk must be atleast twice the size + of the one of g_wk. + solver : str, ['PM', 'IRAM'], optional + Which eigenvalue solver shall be used: + + 'PM' : Use the Power Method implemented in :func:`power_method_LR`. + + 'IRAM' : Use the Implicitly Restarted Arnoldi Method implemented in :func:`implicitly_restarted_arnoldi_method`. + nr_factor : float, optional + Percentage of :math:`\omega` points of the inital delta, which shall not be + randomized. This is needed to assure a working tail fit for the + Fourier transformations. The default is 0.5, meaning that 50% of + the :math:`\omega` points will not be randomized. + seed : int, optional + Set a np.random.seed to enforce predictable results. Returns ------- @@ -102,27 +178,9 @@ def solve_eliashberg_fft(Gamma_pp_wk, g_wk, Gamma_pp_const_k=None, tol=1e-10): See Also -------- - :ref:`eliashberg` - + :ref:`eliashberg` : Theory of the linearized Eliashberg equation. """ - # -- Determine the dynamic and constant part via a tail fit - # -- (This is done even if the constant term is given to get the specific GF types) - Gamma_pp_dyn_wk_fit, Gamma_pp_const_k_fit = split_into_dynamic_wk_and_constant_k(Gamma_pp_wk) - - # -- Use a constant term if explicitly given - if Gamma_pp_const_k: - try: - Gamma_pp_const_k_fit.data[:] = Gamma_pp_const_k - Gamma_pp_dyn_wk_fit.data[:] = Gamma_pp_wk.data - Gamma_pp_const_k - except TypeError: - Gamma_pp_const_k_fit[:] = Gamma_pp_const_k.data - Gamma_pp_dyn_wk_fit.data[:] = Gamma_pp_wk.data - Gamma_pp_const_k.data - - # -- FFT dynamic and constant term to (tau, real) or (real) - Gamma_pp_dyn_tr, Gamma_pp_const_r = dynamic_and_constant_to_tr(Gamma_pp_dyn_wk_fit, - Gamma_pp_const_k_fit) - def from_x_to_wk(delta_x): delta_wk = g_wk.copy() delta_wk.data[:] = delta_x.reshape(delta_wk.data.shape) @@ -131,25 +189,140 @@ def from_x_to_wk(delta_x): def from_wk_to_x(delta_wk): delta_x = delta_wk.data.copy().flatten() return delta_x - - def matvec(delta_x): - delta_wk = from_x_to_wk(delta_x) - delta_out_wk = eliashberg_product_fft(Gamma_pp_dyn_tr, Gamma_pp_const_r, g_wk, delta_wk) - delta_out_x = from_wk_to_x(delta_out_wk) - return delta_out_x - - x = from_wk_to_x(g_wk) - N = x.shape[0] - linop = LinearOperator(matvec=matvec, dtype=np.complex, shape=(N, N)) - np.random.seed(1337) - v0 = np.random.random(N) - Es, U = eigs(linop, which='LR', tol=tol, v0=v0) + if product == 'FFT': + + Gamma_pp_dyn_tr, Gamma_pp_const_r = preprocess_gamma_for_fft(Gamma_pp_wk, Gamma_pp_const_k) + + def matvec(delta_x): + delta_wk = from_x_to_wk(delta_x) + delta_out_wk = eliashberg_product_fft(Gamma_pp_dyn_tr, Gamma_pp_const_r, g_wk, delta_wk) + delta_out_x = from_wk_to_x(delta_out_wk) + return delta_out_x + + elif product == 'SUM': + + def matvec(delta_x): + delta_wk = from_x_to_wk(delta_x) + delta_out_wk = eliashberg_product(Gamma_pp_wk, g_wk, delta_wk) + delta_out_x = from_wk_to_x(delta_out_wk) + return delta_out_x + + else: + raise NotImplementedError('There is no implementation of the eliashberg product' + ' called %s.'%product) + + init = from_wk_to_x(semi_random_initial_delta(g_wk, nr_factor=nr_factor, seed=seed)) + + if solver == 'PM': + es, evs = power_method_LR(matvec, init, tol=tol) + es, evs = [es], [evs] + + elif solver == 'IRAM': + es, evs = implicitly_restarted_arnoldi_method(matvec, init, tol=tol) + + else: + raise NotImplementedError('There is no solver called %s.'%solver) + + eigen_modes = [from_x_to_wk(ele) for ele in evs] + + return es, eigen_modes + +def implicitly_restarted_arnoldi_method(matvec, init, tol=1e-10): + + """Find the eigenvalue with the largest real value via the Implicitly Restarted + Arnoldi Method + + Parameters + ---------- + matvec : callable f(v), + Returns A*v. + init : np.ndarray, + The array representation of the anomalous self-energy to start the iterative + method with. Restriction: len(init.shape) == 1. + tol : float, optional + The tolerance at which the iterative scheme is considered to be converged. + + Returns + ------- + Es : list of float, + The eigenvalues with the largest positive real part. + U : list of np.ndarray, + The corresponding eigenvectors. - eigen_modes = [] - for idx in xrange(U.shape[-1]): - delta_wk = from_x_to_wk(U[:, idx]) - eigen_modes.append(delta_wk) + Notes + ----- + `scipy.sparse.linalg.eigs `_ - return list(Es), eigen_modes + `scipy.sparse.linalg.LinearOperator `_ + """ + N = init.shape[0] + linop = LinearOperator(matvec=matvec, dtype=np.complex, shape=(N, N)) + Es, U = eigs(linop, which='LR', tol=tol, v0=init) + Es = Es.real + return list(Es), list(U.T) + +def power_method_LR(matvec, init, tol=1e-10, max_it=1e5): + + """Find the eigenvalue with the largest real value via the power method + + Parameters + ---------- + matvec : callable f(v), + Returns A*v. + init : np.ndarray, + The array representation of the anomalous self-energy to start the iterative + method with. Restriction: len(init.shape) == 1. + tol : float, optional + The tolerance at which the iterative scheme is considered to be converged. + max_it : float, optional + The maximum number of iterations that shall be done before a error is raised. + + Returns + ------- + norm : float, + The eigenvalue with the largest positive real part. + v_k : np.ndarray, + The corresponding eigenvector. + """ + + def iteration(v_k, offset=0.0): + v_k1 = matvec(v_k) - offset*v_k + v_k1_norm = np.linalg.norm(v_k1) + v_k1 = v_k1 / v_k1_norm + return v_k1_norm+offset, v_k1 + + def power_method(init, offset=0.0, tol=tol, max_it=max_it): + norm, v_k = iteration(init, offset) + it = 1 + while True: + norm, new_v_k = iteration(v_k, offset) + + # -- Convergence criterion + add = np.max(np.abs(v_k + new_v_k)) + diff = np.max(np.abs(v_k - new_v_k)) + + if (np.allclose(add, 0, atol=tol)) or (np.allclose(diff, 0, atol=tol)): + break + + v_k = new_v_k + it += 1 + if it > max_it: + raise AssertionError('Did not converge.') + return norm, v_k + + # Find eigenvalue with maximum magnitude + norm, v_k = power_method(init, tol=tol) + + # Check sign of found eigenvalue + _, v_k_test = iteration(v_k) + + add = np.sum(np.abs(v_k + v_k_test)) # small if sign of E is negative + diff = np.sum(np.abs(v_k - v_k_test)) # small if sign of E is positive + + # -- Return eigenvalue with largest real part + if diff > add: # The eigenvalue with the largest magnitude is negative + norm, v_k = power_method(init, offset=-norm, tol=tol) + return norm, v_k + diff --git a/test/python/CMakeLists.txt b/test/python/CMakeLists.txt index bd1496038..1d0435dfa 100644 --- a/test/python/CMakeLists.txt +++ b/test/python/CMakeLists.txt @@ -4,8 +4,8 @@ foreach(file ${all_h5_tgz_files}) configure_file(${file} ${file} COPYONLY) endforeach() -# List of all tests -set(all_tests chi4_iw_from_tau g_wk_to_from_g_wr_py chi00_square_lattice bse_and_rpa_loc_vs_latt mean_field mean_field_kanamori hartree_response 1d_hubbard_hf_rpa 1d_hubbard_hf_spin_rot_inv 1d_hubbard_hf_rpa_2site_AFM eliashberg compare_general_rpa_to_matrix_rpa interaction_tensor_charge_spin_factorization) +# List all tests +set(all_tests chi4_iw_from_tau g_wk_to_from_g_wr_py chi00_square_lattice bse_and_rpa_loc_vs_latt mean_field mean_field_kanamori hartree_response 1d_hubbard_hf_rpa 1d_hubbard_hf_spin_rot_inv 1d_hubbard_hf_rpa_2site_AFM compare_general_rpa_to_matrix_rpa interaction_tensor_charge_spin_factorization eliashberg/product_summation_vs_fft eliashberg/eigenvalue_solver eliashberg/previous_implementation) foreach(test ${all_tests}) get_filename_component(test_name ${test} NAME_WE) diff --git a/test/python/eliashberg/eigenvalue_solver.py b/test/python/eliashberg/eigenvalue_solver.py new file mode 100644 index 000000000..0b11fc671 --- /dev/null +++ b/test/python/eliashberg/eigenvalue_solver.py @@ -0,0 +1,118 @@ +# ---------------------------------------------------------------------- + +""" Compare the summation implementation of the linearized Eliashberg product +and the one using Fourier transformations. +""" + +# ---------------------------------------------------------------------- + +import itertools + +# ---------------------------------------------------------------------- + +import numpy as np + +# ---------------------------------------------------------------------- + +from triqs_tprf.ParameterCollection import ParameterCollection +from pytriqs.gf import Gf, MeshImFreq, Idx + +from triqs_tprf.tight_binding import TBLattice + +from triqs_tprf.lattice import lattice_dyson_g0_wk, solve_rpa_PH +from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk +from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors +from triqs_tprf.lattice import gamma_PP_singlet +from triqs_tprf.eliashberg import solve_eliashberg + +# ---------------------------------------------------------------------- + +def run_solve_eliashberg(p): + + # -- Setup model, RPA susceptibilities and spin/charge interaction + + full_units = [(1, 0, 0), (0, 1, 0), (0, 0, 1)] + all_nn_hoppings = list(itertools.product([-1, 0, 1], repeat=p.dim)) + non_diagonal_hoppings = [ele for ele in all_nn_hoppings if sum(np.abs(ele)) == 1] + + t = -p.t * np.eye(p.norbs) + + H = TBLattice( + units = full_units[:p.dim], + hopping = {hop : t for hop in non_diagonal_hoppings}, + orbital_positions = [(0,0,0)]*p.norbs, + ) + + e_k = H.on_mesh_brillouin_zone(n_k=[p.nk]*p.dim + [1]*(3-p.dim)) + + # A bigger w-mesh is needed to construct a Gamma with a twice as big w-mesh than GF + + wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nw) + wmesh_big = MeshImFreq(beta=p.beta, S='Fermion', n_max=int(p.big_factor*p.nw)+1) + + g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh) + g0_wk_big = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh_big) + + chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw) + chi0_wk_big = imtime_bubble_chi0_wk(g0_wk_big, nw=int(p.big_factor*p.nw)+1) + + U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norbs, p.U, p.Up, p.J,p.Jp) + + chi_s = solve_rpa_PH(chi0_wk, U_s) + chi_c = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation + chi_s_big = solve_rpa_PH(chi0_wk_big, U_s) + chi_c_big = solve_rpa_PH(chi0_wk_big, -U_c) # Minus for correct charge rpa equation + + gamma = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) + gamma_big = gamma_PP_singlet(chi_c_big, chi_s_big, U_c, U_s) + + if p.product == 'SUM': + gamma = gamma_big + + if p.fit_const: + gamma_const = None + else: + gamma_const = 0.5*(U_s + U_c) + + Es, eigen_modes = solve_eliashberg(gamma, g0_wk, Gamma_pp_const_k=gamma_const, + product=p.product, solver=p.solver, + nr_factor=p.nr_factor, seed=p.seed) + + return Es, eigen_modes + +#================================================================================ + +if __name__ == '__main__': + + p = ParameterCollection( + dim = 1, + norbs = 1, + t = 1.0, + mu = 0.0, + beta = 5, + U = 1.0, + Up = 0.8, + J = 0.1, + Jp = 0.1, + nk = 4, + nw = 350, + fit_const = False, + big_factor = 2, + product = 'FFT', + solver = 'PM', + nr_factor = 0.6, + seed = 1337, + ) + + Es_pm, eigen_modes_pm = run_solve_eliashberg(p) + + p.solver = 'IRAM' + Es_iram, eigen_modes_iram = run_solve_eliashberg(p) + + print(Es_pm[0], Es_iram[0]) + + np.testing.assert_allclose(Es_pm[0], Es_iram[0]) + np.testing.assert_allclose(eigen_modes_pm[0].data, eigen_modes_iram[0].data, atol=1e-8) + + print('Both solvers yield the same results.') + diff --git a/test/python/eliashberg_benchmark.tar.gz b/test/python/eliashberg/eliashberg_benchmark.tar.gz similarity index 100% rename from test/python/eliashberg_benchmark.tar.gz rename to test/python/eliashberg/eliashberg_benchmark.tar.gz diff --git a/test/python/eliashberg.py b/test/python/eliashberg/previous_implementation.py similarity index 98% rename from test/python/eliashberg.py rename to test/python/eliashberg/previous_implementation.py index caf280eb0..6f85b2530 100644 --- a/test/python/eliashberg.py +++ b/test/python/eliashberg/previous_implementation.py @@ -86,7 +86,7 @@ gamma = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) gamma_big = gamma_PP_singlet(chi_c_big, chi_s_big, U_c, U_s) next_delta = eliashberg_product(gamma_big, g0_wk, g0_wk) -E, eigen_modes = solve_eliashberg(gamma_big, g0_wk) +E, eigen_modes = solve_eliashberg(gamma_big, g0_wk, product='SUM', solver='IRAM') # -- Save results diff --git a/test/python/eliashberg/product_summation_vs_fft.py b/test/python/eliashberg/product_summation_vs_fft.py new file mode 100644 index 000000000..74fd7058d --- /dev/null +++ b/test/python/eliashberg/product_summation_vs_fft.py @@ -0,0 +1,219 @@ +# ---------------------------------------------------------------------- + +""" Compare the summation implementation of the linearized Eliashberg product +and the one using Fourier transformations. +""" + +# ---------------------------------------------------------------------- + +import itertools + +# ---------------------------------------------------------------------- + +import numpy as np + +# ---------------------------------------------------------------------- + +from triqs_tprf.ParameterCollection import ParameterCollection +from pytriqs.gf import Gf, MeshImFreq, Idx + +from triqs_tprf.tight_binding import TBLattice + +from triqs_tprf.lattice import lattice_dyson_g0_wk, solve_rpa_PH +from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk +from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors +from triqs_tprf.lattice import gamma_PP_singlet +from triqs_tprf.lattice import eliashberg_product, eliashberg_product_fft +from triqs_tprf.eliashberg import semi_random_initial_delta, preprocess_gamma_for_fft + +# ---------------------------------------------------------------------- + +def compare_deltas(deltas_1, deltas_2=None, static=False): + """ Build comparison matrix of list of Gf + """ + + if not deltas_2: + deltas_2 = deltas_1 + + if static: + deltas_1 = [ele[Idx(0), :] for ele in deltas_1] + deltas_2 = [ele[Idx(0), :] for ele in deltas_2] + + diff = np.zeros(shape=(len(deltas_1), len(deltas_2))) + + for i, delta_1 in enumerate(deltas_1): + for j, delta_2 in enumerate(deltas_2): + + diff[i,j] = np.max(np.abs(delta_1.data - delta_2.data)) + + return diff + +def print_diff(diff): + """ Print output of 'compare_deltas' more readable + """ + + i_max, j_max = diff.shape + + s = "" + s += "\n Differences matrix\n" + dashes = "-"*14*diff.shape[0] + "\n" + s += dashes + + for i in range(i_max): + + for j in range(j_max): + + s += np.format_float_scientific(diff[i,j], precision=2, pad_left=3) + s += "\t" + + s += "\n" + s += dashes + print(s) + +def compare_next_delta(p): + + # -- Setup model, RPA susceptibilities and spin/charge interaction + + full_units = [(1, 0, 0), (0, 1, 0), (0, 0, 1)] + all_nn_hoppings = list(itertools.product([-1, 0, 1], repeat=p.dim)) + non_diagonal_hoppings = [ele for ele in all_nn_hoppings if sum(np.abs(ele)) == 1] + + t = -p.t * np.eye(p.norbs) + + H = TBLattice( + units = full_units[:p.dim], + hopping = {hop : t for hop in non_diagonal_hoppings}, + orbital_positions = [(0,0,0)]*p.norbs, + ) + + e_k = H.on_mesh_brillouin_zone(n_k=[p.nk]*p.dim + [1]*(3-p.dim)) + + # A bigger w-mesh is needed to construct a Gamma with a twice as big w-mesh than GF + + wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nw) + wmesh_big = MeshImFreq(beta=p.beta, S='Fermion', n_max=int(p.big_factor*p.nw)+1) + + g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh) + g0_wk_big = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh_big) + + chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw) + chi0_wk_big = imtime_bubble_chi0_wk(g0_wk_big, nw=int(p.big_factor*p.nw)+1) + + U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norbs, p.U, p.Up, p.J,p.Jp) + + chi_s = solve_rpa_PH(chi0_wk, U_s) + chi_c = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation + chi_s_big = solve_rpa_PH(chi0_wk_big, U_s) + chi_c_big = solve_rpa_PH(chi0_wk_big, -U_c) # Minus for correct charge rpa equation + + gamma = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) + gamma_big = gamma_PP_singlet(chi_c_big, chi_s_big, U_c, U_s) + + # -- Preprocess gamma for the FFT implementations + + + if p.fit_const: + gamma_dyn_tr, gamma_const_r = preprocess_gamma_for_fft(gamma, None) + else: + gamma_dyn_tr, gamma_const_r = preprocess_gamma_for_fft(gamma, 0.5*(U_s + U_c)) + + # -- Creating Semi-Random input Delta + + v0 = semi_random_initial_delta(g0_wk, nr_factor=p.nr_factor, seed=1337) + p.v0 = v0 + + # -- Test the Eliashberg product + + print('Start the summation') + next_delta = eliashberg_product(gamma_big, g0_wk, p.v0) + print('Start the FFT') + next_delta_fft = eliashberg_product_fft(gamma_dyn_tr, gamma_const_r, g0_wk, p.v0) + + from pytriqs.plot.mpl_interface import oplot, plt + import warnings + warnings.filterwarnings("ignore") #ignore some matplotlib warnings + subp = [4, 3, 1] + fig = plt.figure(figsize=(18, 15)) + + deltas = [v0, next_delta, next_delta_fft] + titles = ['Input', 'Summation', 'FFT'] + + for k_point in [Idx(0,0,0), Idx(1,0,0)]: + + ax = plt.subplot(*subp); subp[-1] += 1 + oplot(g0_wk[:, k_point]) + plt.title('GF') + + ax = plt.subplot(*subp); subp[-1] += 1 + oplot(gamma[:, k_point]) + plt.title('Gamma') + + ax = plt.subplot(*subp); subp[-1] += 1 + oplot(gamma_dyn_tr[:, k_point]) + plt.title('Gamma dyn tr') + + for delta, title in zip(deltas, titles): + + ax = plt.subplot(*subp); subp[-1] += 1 + oplot(delta[:, k_point]) + plt.title(title) + + ax.legend_ = None + + #plt.show() + + diff = compare_deltas(deltas[1:]) + + print_diff(diff) + try: + np.testing.assert_allclose(diff, 0, atol=1e-9) + except AssertionError as e: + print('The test failed for the parameter set:') + p.__dict__.pop("v0") + print(p) + raise e + + return deltas + + +#================================================================================ + +if __name__ == '__main__': + + p = ParameterCollection( + dim = 1, + norbs = 2, + t = 2.0, + mu = 0.0, + beta = 5, + U = 1.0, + Up = 0.8, + J = 0.1, + Jp = 0.1, + nk = 4, + nw = 200, + nr_factor = 0.5, + fit_const = False, + big_factor = 2, + ) + + for norbs in [1, 2]: + p.norbs = norbs + deltas = compare_next_delta(p) + + print('The summation and FFT implementation of the eliashberg product' + ' both yield the same result.') + + p.fit_const = True + + deltas_with_fit = compare_next_delta(p) + + diff = compare_deltas(deltas[2:], deltas_with_fit[2:]) + + print('Compare explicit given constant vs. fit:') + + print_diff(diff) + np.testing.assert_allclose(diff, 0, atol=1e-9) + + print('Fitting the constant part works.') + diff --git a/test/python/eliashberg_fft.py b/test/python/eliashberg_fft.py deleted file mode 100644 index 6326c9f56..000000000 --- a/test/python/eliashberg_fft.py +++ /dev/null @@ -1,128 +0,0 @@ -# ---------------------------------------------------------------------- - -""" Compare the naive implementation of the linearized Eliashberg product -and the one using Fourier transformations. -This test is quite computational intensive, because of the inefficiency of -the naive implementations. In the future the Fourier transformation -implementation will subsitute the naive one. -""" - -# ---------------------------------------------------------------------- - -import itertools - -# ---------------------------------------------------------------------- - -import numpy as np - -# ---------------------------------------------------------------------- - -from triqs_tprf.ParameterCollection import ParameterCollection -from pytriqs.gf import Gf, MeshImFreq - -from triqs_tprf.tight_binding import TBLattice - -from triqs_tprf.lattice import lattice_dyson_g0_wk, solve_rpa_PH -from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk -from triqs_tprf.lattice import gamma_PP_singlet -from triqs_tprf.lattice import eliashberg_product, eliashberg_product_fft -from triqs_tprf.lattice import split_into_dynamic_wk_and_constant_k, dynamic_and_constant_to_tr -from triqs_tprf.eliashberg import solve_eliashberg, solve_eliashberg_fft -from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors - -# ---------------------------------------------------------------------- - -p = ParameterCollection( - dim = 1, - norbs = 1, - t = 1.0, - mu = 0.0, - beta = 5, - U = 1.0, - nk = 4, - nw = 500, - ) - -# -- Setup model, RPA susceptibilities and spin/charge interaction - -full_units = [(1, 0, 0), (0, 1, 0), (0, 0, 1)] -all_nn_hoppings = list(itertools.product([-1, 0, 1], repeat=p.dim)) -non_diagonal_hoppings = [ele for ele in all_nn_hoppings if sum(np.abs(ele)) == 1] - -t = -p.t * np.eye(p.norbs) - -H = TBLattice( - units = full_units[:p.dim], - hopping = {hop : t for hop in non_diagonal_hoppings}, - orbital_positions = [(0,0,0)]*p.norbs, - ) - -e_k = H.on_mesh_brillouin_zone(n_k=[p.nk]*p.dim + [1]*(3-p.dim)) - -# A bigger w-mesh is needed to construct a Gamma with a twice as big w-mesh than GF -big_factor = 2.0 - -wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nw) -wmesh_big = MeshImFreq(beta=p.beta, S='Fermion', n_max=int(big_factor*p.nw)) - -g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh) -g0_wk_big = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh_big) - -chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw) -chi0_wk_big = imtime_bubble_chi0_wk(g0_wk_big, nw=int(big_factor*p.nw)+1) - -U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norbs, p.U, 0, 0, 0) - -chi_s = solve_rpa_PH(chi0_wk, U_s) -chi_c = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation -chi_s_big = solve_rpa_PH(chi0_wk_big, U_s) -chi_c_big = solve_rpa_PH(chi0_wk_big, -U_c) # Minus for correct charge rpa equation - -gamma = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) -gamma_big = gamma_PP_singlet(chi_c_big, chi_s_big, U_c, U_s) - -print(gamma.mesh[0]) -print(gamma.mesh[0].first_index()) -print(gamma.mesh[0].last_index()) -print(gamma_big.mesh[0].first_index()) -print(gamma_big.mesh[0].last_index()) -print(g0_wk.mesh[0].first_index()) -print(g0_wk.mesh[0].last_index()) - -# -- Preprocess gamma for the FFT implementation - -gamma_dyn_wk, gamma_const_k = split_into_dynamic_wk_and_constant_k(gamma) -gamma_dyn_tr, gamma_const_r = dynamic_and_constant_to_tr(gamma_dyn_wk, gamma_const_k) - - -print(len(list(gamma_dyn_tr.mesh[0].values()))) - - -# -- Test the Eliashberg equation - -v0 = g0_wk.copy() -#v0.data[:] = v0.data[:] +1.0 -#v0.data[:] = np.random.random(g0_wk.data.shape) - -next_delta = eliashberg_product(gamma_big, g0_wk, v0) -next_delta_fft = eliashberg_product_fft(gamma_dyn_tr, gamma_const_r, g0_wk, v0) - -#np.testing.assert_allclose(next_delta.data, next_delta_fft.data, atol=1e-7) - - -Es, eigen_modes = solve_eliashberg(gamma_big, g0_wk) -Es_fft, eigen_modes_fft = solve_eliashberg_fft(gamma, g0_wk) - -E = Es[0] -eigen_mode = eigen_modes[0] -E_fft = Es_fft[0] -eigen_mode_fft = eigen_modes_fft[0] - -np.testing.assert_allclose(E, E_fft, atol=1e-7) - -try: - np.testing.assert_allclose(eigen_mode.data, eigen_mode_fft.data, atol=1e-7) -except AssertionError: - np.testing.assert_allclose(-eigen_mode.data, eigen_mode_fft.data, atol=1e-7) - -print('\nSame results for both implementations of the linearized Eliashberg equation.') diff --git a/test/python/eliashberg_impl_comparison.py b/test/python/eliashberg_impl_comparison.py deleted file mode 100644 index 6aca8f1dd..000000000 --- a/test/python/eliashberg_impl_comparison.py +++ /dev/null @@ -1,246 +0,0 @@ -# ---------------------------------------------------------------------- - -""" Compare the naive implementation of the linearized Eliashberg product -and the one using Fourier transformations. -This test is quite computational intensive, because of the inefficiency of -the naive implementations. In the future the Fourier transformation -implementation will subsitute the naive one. -""" - -# ---------------------------------------------------------------------- - -import itertools - -# ---------------------------------------------------------------------- - -import numpy as np - -# ---------------------------------------------------------------------- - -from triqs_tprf.ParameterCollection import ParameterCollection -from pytriqs.gf import Gf, MeshImFreq, Idx - -from triqs_tprf.tight_binding import TBLattice - -from triqs_tprf.lattice import lattice_dyson_g0_wk, solve_rpa_PH -from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk -from triqs_tprf.lattice import gamma_PP_singlet -from triqs_tprf.lattice import eliashberg_product -from triqs_tprf.lattice import eliashberg_product_fft, eliashberg_product_fft_v2 -from triqs_tprf.lattice import split_into_dynamic_wk_and_constant_k, dynamic_and_constant_to_tr -from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors - -# ---------------------------------------------------------------------- - -def compare_deltas(deltas_1, deltas_2=None, static=False): - - if not deltas_2: - deltas_2 = deltas_1 - - if static: - deltas_1 = [ele[Idx(0), :] for ele in deltas_1] - deltas_2 = [ele[Idx(0), :] for ele in deltas_2] - - diff = np.zeros(shape=(len(deltas_1), len(deltas_2))) - - for i, delta_1 in enumerate(deltas_1): - for j, delta_2 in enumerate(deltas_2): - - diff[i,j] = np.max(np.abs(delta_1.data - delta_2.data)) - - return diff - -def print_diff(diff): - - i_max, j_max = diff.shape - - s = "" - - for i in range(i_max): - - for j in range(j_max): - - s += np.format_float_scientific(diff[i,j], precision=2, pad_left=3) - s += "\t" - - s += "\n" - print(s) - - - - - - -def compare_next_delta(p): - -# -- Setup model, RPA susceptibilities and spin/charge interaction - - full_units = [(1, 0, 0), (0, 1, 0), (0, 0, 1)] - all_nn_hoppings = list(itertools.product([-1, 0, 1], repeat=p.dim)) - non_diagonal_hoppings = [ele for ele in all_nn_hoppings if sum(np.abs(ele)) == 1] - - t = -p.t * np.eye(p.norbs) - - H = TBLattice( - units = full_units[:p.dim], - hopping = {hop : t for hop in non_diagonal_hoppings}, - orbital_positions = [(0,0,0)]*p.norbs, - ) - - e_k = H.on_mesh_brillouin_zone(n_k=[p.nk]*p.dim + [1]*(3-p.dim)) - -# A bigger w-mesh is needed to construct a Gamma with a twice as big w-mesh than GF - - wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nw) - wmesh_small = MeshImFreq(beta=p.beta, S='Fermion', n_max=int(p.small_factor*p.nw)+1) - wmesh_big = MeshImFreq(beta=p.beta, S='Fermion', n_max=int(p.big_factor*p.nw)+1) - - g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh) - g0_wk_small = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh_small) - g0_wk_big = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh_big) - - chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw) - chi0_wk_small = imtime_bubble_chi0_wk(g0_wk_big, nw=int(p.small_factor*p.nw)+1) - chi0_wk_big = imtime_bubble_chi0_wk(g0_wk_big, nw=int(p.big_factor*p.nw)+1) - - U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norbs, p.U, 0, 0, 0) - - chi_s = solve_rpa_PH(chi0_wk, U_s) - chi_c = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation - chi_s_small = solve_rpa_PH(chi0_wk_small, U_s) - chi_c_small = solve_rpa_PH(chi0_wk_small, -U_c) # Minus for correct charge rpa equation - chi_s_big = solve_rpa_PH(chi0_wk_big, U_s) - chi_c_big = solve_rpa_PH(chi0_wk_big, -U_c) # Minus for correct charge rpa equation - - gamma = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) - gamma_small = gamma_PP_singlet(chi_c_small, chi_s_small, U_c, U_s) - gamma_big = gamma_PP_singlet(chi_c_big, chi_s_big, U_c, U_s) - -# -- Preprocess gamma for the FFT implementations - - gamma_dyn_wk, gamma_const_k = split_into_dynamic_wk_and_constant_k(gamma) - gamma_dyn_wk_small, gamma_const_k_small = split_into_dynamic_wk_and_constant_k(gamma_small) - gamma_dyn_wk_big, gamma_const_k_big = split_into_dynamic_wk_and_constant_k(gamma_big) - - if not p.const: - - gamma.data[:] = gamma.data - p.U - gamma_small.data[:] = gamma_small.data - p.U - gamma_big.data[:] = gamma_big.data - p.U - - gamma_dyn_wk.data[:] = gamma.data - gamma_dyn_wk_small.data[:] = gamma_small.data - gamma_dyn_wk_big.data[:] = gamma_big.data - - gamma_const_k.data[:] = 0.0 - gamma_const_k_small.data[:] = 0.0 - gamma_const_k_big.data[:] = 0.0 - - if not p.fit_const: - - gamma_dyn_wk.data[:] = gamma.data - p.U - gamma_dyn_wk_small.data[:] = gamma_small.data - p.U - gamma_dyn_wk_big.data[:] = gamma_big.data - p.U - - gamma_const_k.data[:] = p.U - gamma_const_k_small.data[:] = p.U - gamma_const_k_big.data[:] = p.U - - gamma_dyn_tr, gamma_const_r = dynamic_and_constant_to_tr(gamma_dyn_wk, gamma_const_k) - gamma_dyn_tr_small, gamma_const_r_small = dynamic_and_constant_to_tr(gamma_dyn_wk_small, - gamma_const_k_small) - gamma_dyn_tr_big, gamma_const_r_big = dynamic_and_constant_to_tr(gamma_dyn_wk_big, - gamma_const_k_big) - - # -- Creating Semi-Random input Delta - - np.random.seed(1337) - - v0 = g0_wk.copy() - v0.data[:] = v0.data.real - random_data = np.random.random(v0.data.shape[1:]) - freq_data = np.mean(np.abs(v0.data), axis=tuple(range(len(v0.data.shape))[1:])) - not_randomized = 40 - start, stop = not_randomized, v0.data.shape[0]-not_randomized - freq_data[start:stop] *= np.random.random(stop-start) - - v0.data[:] = np.tensordot(freq_data, random_data, axes=0) - - - p.v0 = v0 - -# -- Test the Eliashberg equation - - print('summation') - next_delta = eliashberg_product(gamma_big, g0_wk, p.v0) - print('fft') - next_delta_fft = eliashberg_product_fft(gamma_dyn_tr, gamma_const_r, g0_wk, p.v0) - print('fft_small') - next_delta_fft_small = eliashberg_product_fft(gamma_dyn_tr_small, gamma_const_r_small, g0_wk, p.v0) - print('fft_big') - next_delta_fft_big = eliashberg_product_fft(gamma_dyn_tr_big, gamma_const_r_big, g0_wk, p.v0) - print('fft_v2') - next_delta_fft_v2 = eliashberg_product_fft(gamma_dyn_tr, gamma_const_r, g0_wk, p.v0) - - - from pytriqs.plot.mpl_interface import oplot, plt - subp = [2, 6, 1] - fig = plt.figure(figsize=(18, 15)) - - deltas = [v0, next_delta, next_delta_fft, next_delta_fft_small, next_delta_fft_big, next_delta_fft_v2] - titles = ['input', 'summation', 'fft', 'fft_small', 'fft_big', 'fft_v2'] - - for k_point in [Idx(0,0,0), Idx(1,0,0)]: - - - for delta, title in zip(deltas, titles): - - ax = plt.subplot(*subp); subp[-1] += 1 - oplot(delta[:, k_point]) - plt.title(title) - - ax.legend_ = None - - - plt.show() - - diff = compare_deltas(deltas[1:]) - - print_diff(diff) - - return deltas - - - - -# ---------------------------------------------------------------------- - -p = ParameterCollection( - dim = 1, - norbs = 1, - t = 2.0, - mu = 0.0, - beta = 5, - U = 1.0, - nk = 4, - nw = 200, - const = True, - fit_const = False, - big_factor = 2, - small_factor = 1.0, - ) - -deltas_1 = compare_next_delta(p) - -exit() - -p.nw = 100 - - -deltas_2 = compare_next_delta(p) - -diff = compare_deltas(deltas_1[1:], deltas_2[1:], static=True) - -print_diff(diff) - - From 129893fd164ef10f64720d5388c5efdf666b8d57 Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 15 Apr 2019 09:13:00 +0200 Subject: [PATCH 003/121] [eli] fix bug in gamma creation The constant part was included in matrix product like summation. --- c++/triqs_tprf/lattice/eliashberg.cpp | 20 ++++++++++++-------- 1 file changed, 12 insertions(+), 8 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index efc064c72..c8f40d189 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -164,12 +164,14 @@ chi_wk_t gamma_PP_singlet(chi_wk_vt chi_c, chi_wk_vt chi_s, \ Gamma_pp_wk *= 0; for (const auto [w, k] : Gamma_pp_wk.mesh()) - for (auto [a, b, c, d] : Gamma_pp_wk.target_indices()) - for (auto [A, B, C, D] : chi_c.target_indices()) + for (auto [a, b, c, d] : Gamma_pp_wk.target_indices()){ + for (auto [A, B, C, D] : chi_c.target_indices()){ Gamma_pp_wk[w,k](a, b, c, d) += 1.5 * U_s(a, b, A, B) * chi_s[w, k](B, A, C, D) * U_s(D, C, c, d) \ - - 0.5 * U_c(a, b, A, B) * chi_c[w, k](B, A, C, D) * U_c(D, C, c, d) \ - + 0.5 * (U_s(a, b, c, d) + U_c(a, b, c, d)); + - 0.5 * U_c(a, b, A, B) * chi_c[w, k](B, A, C, D) * U_c(D, C, c, d); + } + Gamma_pp_wk[w,k](a, b, c, d) += 0.5 * (U_s(a, b, c, d) + U_c(a, b, c, d)); + } return Gamma_pp_wk; } @@ -183,12 +185,14 @@ chi_wk_t gamma_PP_triplet(chi_wk_vt chi_c, chi_wk_vt chi_s, \ Gamma_pp_wk *= 0; for (const auto [w, k] : Gamma_pp_wk.mesh()) - for (auto [a, b, c, d] : Gamma_pp_wk.target_indices()) - for (auto [A, B, C, D] : chi_c.target_indices()) + for (auto [a, b, c, d] : Gamma_pp_wk.target_indices()){ + for (auto [A, B, C, D] : chi_c.target_indices()){ Gamma_pp_wk[w,k](a, b, c, d) += - 0.5 * U_s(a, b, A, B) * chi_s[w, k](B, A, C, D) * U_s(D, C, c, d) \ - - 0.5 * U_c(a, b, A, B) * chi_c[w, k](B, A, C, D) * U_c(D, C, c, d) \ - + 0.5 * (U_s(a, b, c, d) + U_c(a, b, c, d)); + - 0.5 * U_c(a, b, A, B) * chi_c[w, k](B, A, C, D) * U_c(D, C, c, d); + } + Gamma_pp_wk[w,k](a, b, c, d) += 0.5 * (U_s(a, b, c, d) + U_c(a, b, c, d)); + } return Gamma_pp_wk; } From 001c42b6928e185d8e5d37e180a1df0da38ce7e3 Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 15 Apr 2019 15:35:46 +0200 Subject: [PATCH 004/121] [tests] add macro for python tests Also: - use this macro in cmake files - add cmakefile for eliashberg tests - add matrix_rpa.py as a module - minor eliashberg test changes - adjust to new folder hierarchy --- .../triqs_tprf}/matrix_rpa.py | 0 test/CMakeLists.txt | 10 +++++++++ test/python/CMakeLists.txt | 21 ++++++++++++------- .../compare_general_rpa_to_matrix_rpa.py | 8 +++---- test/python/eliashberg/CMakeLists.txt | 8 +++++++ .../eliashberg/product_summation_vs_fft.py | 7 ++++--- 6 files changed, 39 insertions(+), 15 deletions(-) rename {test/python => python/triqs_tprf}/matrix_rpa.py (100%) create mode 100644 test/python/eliashberg/CMakeLists.txt diff --git a/test/python/matrix_rpa.py b/python/triqs_tprf/matrix_rpa.py similarity index 100% rename from test/python/matrix_rpa.py rename to python/triqs_tprf/matrix_rpa.py diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt index 51d3086fe..dea80bc45 100644 --- a/test/CMakeLists.txt +++ b/test/CMakeLists.txt @@ -1,3 +1,13 @@ +# runs a python test +# Example: add_python_test(my_script) +# where my_script.py is the script +macro(add_python_test test) + get_filename_component(test_name ${test} NAME_WE) + get_filename_component(test_dir ${test} DIRECTORY) + add_test(NAME Py_${test_name} COMMAND ${TRIQS_PYTHON_INTERPRETER} ${CMAKE_CURRENT_SOURCE_DIR}/${test_dir}/${test_name}.py WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}/${test_dir}) + set_property(TEST Py_${test_name} APPEND PROPERTY ENVIRONMENT PYTHONPATH=${CMAKE_BINARY_DIR}/python:$ENV{PYTHONPATH} ${SANITIZER_RT_PRELOAD}) +endmacro(add_python_test) + add_subdirectory(c++) if(${TRIQS_WITH_PYTHON_SUPPORT}) diff --git a/test/python/CMakeLists.txt b/test/python/CMakeLists.txt index 1d0435dfa..45101375e 100644 --- a/test/python/CMakeLists.txt +++ b/test/python/CMakeLists.txt @@ -4,12 +4,17 @@ foreach(file ${all_h5_tgz_files}) configure_file(${file} ${file} COPYONLY) endforeach() -# List all tests -set(all_tests chi4_iw_from_tau g_wk_to_from_g_wr_py chi00_square_lattice bse_and_rpa_loc_vs_latt mean_field mean_field_kanamori hartree_response 1d_hubbard_hf_rpa 1d_hubbard_hf_spin_rot_inv 1d_hubbard_hf_rpa_2site_AFM compare_general_rpa_to_matrix_rpa interaction_tensor_charge_spin_factorization eliashberg/product_summation_vs_fft eliashberg/eigenvalue_solver eliashberg/previous_implementation) +add_python_test(chi4_iw_from_tau) +add_python_test(g_wk_to_from_g_wr_py) +add_python_test(chi00_square_lattice) +add_python_test(bse_and_rpa_loc_vs_latt) +add_python_test(mean_field) +add_python_test(mean_field_kanamori) +add_python_test(hartree_response) +add_python_test(1d_hubbard_hf_rpa) +add_python_test(1d_hubbard_hf_spin_rot_inv) +add_python_test(1d_hubbard_hf_rpa_2site_AFM) +add_python_test(compare_general_rpa_to_matrix_rpa) +add_python_test(interaction_tensor_charge_spin_factorization) -foreach(test ${all_tests}) - get_filename_component(test_name ${test} NAME_WE) - get_filename_component(test_dir ${test} DIRECTORY) - add_test(NAME Py_${test_name} COMMAND ${TRIQS_PYTHON_INTERPRETER} ${CMAKE_CURRENT_SOURCE_DIR}/${test_dir}/${test_name}.py WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}/${test_dir}) - set_property(TEST Py_${test_name} APPEND PROPERTY ENVIRONMENT PYTHONPATH=${CMAKE_BINARY_DIR}/python:$ENV{PYTHONPATH} ${SANITIZER_RT_PRELOAD}) -endforeach() +add_subdirectory(eliashberg) diff --git a/test/python/compare_general_rpa_to_matrix_rpa.py b/test/python/compare_general_rpa_to_matrix_rpa.py index 57e24a994..484fedc62 100644 --- a/test/python/compare_general_rpa_to_matrix_rpa.py +++ b/test/python/compare_general_rpa_to_matrix_rpa.py @@ -94,7 +94,7 @@ # -- Showcase reshaping from 4-rank tensors to matrix as done in papers # -- and test if the process is reversable -from matrix_rpa import tensor_to_matrix, matrix_to_tensor +from triqs_tprf.matrix_rpa import tensor_to_matrix, matrix_to_tensor test_chi = np.chararray([norb]*4, itemsize=4) @@ -156,13 +156,13 @@ # ---------------------------------------------------------------------- # -- Calculate chi spin/charge with spin independent chi0 -from matrix_rpa import lose_spin_degree_of_freedom, tprf_order_to_matrix_rpa_order +from triqs_tprf.matrix_rpa import lose_spin_degree_of_freedom, tprf_order_to_matrix_rpa_order chi00_wk_wo_spin_array = lose_spin_degree_of_freedom(chi00_wk.data, rank=4, spin_fast=False) # c^+cc^+c chi00_wk_matrix_rpa = tprf_order_to_matrix_rpa_order(chi00_wk_wo_spin_array) # now in c^+ccc^+ order -from matrix_rpa import get_rpa_us_tensor, get_rpa_uc_tensor +from triqs_tprf.matrix_rpa import get_rpa_us_tensor, get_rpa_uc_tensor U = 1.0 Up = 0.8 @@ -172,7 +172,7 @@ us_matrix_rpa = get_rpa_us_tensor(norb, U, Up, J ,Jp) # given in cc^+c^+c uc_matrix_rpa = get_rpa_uc_tensor(norb, U, Up, J ,Jp) # given in cc^+c^+c -from matrix_rpa import chi_rpa_spin, chi_rpa_charge +from triqs_tprf.matrix_rpa import chi_rpa_spin, chi_rpa_charge chi_spin_matrix_rpa = chi_rpa_spin(chi00_wk_matrix_rpa, us_matrix_rpa) # given in c^+ccc^+ chi_charge_matrix_rpa = chi_rpa_charge(chi00_wk_matrix_rpa, uc_matrix_rpa) # given in c^+ccc^+ diff --git a/test/python/eliashberg/CMakeLists.txt b/test/python/eliashberg/CMakeLists.txt new file mode 100644 index 000000000..d02665b61 --- /dev/null +++ b/test/python/eliashberg/CMakeLists.txt @@ -0,0 +1,8 @@ +FILE(GLOB all_tgz_files RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} *.tar.gz) +file(COPY ${CMAKE_CURRENT_SOURCE_DIR}/${all_tgz_files} DESTINATION ${CMAKE_CURRENT_BINARY_DIR}) + +set(PREFIX eliashberg-) + +add_python_test(product_summation_vs_fft ${PREFIX}) +add_python_test(eigenvalue_solver ${PREFIX}) +add_python_test(previous_implementation ${PREFIX}) diff --git a/test/python/eliashberg/product_summation_vs_fft.py b/test/python/eliashberg/product_summation_vs_fft.py index 74fd7058d..065202e1b 100644 --- a/test/python/eliashberg/product_summation_vs_fft.py +++ b/test/python/eliashberg/product_summation_vs_fft.py @@ -166,7 +166,7 @@ def compare_next_delta(p): print_diff(diff) try: - np.testing.assert_allclose(diff, 0, atol=1e-9) + np.testing.assert_allclose(diff, 0, atol=p.atol) except AssertionError as e: print('The test failed for the parameter set:') p.__dict__.pop("v0") @@ -182,7 +182,7 @@ def compare_next_delta(p): p = ParameterCollection( dim = 1, - norbs = 2, + norbs = 1, t = 2.0, mu = 0.0, beta = 5, @@ -195,6 +195,7 @@ def compare_next_delta(p): nr_factor = 0.5, fit_const = False, big_factor = 2, + atol = 1e-9, ) for norbs in [1, 2]: @@ -213,7 +214,7 @@ def compare_next_delta(p): print('Compare explicit given constant vs. fit:') print_diff(diff) - np.testing.assert_allclose(diff, 0, atol=1e-9) + np.testing.assert_allclose(diff, 0, atol=p.atol) print('Fitting the constant part works.') From f6f30b2a8a47effaf253f60a1614f3a628c177bb Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 17 Apr 2019 10:34:55 +0200 Subject: [PATCH 005/121] [eli] add minor changes - If the plot is done in eliashberg/product_summation_vs_fft is now regulated by a parameter. - The solve_eliashberg method does now take initial deltas as input to start the iterative solvers. It only uses the one produced by semi_randomized_initial_delta if none is given to it. --- python/triqs_tprf/ParameterCollection.py | 32 ++++++++++- python/triqs_tprf/eliashberg.py | 29 +++++----- test/python/eliashberg/eigenvalue_solver.py | 8 +-- .../eliashberg/product_summation_vs_fft.py | 54 +++++++++---------- 4 files changed, 74 insertions(+), 49 deletions(-) diff --git a/python/triqs_tprf/ParameterCollection.py b/python/triqs_tprf/ParameterCollection.py index 5587c78be..bc79ad407 100644 --- a/python/triqs_tprf/ParameterCollection.py +++ b/python/triqs_tprf/ParameterCollection.py @@ -78,6 +78,16 @@ def keys(self): def dict(self): return self.__dict__ + def update(self, **kwargs): + self.__dict__.update(kwargs) + + def copy(self, **kwargs): + """Shallow copy that allows for changing/adding attributes + """ + p = ParameterCollection(**self.dict()) + p.update(**kwargs) + return p + def __getitem__(self, key): return self.__dict__[key] @@ -136,6 +146,8 @@ def __str__(self): out += ''.join([key, ' = ', str_value]) + '\n' return out + __repr__ = __str__ + def get_my_name(self): ans = [] frame = inspect.currentframe().f_back @@ -195,7 +207,7 @@ def set_sorted_order(self, sorted_idx): self.objects = list(np.array(self.objects)[sidx]) def getattr_from_objects(self, attr): - return np.array([getattr(o, attr) for o in self.objects ]) + return np.array([getattr(o, attr, None) for o in self.objects ]) def __getattr__(self, attr): return self.getattr_from_objects(attr) @@ -208,6 +220,24 @@ def __factory_from_dict__(cls, name, d): ret = cls(d['objects']) return ret + def __iter__(self): + return self.objects.__iter__() + + def __next__(self): + return self.objects.__next__() + + def __getitem__(self, idx): + return self.objects[idx] + + def __str__(self): + out = '' + for p in self: + out += p.__str__() + out += '\n' + return out + + __repr__ = __str__ + # ---------------------------------------------------------------------- # -- Register ParameterCollection in Triqs hdf_archive_schemes diff --git a/python/triqs_tprf/eliashberg.py b/python/triqs_tprf/eliashberg.py index fa0317995..48a100af9 100644 --- a/python/triqs_tprf/eliashberg.py +++ b/python/triqs_tprf/eliashberg.py @@ -58,8 +58,8 @@ def semi_random_initial_delta(g_wk, nr_factor=0.5, seed=None): Returns ------- delta : Gf, - An inital anomalous self-energy :math:`\Delta(i\nu_n, \mathbf{k})` to start - a iterative solver, given as a Gf with MeshProduct with the components + An initial anomalous self-energy :math:`\Delta(i\nu_n, \mathbf{k})` to start + an iterative solver, given as a Gf with MeshProduct with the components (MeshImFreq, MeshBrillouinZone). """ @@ -121,8 +121,8 @@ def preprocess_gamma_for_fft(Gamma_pp_wk, Gamma_pp_const_k): return Gamma_pp_dyn_tr, Gamma_pp_const_r -def solve_eliashberg(Gamma_pp_wk, g_wk, Gamma_pp_const_k=None, tol=1e-10, - product='FFT', solver='PM', nr_factor=0.5, seed=None): +def solve_eliashberg(Gamma_pp_wk, g_wk, initial_delta=None, Gamma_pp_const_k=None, tol=1e-10, + product='FFT', solver='PM'): r""" Solve the linearized Eliashberg equation @@ -138,6 +138,11 @@ def solve_eliashberg(Gamma_pp_wk, g_wk, Gamma_pp_const_k=None, tol=1e-10, g_wk : Gf, Green's function :math:`G(i\nu_n, \mathbf{k})`. The mesh attribute of the Gf must be a MeshProduct with the components (MeshImFreq, MeshBrillouinZone). + initial_delta : Gf, optional + An initial anomalous self-energy :math:`\Delta(i\nu_n, \mathbf{k})` to start + an iterative solver, given as a Gf with MeshProduct with the components + (MeshImFreq, MeshBrillouinZone). + If not given :func:`semi_random_initial_delta` will be called. Gamma_pp_const_k : float or np.ndarray or Gf, optional Part of the pairing vertex that is constant in Matsubara frequency space :math:`\Gamma(\mathbf{k})`. If given as a Gf its mesh attribute needs to @@ -159,13 +164,6 @@ def solve_eliashberg(Gamma_pp_wk, g_wk, Gamma_pp_const_k=None, tol=1e-10, 'PM' : Use the Power Method implemented in :func:`power_method_LR`. 'IRAM' : Use the Implicitly Restarted Arnoldi Method implemented in :func:`implicitly_restarted_arnoldi_method`. - nr_factor : float, optional - Percentage of :math:`\omega` points of the inital delta, which shall not be - randomized. This is needed to assure a working tail fit for the - Fourier transformations. The default is 0.5, meaning that 50% of - the :math:`\omega` points will not be randomized. - seed : int, optional - Set a np.random.seed to enforce predictable results. Returns ------- @@ -211,15 +209,16 @@ def matvec(delta_x): else: raise NotImplementedError('There is no implementation of the eliashberg product' ' called %s.'%product) - - init = from_wk_to_x(semi_random_initial_delta(g_wk, nr_factor=nr_factor, seed=seed)) + if not initial_delta: + initial_delta = semi_random_initial_delta(g_wk) + initial_delta = from_wk_to_x(initial_delta) if solver == 'PM': - es, evs = power_method_LR(matvec, init, tol=tol) + es, evs = power_method_LR(matvec, initial_delta, tol=tol) es, evs = [es], [evs] elif solver == 'IRAM': - es, evs = implicitly_restarted_arnoldi_method(matvec, init, tol=tol) + es, evs = implicitly_restarted_arnoldi_method(matvec, initial_delta, tol=tol) else: raise NotImplementedError('There is no solver called %s.'%solver) diff --git a/test/python/eliashberg/eigenvalue_solver.py b/test/python/eliashberg/eigenvalue_solver.py index 0b11fc671..a20c953db 100644 --- a/test/python/eliashberg/eigenvalue_solver.py +++ b/test/python/eliashberg/eigenvalue_solver.py @@ -75,8 +75,7 @@ def run_solve_eliashberg(p): gamma_const = 0.5*(U_s + U_c) Es, eigen_modes = solve_eliashberg(gamma, g0_wk, Gamma_pp_const_k=gamma_const, - product=p.product, solver=p.solver, - nr_factor=p.nr_factor, seed=p.seed) + product=p.product, solver=p.solver) return Es, eigen_modes @@ -100,14 +99,11 @@ def run_solve_eliashberg(p): big_factor = 2, product = 'FFT', solver = 'PM', - nr_factor = 0.6, - seed = 1337, ) Es_pm, eigen_modes_pm = run_solve_eliashberg(p) - p.solver = 'IRAM' - Es_iram, eigen_modes_iram = run_solve_eliashberg(p) + Es_iram, eigen_modes_iram = run_solve_eliashberg(p.copy(solver='IRAM') print(Es_pm[0], Es_iram[0]) diff --git a/test/python/eliashberg/product_summation_vs_fft.py b/test/python/eliashberg/product_summation_vs_fft.py index 065202e1b..ec9c10156 100644 --- a/test/python/eliashberg/product_summation_vs_fft.py +++ b/test/python/eliashberg/product_summation_vs_fft.py @@ -129,38 +129,41 @@ def compare_next_delta(p): print('Start the FFT') next_delta_fft = eliashberg_product_fft(gamma_dyn_tr, gamma_const_r, g0_wk, p.v0) - from pytriqs.plot.mpl_interface import oplot, plt - import warnings - warnings.filterwarnings("ignore") #ignore some matplotlib warnings - subp = [4, 3, 1] - fig = plt.figure(figsize=(18, 15)) - deltas = [v0, next_delta, next_delta_fft] - titles = ['Input', 'Summation', 'FFT'] - for k_point in [Idx(0,0,0), Idx(1,0,0)]: + if p.plot: - ax = plt.subplot(*subp); subp[-1] += 1 - oplot(g0_wk[:, k_point]) - plt.title('GF') + from pytriqs.plot.mpl_interface import oplot, plt + import warnings + warnings.filterwarnings("ignore") #ignore some matplotlib warnings + subp = [4, 3, 1] + fig = plt.figure(figsize=(18, 15)) - ax = plt.subplot(*subp); subp[-1] += 1 - oplot(gamma[:, k_point]) - plt.title('Gamma') + titles = ['Input', 'Summation', 'FFT'] - ax = plt.subplot(*subp); subp[-1] += 1 - oplot(gamma_dyn_tr[:, k_point]) - plt.title('Gamma dyn tr') + for k_point in [Idx(0,0,0), Idx(1,0,0)]: - for delta, title in zip(deltas, titles): + ax = plt.subplot(*subp); subp[-1] += 1 + oplot(g0_wk[:, k_point]) + plt.title('GF') ax = plt.subplot(*subp); subp[-1] += 1 - oplot(delta[:, k_point]) - plt.title(title) + oplot(gamma[:, k_point]) + plt.title('Gamma') + + ax = plt.subplot(*subp); subp[-1] += 1 + oplot(gamma_dyn_tr[:, k_point]) + plt.title('Gamma dyn tr') + + for delta, title in zip(deltas, titles): - ax.legend_ = None + ax = plt.subplot(*subp); subp[-1] += 1 + oplot(delta[:, k_point]) + plt.title(title) - #plt.show() + ax.legend_ = None + + plt.show() diff = compare_deltas(deltas[1:]) @@ -175,7 +178,6 @@ def compare_next_delta(p): return deltas - #================================================================================ if __name__ == '__main__': @@ -196,6 +198,7 @@ def compare_next_delta(p): fit_const = False, big_factor = 2, atol = 1e-9, + plot = False, ) for norbs in [1, 2]: @@ -205,9 +208,7 @@ def compare_next_delta(p): print('The summation and FFT implementation of the eliashberg product' ' both yield the same result.') - p.fit_const = True - - deltas_with_fit = compare_next_delta(p) + deltas_with_fit = compare_next_delta(p.copy(fit_const=True)) diff = compare_deltas(deltas[2:], deltas_with_fit[2:]) @@ -217,4 +218,3 @@ def compare_next_delta(p): np.testing.assert_allclose(diff, 0, atol=p.atol) print('Fitting the constant part works.') - From 0dd1e86e3dba745090b4caed3ddaebfce75f3689 Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 8 May 2019 15:38:42 +0200 Subject: [PATCH 006/121] [latutl] output k-points scaled by BZ input --- python/triqs_tprf/lattice_utils.py | 14 ++++++-------- 1 file changed, 6 insertions(+), 8 deletions(-) diff --git a/python/triqs_tprf/lattice_utils.py b/python/triqs_tprf/lattice_utils.py index a2cca5a46..1fd4d55a1 100644 --- a/python/triqs_tprf/lattice_utils.py +++ b/python/triqs_tprf/lattice_utils.py @@ -412,24 +412,22 @@ def k_space_path(paths, num=100, bz=None): k_vecs = [] + def rel_to_abs(k_vec, cell): + return np.einsum('ba,ib->ia', cell, k_vec) + for path in paths: ki, kf = path x = np.linspace(0., 1., num=num)[:, None] k_vec = (1. - x) * ki[None, :] + x * kf[None, :] - k_vecs.append(k_vec) - - def rel_to_abs(k_vec, cell): - return np.einsum('ba,ib->ia', cell, k_vec) + k_vecs.append(rel_to_abs(k_vec, cell)) k_vec = k_vecs[0] - k_vec_abs = rel_to_abs(k_vec, cell) - k_plot = np.linalg.norm(k_vec_abs - k_vec_abs[0][None, :], axis=1) + k_plot = np.linalg.norm(k_vec - k_vec[0][None, :], axis=1) K_plot = [0.] for kidx, k_vec in enumerate(k_vecs[1:]): - k_vec_abs = rel_to_abs(k_vec, cell) - k_plot_new = np.linalg.norm(k_vec_abs - k_vec_abs[0][None, :], axis=1) + k_plot[-1] + k_plot_new = np.linalg.norm(k_vec - k_vec[0][None, :], axis=1) + k_plot[-1] K_plot.append(k_plot[-1]) k_plot = np.concatenate((k_plot, k_plot_new)) From 3bfd29a3647a657074bc91eb11a13d1bea0f1e1b Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 8 May 2019 15:40:59 +0200 Subject: [PATCH 007/121] [eli] add user guide WIP - Add a first implementation for bandstructure like plotting WIP - Add a matplotlib style sheet to use with the notebooks - Add a user guide that uses the linearized Eliashberg equation WIP --- doc/documentation.rst | 1 + doc/user_guide/PHT_Hubbard_Model.ipynb | 1933 ++++++++++++++++++++++++ doc/user_guide/notebook.mplstyle | 39 + doc/user_guide/plotting_tools.py | 64 + 4 files changed, 2037 insertions(+) create mode 100644 doc/user_guide/PHT_Hubbard_Model.ipynb create mode 100644 doc/user_guide/notebook.mplstyle create mode 100644 doc/user_guide/plotting_tools.py diff --git a/doc/documentation.rst b/doc/documentation.rst index a702577fd..9625e6096 100644 --- a/doc/documentation.rst +++ b/doc/documentation.rst @@ -13,6 +13,7 @@ Tutorials user_guide/Bethe-Salpeter Equation on the Hubbard atom.ipynb user_guide/Lattice BSE on Hubbard atom.ipynb user_guide/dmft_susceptibility/dmft_susceptibility + user_guide/PHT_Hubbard_Model.ipynb Python reference manual ----------------------- diff --git a/doc/user_guide/PHT_Hubbard_Model.ipynb b/doc/user_guide/PHT_Hubbard_Model.ipynb new file mode 100644 index 000000000..46b081581 --- /dev/null +++ b/doc/user_guide/PHT_Hubbard_Model.ipynb @@ -0,0 +1,1933 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "nbsphinx": "hidden" + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "import numpy as np\n", + "\n", + "from pytriqs.plot.mpl_interface import plt" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "nbsphinx": "hidden" + }, + "outputs": [], + "source": [ + "plt.style.use('./notebook.mplstyle')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Using the (semi) particle-hole transformation on the Hubbard model on a square lattice" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Hubbard model on a square lattice" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Hamiltonian of the Hubbard model on a square lattice is given by\n", + "\n", + "$$\n", + "H=-t \\sum_{\\langle j, 1\\rangle \\sigma}\\left(c_{j \\sigma}^{\\dagger} c_{1 \\sigma}+c_{1 \\sigma}^{\\dagger} c_{j \\sigma}\\right)+U \\sum_{j} n_{j \\uparrow} n_{j \\downarrow}-\\mu \\sum_{j}\\left(n_{j \\uparrow}+n_{j \\downarrow}\\right)\\,.\n", + "$$\n", + "\n", + "The first term describes the kinetic energy in terms of hopping processes between adjoining lattice sites, indicated by the angular brakets.\n", + "The second term desribes the onsite interaction.\n", + "The third term determines the filling via the chemical potential." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here $c_{j\\sigma}^{\\dagger}$ creates an electron on site $j$ with spin $\\sigma$ while $c_{j\\sigma}$ destroys such an electron, further the operator $n_{j\\sigma}$ count the number of electrons on site $j$ with spin $\\sigma$.\n", + "The first term describes the kinetic energy of the electrons, which can be interpreted as an electron with spin $\\sigma$ *hopping* from site $l$ to site $j$ and vice versa.\n", + "Here the angular braket under the sum means that we only take *hopping* terms between neighboring lattice sites into account.\n", + "This is the most basic version of the kinetic part of the Hubbard model which can, and will be, extended later.\n", + "\n", + "The second term describes the repulsive interaction between the electrons.\n", + "This repulsion is crudely approximated in the Hubbard model in the sense, that electrons only *see* each other if the occupy the same lattice site.\n", + "\n", + "The last term describes the filling of the lattice via an energy offset by the chemical potential $\\mu$.\n", + "\n", + "The Hubbard model is therefore defined by the parameters $t$, $U$ and $mu$, but we also need to know the temperature $T$ at which we shal observe the Hubbard model.\n", + "We will record these parameters using the `ParameterCollection` class in `triqs_tprf.ParameterCollection`." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "T = 1000\n", + "U = 1.0\n", + "mu = 0.0\n", + "nk = 16\n", + "norb = 1\n", + "nw = 50\n", + "t = 1.0" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from triqs_tprf.ParameterCollection import ParameterCollection\n", + "\n", + "hubbard = ParameterCollection( # -- Model Parameter\n", + " norb=1, # Number of orbitals.\n", + " t=1.0, # Hopping to nearest neighbor\n", + " U=1.0, # Strength of the on-site interaction\n", + " mu=0.0, # Chemical potential determining the filling.\n", + " T=1000, # Temperature.\n", + " \n", + " # -- Technical parameter\n", + " nk=16, # Number of points in one dimension considered in the Brillouin zone.\n", + " nw=50, # Number of Matsubara points in positive dimension.\n", + " )\n", + "hubbard" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A representation of the kinetic part of the Hubbard model can be constructed using the `TBLattice` class in `triqs_tprf.tight_binding` where the hoppings are given as a dictionary with relative coordinate vectors as keys and hopping matrices as values. The unit vectors of the lattice, the position of the site local orbitals and names also needs to be setup, see below.\n", + "Here we also added the functionality for next-nearest neighbor hopping, which will be used later.\n", + "\n", + "From this `TBLattice` object we can obtain the dispersion relation as a mesh over the Brillouin zone via its member function `on_mesh_brillouin_zone`.\n", + "All of this is condensed in the `get_disperion_relation` which only cares about the Hubbard model parameters.\n", + "Also lets plot the bandstructure and density of states.\n", + "There we can see, that the system has a particle hole symmetric density of states." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Starting run with 1 MPI threads at : 2019-04-29 18:54:47.073302\n" + ] + } + ], + "source": [ + "from triqs_tprf.tight_binding import TBLattice\n", + "\n", + "def get_disperion_relation(p):\n", + " \"\"\"Return the disperion relation for model parameters in a ParameterCollection\n", + " \"\"\"\n", + " \n", + " t = -p.t * np.eye(p.norb)\n", + " \n", + " # next-nearest neighbour hopping only if p has `tp` attribute\n", + " try:\n", + " tp = -p.tp * np.eye(p.norb)\n", + " except AttributeError:\n", + " tp = 0 * np.eye(p.norb)\n", + " \n", + " H = TBLattice(\n", + " units = [(1, 0, 0), (0, 1, 0)],\n", + " hopping = {\n", + " # nearest neighbour hopping\n", + " ( 0,+1): t,\n", + " ( 0,-1): t,\n", + " (+1, 0): t,\n", + " (-1, 0): t,\n", + " \n", + " # next-nearest neighbour hopping\n", + " ( +1,+1): tp,\n", + " ( -1,-1): tp,\n", + " (+1, -1): tp,\n", + " (-1, +1): tp,\n", + " },\n", + " orbital_positions = [(0,0,0)]*p.norb,\n", + " )\n", + " \n", + " e_k = H.on_mesh_brillouin_zone(n_k = (p.nk, p.nk, 1))\n", + "\n", + " return e_k\n", + "\n", + "e_k = get_disperion_relation(hubbard)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from matplotlib import gridspec\n", + "from scipy.stats import gaussian_kde\n", + "from plotting_tools import bsplot\n", + "\n", + "fig = plt.figure()\n", + "\n", + "gs = gridspec.GridSpec(1, 2, width_ratios=[3, 1]) \n", + "gs.update(wspace=0.025, hspace=0.05)\n", + "\n", + "# -- Bandstructure\n", + "ax_bs = plt.subplot(gs[0])\n", + "\n", + "lower_limit = np.min(e_k.data.real)\n", + "upper_limit = np.max(e_k.data.real)\n", + "\n", + "path = 'G-X-M-G'\n", + "ax_bs.bsplot(e_k, path)\n", + "\n", + "ax_bs.spines['left'].set_bounds(lower_limit, upper_limit)\n", + "ax_bs.spines['bottom'].set_bounds(ax_bs.get_xticks()[0], ax_bs.get_xticks()[-1])\n", + "\n", + "ax_bs.set_ylabel('$\\epsilon(\\mathbf{k})$')\n", + "# -- Density of states\n", + "ax_dos = plt.subplot(gs[1])\n", + "\n", + "dos = gaussian_kde(e_k.data[:,0,0].real)\n", + "xs = np.linspace(lower_limit, upper_limit , 500)\n", + "dos.covariance_factor = lambda : .1\n", + "dos._compute_covariance()\n", + "\n", + "ax_dos.plot(dos(xs).real, xs)\n", + "ax_dos.fill_betweenx(xs, dos(xs).real, [0]*len(xs), alpha=0.25)\n", + "#ax_dos.set_xlim()\n", + "\n", + "#ax_dos.spines['left'].set_visible(False)\n", + "ax_dos.set_xlabel('DOS')\n", + "\n", + "ax_dos.set_yticklabels([''])\n", + "ax_dos.set_xticks([])\n", + "\n", + "ax_dos.spines['left'].set_bounds(lower_limit, upper_limit)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Spin and charge susceptibility\n", + "\n", + "Lets first introduce some helper function to convert between temperature in Kelvin and beta in 1/eV." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "def beta_to_temperature(beta):\n", + " \"\"\"Convert beta in 1/eV to Temperature in Kelvin\n", + " \"\"\"\n", + " \n", + " def eV_to_Kelvin(ev):\n", + " return 11604.5250061657 * ev\n", + "\n", + " T = 1. / beta\n", + " return eV_to_Kelvin(T)\n", + "\n", + "def temperature_to_beta(T):\n", + " \"\"\"Convert Temperature in Kelvin to beta in 1/eV\n", + " \"\"\"\n", + " \n", + " def Kelvin_to_eV(K):\n", + " return K / 11604.5250061657\n", + "\n", + " T = Kelvin_to_eV(T)\n", + " beta = 1./ T\n", + " return beta" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will then calculate the non-interacting susceptibiliy as previous and wrap it in a function that only cares about the Hubbard model parameters." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.6045250062\n", + "nk = 256\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.00 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n" + ] + } + ], + "source": [ + "from pytriqs.gf import MeshImFreq\n", + "from triqs_tprf.lattice import lattice_dyson_g0_wk\n", + "from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk\n", + "\n", + "\n", + "def get_chi0(p, e_k=None):\n", + " \"\"\"Return the non-interaction susceptibility for model parameters in a ParameterCollection\n", + " \"\"\"\n", + " if not e_k:\n", + " e_k = get_disperion_relation(p)\n", + "\n", + " wmesh = MeshImFreq(beta=temperature_to_beta(p.T), S='Fermion', n_max=p.nw)\n", + " g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh)\n", + " \n", + " chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw)\n", + " \n", + " return chi0_wk\n", + "\n", + "chi0_wk = get_chi0(hubbard, e_k)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We then calculate the spin and charge susceptibiliy in the RPA limit with the know equations.\n", + "\n", + "$$\n", + "EQ here lol\n", + "$$\n", + "\n", + "We also wrap this is a small function that only cares about the Hubbard model parameters." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors\n", + "from triqs_tprf.lattice import solve_rpa_PH\n", + "\n", + "def get_chiRPA(p, chi0_wk=None):\n", + " \"\"\"Return the spin and charge susceptibility in the RPA limit for model parameters in a ParameterCollection\n", + " \"\"\"\n", + " \n", + " if not chi0_wk:\n", + " chi0_wk = get_chi0(p)\n", + " \n", + " U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norb, p.U, 0.0, 0.0, 0.0)\n", + "\n", + " chi_c_wk = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation\n", + " chi_s_wk = solve_rpa_PH(chi0_wk, U_s)\n", + " \n", + " return chi_c_wk, chi_s_wk\n", + "\n", + "chi_c_wk, chi_s_wk = get_chiRPA(hubbard, chi0_wk)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We cann now easily acces the spin and charge susceptibility and have a look at it.\n", + "Again we see the the peak of the spin susceptibiliy at the M-point telling us, that the system will order antiferromagnetically." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.55,0.18,'$\\\\chi^{(c)}$')" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from pytriqs.gf import Idx\n", + "\n", + "chi_c_k = chi_c_wk[Idx(0), :]\n", + "chi_s_k = chi_s_wk[Idx(0), :]\n", + "\n", + "fig = plt.figure()\n", + "\n", + "ax_bs = fig.add_subplot(111)\n", + "\n", + "ax_bs.bsplot(chi_s_k, path)\n", + "ax_bs.bsplot(chi_c_k, path)\n", + "\n", + "lower_limit = np.round(np.min(chi_c_k.data.real), 2)\n", + "upper_limit = np.round(np.max(chi_s_k.data.real), 2)\n", + "\n", + "ax_bs.set_yticks([lower_limit, upper_limit])\n", + "\n", + "ax_bs.spines['left'].set_bounds(lower_limit, upper_limit)\n", + "ax_bs.spines['bottom'].set_bounds(ax_bs.get_xticks()[0], ax_bs.get_xticks()[-1])\n", + "\n", + "ax_bs.set_ylabel(r'$\\chi(\\nu=0, \\mathbf{k})$', rotation=0, ha='right')\n", + "ax_bs.text(0.62, 0.6, \"$\\chi^{(s)}$\", transform = ax_bs.transAxes, size=22, color='C0')\n", + "ax_bs.text(0.55, 0.18, \"$\\chi^{(c)}$\", transform = ax_bs.transAxes, size=22, color='C1')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will now introduce a small function that will find $U_\\mathrm{c}$, the interaction strength at which the Hubbard model goes into a spin ordered phase.\n", + "This is done by searching for the $U$ at which \n", + "\n", + "$$\n", + "\\frac{1}{\\chi^{(s)}} \\approx 0\\,,\n", + "$$\n", + "\n", + "via [`scipy.optimize.brentq`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.brentq.html#scipy.optimize.brentq)." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.optimize import brentq\n", + "\n", + "def get_spin_phase_transistion(p):\n", + " \"\"\"Return U at which model p transitions to spin order via root search\n", + " \"\"\"\n", + " p = p.copy()\n", + " \n", + " chi0_wk = get_chi0(p)\n", + " \n", + " def one_over_spin(U):\n", + " \n", + " p.U = U\n", + " _, chi_s_wk = get_chiRPA(p, chi0_wk)\n", + " \n", + " # -- If any value is below zero we are already in an ordered phase\n", + " if np.any(chi_s_wk.data[np.abs(chi_s_wk.data) > 1e-3] < 0.0 ):\n", + " return -1\n", + " \n", + " chi_at_critical_k = np.max(chi_s_wk.data)\n", + " return 1./chi_at_critical_k\n", + " \n", + " U_c = brentq(one_over_spin, 0.0, 10.0)\n", + " \n", + " return U_c" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To scan through some parameters we will copy our base model `hubbard`, which parameters are stored as a `ParameterCollection`, and only change the specific parameters.\n", + "We do this with the function `parameter_scan` which outputs us a `ParameterCollections` objects which is a container for multiple `ParameterCollection`.\n", + "We can then loop over the `ParameterCollections` object." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "import itertools\n", + "from triqs_tprf.ParameterCollection import ParameterCollections\n", + "\n", + "def parameter_scan(p, **kwargs):\n", + " parameter_values = []\n", + "\n", + " for key, value in kwargs.iteritems():\n", + " parameter_values.append(zip([key]*len(value), value))\n", + " \n", + " ps = []\n", + " \n", + " for parameter_value in itertools.product(*parameter_values):\n", + " ps.append(p.copy(**dict(parameter_value)))\n", + "\n", + " return ParameterCollections(ps)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can now do a crude scan of a $T-U$ phase diagram to map out the antiferromagnetic (AFM) phase." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "%%capture\n", + "\n", + "Ts = [1000, 750, 500, 250]\n", + "# -- Use the hubbard model as a base for the parameters and only change T\n", + "hubbard_models = parameter_scan(hubbard, T=Ts)\n", + "\n", + "U_cs = []\n", + "\n", + "for hubbard_model in hubbard_models:\n", + " \n", + " U_c = get_spin_phase_transistion(hubbard_model) \n", + " U_cs.append(U_c)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.625,0.3,'AFM')" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "\n", + "ax_pd = fig.add_subplot(111)\n", + "\n", + "ax_pd.plot(U_cs, Ts, \"o\", ls=\"-\")\n", + "ax_pd.fill_between(U_cs, Ts, [Ts[-1]]*len(Ts), alpha=0.25)\n", + "\n", + "ax_pd.set_ylabel('Temperature\\n[Kelvin]', rotation=0, ha='right', multialignment='center')\n", + "ax_pd.set_xlabel('U [eV]')\n", + "\n", + "ax_pd.set_yticks(Ts)\n", + "ax_pd.set_xticks([np.round(ele,2) for ele in U_cs])\n", + "\n", + "ax_pd.spines['left'].set_bounds(Ts[-1], Ts[0])\n", + "ax_pd.spines['bottom'].set_bounds(ax_pd.get_xticks()[0], ax_pd.get_xticks()[-1])\n", + "\n", + "ax_pd.text(0.625, 0.3, \"AFM\", transform = ax_pd.transAxes, size=24, color='C0')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Particle-Hole Symmetry\n", + "\n", + "The Hubbard model with only nearest neighbor hopping inhibts a useful particle-hole symmetry.\n", + "To introduce this, let us first introduce the notation of a bipartite lattice.\n", + "A bipartite lattice can be subdivided into two sublattices for which every lattice site on one of them only has neighboring sites from the other sublattice.\n", + "This is the case for our square lattice.\n", + "\n", + "Let us now introduce a new kind of creation and annihilation operator\n", + "\n", + "$$\n", + "d_{l \\sigma}=(-1)^{l} c^\\dagger_{l \\sigma}\\,,\\quad\n", + "\\mathrm{and}\\quad\n", + "d_{l \\sigma}^{\\dagger}=(-1)^{l} c_{l \\sigma}\\,.\\\\\n", + "$$\n", + "\n", + "Here $l$ is either $0$ for one sublattice and $1$ for the other.\n", + "\n", + "Using this substitution is called particle-hole transformation (PHT), because the analog of the number operator for these new ones counts the number of holes, i.e.\n", + "\n", + "$$\n", + "\\tilde{n}_{l \\sigma} = d_{l \\sigma}^{\\dagger} d_{l \\sigma}= \\underbrace{(-1)^{2l}}_{=1} c_{l \\sigma}c_{l \\sigma}^{\\dagger} = 1-c_{l \\sigma}^{\\dagger} c_{l \\sigma}=\n", + "1-n_{l \\sigma}\\,.\n", + "$$\n", + "\n", + "Let us now inspect how the Hubbard Hamiltonian changes under such a PHT.\n", + "The kinetic part consists for only nearest neighbor hopping of terms of the form $c_{1 \\sigma}^{\\dagger} c_{j \\sigma}$, where $l$ and $j$ are always from a different sublattice.\n", + "Using the PHT on it yields\n", + "\n", + "$$\n", + "c_{l \\sigma}^{\\dagger} c_{j \\sigma} \\xrightarrow{\\mathrm{PHT}} \\underbrace{(-1)^{j+l}}_{=-1} d_{l \\sigma} d_{j \\sigma}^{\\dagger}=\n", + "-d_{l \\sigma} d_{j \\sigma}^{\\dagger}= d_{l \\sigma}^{\\dagger} d_{j \\sigma}\\,,\n", + "$$\n", + "\n", + "showing that the kinetic part is invariant.\n", + "\n", + "The interaction has terms of the form $n_{j \\uparrow} n_{j \\downarrow}$, using the PHT here yields\n", + "\n", + "$$\n", + "n_{j \\uparrow} n_{j \\downarrow} = c_{j \\uparrow}^{\\dagger} c_{j \\uparrow} c_{j \\downarrow}^{\\dagger} c_{j \\downarrow}\n", + "\\xrightarrow{\\mathrm{PHT}}\n", + "(-1)^{4j} d_{j \\uparrow} d_{j \\uparrow}^{\\dagger} d_{j \\downarrow} d_{j \\downarrow}^{\\dagger}=\n", + "(1- d_{j \\uparrow}^{\\dagger}d_{j \\uparrow}) (1-d_{j \\downarrow}^{\\dagger}d_{j \\downarrow})=\\\\ \n", + "(1 - \\tilde{n}_{j \\uparrow}) (1 -\\tilde{n}_{j \\downarrow})=\n", + "1 - \\tilde{n}_{j \\uparrow} - \\tilde{n}_{j \\downarrow} + \\tilde{n}_{j \\uparrow}\\tilde{n}_{j \\downarrow}\\,,\n", + "$$\n", + "\n", + "which leads to additional terms.\n", + "But those terms only consist of a shift in chemical potential and an constant energy.\n", + "We can therfore write a new Hamiltonian for the Hubbard model which is also invariant in the interaction term for a PHT.\n", + "\n", + "$$\n", + "H=-t \\sum_{\\langle j, l\\rangle \\sigma}\\left(c_{j \\sigma}^{\\dagger} c_{l \\sigma}+c_{l \\sigma}^{\\dagger} c_{j \\sigma}\\right)+U \\sum_{j}\\left(n_{j \\uparrow}-\\frac{1}{2}\\right)\\left(n_{j \\downarrow}-\\frac{1}{2}\\right)-\\mu \\sum_{j}\\left(n_{j \\uparrow}+n_{j \\downarrow}\\right)\n", + "$$\n", + "\n", + "Doing the PHT here yields\n", + "\n", + "$$\n", + "\\left(n_{j \\uparrow}-\\frac{1}{2}\\right)\\left(n_{j \\downarrow}-\\frac{1}{2}\\right) \\xrightarrow{\\mathrm{PHT}}\n", + "\\left(1-\\tilde{n}_{j \\uparrow}-\\frac{1}{2}\\right)\\left(1-\\tilde{n}_{j \\downarrow}-\\frac{1}{2}\\right) = \n", + "\\left(-\\tilde{n}_{j \\uparrow}+\\frac{1}{2}\\right)\\left(-\\tilde{n}_{j \\downarrow}+\\frac{1}{2}\\right)=\\\\\n", + "(-1)^2 \\left(\\tilde{n}_{j \\uparrow}-\\frac{1}{2}\\right)\\left(\\tilde{n}_{j \\downarrow}-\\frac{1}{2}\\right)=\n", + "\\left(\\tilde{n}_{j \\uparrow}-\\frac{1}{2}\\right)\\left(\\tilde{n}_{j \\downarrow}-\\frac{1}{2}\\right)\n", + "$$\n", + "\n", + "showing the invariance.\n", + "\n", + "Using the PHT on the chemical potential term yields\n", + "\n", + "$$\n", + "n_{j \\uparrow}+n_{j \\downarrow} \\xrightarrow{\\mathrm{PHT}} (1-\\tilde{n}_{j \\uparrow}) + (1-\\tilde{n}_{j \\downarrow}) = 2 - (\\tilde{n}_{j \\uparrow} + \\tilde{n}_{j \\downarrow})\\,,\n", + "$$\n", + "\n", + "and therefore an unimportant constant term, but also a sign change.\n", + "\n", + "The Hubbard hamiltonian in equation REFHERE can therfore be mapped via a PHT to an identical Hubbard model with only a negative chemical potential.\n", + "\n", + "To use this knowledge let us now see how the spin operator in $z$-direction changes under a PHT\n", + "\n", + "$$\n", + "S^z_j = n_{j \\uparrow} - n_{j \\downarrow} \\xrightarrow{\\mathrm{PHT}} (1 - \\tilde{n}_{j \\uparrow}) - (1 - \\tilde{n}_{j \\downarrow}) = \\tilde{n}_{j \\downarrow} - \\tilde{n}_{j \\uparrow} = \\tilde{S}^z_j\\,.\n", + "$$\n", + "\n", + "This sign change for the direction of the spin is unimportant for the calculation of suscpeitbilites and therefore the spin susceptibility is invariant under PHT\n", + "\n", + "$$\n", + "\\langle S^z_jS^z_j \\rangle = \\langle \\tilde{S}^z_j\\tilde{S}^z_j \\rangle\\,.\n", + "$$\n", + "\n", + "The spin susceptibility calculated at a Hubbard model with some chemical potential $\\mu$ is therefore the same as for a Hubbard model with chemical potential $-\\mu$.\n", + "We test this by calculating the phase transition to the AFM for a few chemical potential" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "%%capture\n", + "\n", + "mus = [-.5, -.25, -0.1, 0.1, .25, .5]\n", + "\n", + "hubbard_models = parameter_scan(hubbard, mu=mus)\n", + "\n", + "U_cs = []\n", + "\n", + "for hubbard_model in hubbard_models:\n", + " \n", + " U_c = get_spin_phase_transistion(hubbard_model) \n", + " U_cs.append(U_c)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.125,0.3,'AFM')" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "\n", + "ax_pd = fig.add_subplot(111)\n", + "\n", + "ax_pd.plot(mus, U_cs, \"o\", ls=\"-\")\n", + "ax_pd.fill_between(mus,[min(U_cs)]*len(U_cs),U_cs, alpha=0.25)\n", + "\n", + "ax_pd.set_ylabel('U [eV]', rotation=0, ha='right')\n", + "ax_pd.set_xlabel('$\\mu$ [eV]')\n", + "\n", + "ax_pd.set_yticks([min(U_cs), max(U_cs)])\n", + "ax_pd.set_xticks(mus)\n", + "ax_pd.set_xticklabels(mus, rotation=25)\n", + "\n", + "ax_pd.spines['left'].set_bounds(min(U_cs), max(U_cs))\n", + "ax_pd.spines['bottom'].set_bounds(min(mus), max(mus))\n", + "\n", + "\n", + "ax_pd.text(0.725, 0.3, \"AFM\", transform = ax_pd.transAxes, size=24, color='C0')\n", + "ax_pd.text(0.125, 0.3, \"AFM\", transform = ax_pd.transAxes, size=24, color='C0')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we see that the AFM phase is indeed symmetric for $\\mu=0$.\n", + "\n", + "If we now introduce a next-nearest neighbor hopping we introduce hopping between sublattices of the same type.\n", + "The kinetic term of the Hubbard model does then contain terms of the form $c_{1 \\sigma}^{\\dagger} c_{l \\sigma}$, which are not invariant under PHT\n", + "\n", + "$$\n", + "c_{l \\sigma}^{\\dagger} c_{l \\sigma} \\longrightarrow \\underbrace{(-1)^{2l}}_{=1} d_{l \\sigma} d_{l \\sigma}^{\\dagger}=\n", + "d_{l \\sigma} d_{l \\sigma}^{\\dagger}= -d_{l \\sigma}^{\\dagger} d_{l \\sigma}\\,.\n", + "$$\n", + "\n", + "Such a model is therefore not symmetric for $\\mu=0$, which we can test." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "hubbard_next_nearest_neighbor_hopping = hubbard.copy(tp=-0.05)\n", + "\n", + "e_k = get_disperion_relation(hubbard_next_nearest_neighbor_hopping)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from matplotlib import gridspec\n", + "from scipy.stats import gaussian_kde\n", + "from plotting_tools import bsplot\n", + "\n", + "fig = plt.figure()\n", + "\n", + "gs = gridspec.GridSpec(1, 2, width_ratios=[3, 1]) \n", + "gs.update(wspace=0.025, hspace=0.05)\n", + "\n", + "# -- Bandstructure\n", + "ax_bs = plt.subplot(gs[0])\n", + "\n", + "lower_limit = np.min(e_k.data.real)\n", + "upper_limit = np.max(e_k.data.real)\n", + "\n", + "path = 'G-X-M-G'\n", + "ax_bs.bsplot(e_k, path)\n", + "\n", + "ax_bs.spines['left'].set_bounds(lower_limit, upper_limit)\n", + "ax_bs.spines['bottom'].set_bounds(ax_bs.get_xticks()[0], ax_bs.get_xticks()[-1])\n", + "\n", + "ax_bs.set_ylabel('$\\epsilon(\\mathbf{k})$')\n", + "# -- Density of states\n", + "ax_dos = plt.subplot(gs[1])\n", + "\n", + "dos = gaussian_kde(e_k.data[:,0,0].real)\n", + "xs = np.linspace(lower_limit, upper_limit , 500)\n", + "dos.covariance_factor = lambda : .1\n", + "dos._compute_covariance()\n", + "\n", + "ax_dos.plot(dos(xs).real, xs)\n", + "ax_dos.fill_betweenx(xs, dos(xs).real, [0]*len(xs), alpha=0.25)\n", + "#ax_dos.set_xlim()\n", + "\n", + "#ax_dos.spines['left'].set_visible(False)\n", + "ax_dos.set_xlabel('DOS')\n", + "\n", + "ax_dos.set_yticklabels([''])\n", + "ax_dos.set_xticks([])\n", + "\n", + "ax_dos.spines['left'].set_bounds(lower_limit, upper_limit)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "%%capture\n", + "\n", + "mus = [-.5, -.25, -0.1, 0.1, .25, .5]\n", + "\n", + "hubbard_models = parameter_scan(hubbard_next_nearest_neighbor_hopping, mu=mus)\n", + "\n", + "U_cs = []\n", + "\n", + "for hubbard_model in hubbard_models:\n", + " \n", + " U_c = get_spin_phase_transistion(hubbard_model) \n", + " U_cs.append(U_c)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.125,0.1,'AFM')" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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zjDFLk7i/ZcDnOB8ELgA6TLrAWTgJtx54ommhMWY4gLV2KPBZEmMUEelQpL6e8quujrVzRx9E7l57uhiRdFa3r142xkSAB6PNs6y1OQlsdkH09U/GmNLURJa9gmvXUrbwKtYNH8HX227PuuEjKFt4FcG1a90OTaRbq7znXoKffgqAJz+fogsvdDki6axM7OmmwoPAtUB/4Fjgj22taK3dGTgw2nygqwe21vYHTgaOA/YAtsG5bP4ecD9wvzGmg7r/2L7W4vTYW/OtMSblVROtzmpSVUX1o49R8/un6LfkPvIOPyzVYYj0OMG1a6m8885Yu+Dss/D27etiRLIlsjLpWmu9wLk4PdK9cYqbvgNWArcZY95ovr4x5hNr7SvA6Og2bSZdNvdyvwX+kYRwTwfuAb4BXgK+ALYGTgF+AxxjrT092iNPRDnwi1aWVyUh1na1mNXke28GiQSDlEyewsAXnsc/dGiqwxHpMSKRCGXXXAt19QD4dtiBvCOPcjkq2RJZl3SttcXAM8C46KIIUAkMBs4ATrPWzjLG3BW36QM4SXe8tbZva5eNrbUe4Lxo8xFjTAejiSfkY+AE4K/Ne7TW2qtw7i+fipOAn05wf2VbWKDWZYnMahJpbKRqyW/oc8NP0xSVSPdX99e/Uf/SMqfh8VA0eRIeX7e/O9gtZeP/2oM4CfdfOJdsC40xvYG+wFVAEPiltXZ03HZP4lQe5wJntrHvMcDQZsfpMmPMi8aYP8dfQjbGrAeaqqIPTcaxUi2hWU2CQWqeSfTzg4h0JFxVRVmzz9l5P/4xOTvt5F5A0iVZ1dO11o4DTgLW4jzDG5ud2RhTBtxorQ0BNwMLgfHN3i+31j6LU5l8AZsTXnNNl5ZXG2PWpOSbaKmp29iZHnXAWnsesD1QjfPhY4UxJpTs4OIlPKtJVWLriUjHKm79OeH16wHw9O5NwTlnuxyRdEVWJV2gqVRvafOEG+dRnKR7mLXWF5eMHsBJuqOstTsZYz5pesNamw+c1my9lLLW+tmc5J/rxKaDgIfiln1mrb3IGLO8neNNACa08tbeiR7YU1hIpKrjW8eeosRmPxGR9jV+8G+qf3d/rF144QV4E5xdSDJTtiXdg6Kvc6y10zpYtwCnWnlDs2X/BNYBPwDOB0yz904CeuH0Oh9NSrTtuwnYHfibMSbRgq37cYrFPsC5j70jcCkwGfi7tXZUOz30oXx/xK9OKTjlZKoffaz9S8x+PwWnnNqVw4gIEAmHKb1yIYScfkPO7rsTOPhgl6OSrsq2pDs4+tqbuOEY21DQvGGMCVlrHwYuB8631i5qVjUc63UaY5on6qSz1s4E5gH/wUn+CTHG2LhF7wNTrbVV0f0twnk8qTVrgdZ6wk3V3x0qmjKZmt8/RaSD+7pFkycmsjsRaUfNo4/R+M47TsPno3DiJXg8GnU22yWadOuir/kJrNuU6Fp5rqTLmgq/TjTG/GkL9/EATtLdATgYWGmtHQT8uNn7KWOtnQH8Evg3cEQ7l8k7416cpNvmxJnRUb6WthLPMhLsAfuHDqXfkvu+95xuC8Egoa/X6ZEhkS4Iffcd5TfeGGvnn3gi/m22cTEiSZZEq5c3RV8Ht7eStTYA9IvbJpm+jb7+cEt3YIz5N/B2tNnUyzwXZzzlUuDPWxxdB6y1s4G7cHqoh0UrmJOhqWee8ps9eYcfxsAXnqfw3HPxFBWBx4MnPx9Ps4f0Sy69jNDGjakORaTbqvjp9UTKygHwbr01Baec4nJEkiyJJt13o68HtbsWHICTvJpvk0yvRV+7etOwqTd7hrU2j82Xlh83xtR3cd+tstZeAdwOrMZJuMm8hD0q+vppEvfZJv/QofS54acMfv9fbPXkE/R/8AH63HQjnl69AAhv2EDpzFlEOppgW0S+p/7116n5/VOxdtElF+MJaEKD7iLRpNv04OUwa+2J7aw3N/r6GalJukujr/tbay9ob8XoTEFteQxnKMbewDVA04jhKbm0bK29FqdwahXOJeXv2lk3x1q7q7V2WNzy3ay1/VpZfwhO7xng4SSG3Sm+fv0onnkZRO851a9YSdWd8eOTiEh7Ig0NlC1sNqHByJHk7rOPixFJsiV0T9cY85K19p849z0fttbOx+kVlgNYa4fjjG18UnSTaxIdT7gzjDHPWWufwRnB6XfRxHSvMeabaBx9ce5rXgyUABe1sZ9N1tq/4hQdLYwu/ih++MhksNZeCCwGQjiVxzOtja+HYm2zmZW2AT7EmRlpaLN1TgeutNa+hPOhphIYhjNASB7wN+DWZMffGbl77UX+ySdT+8wzgPN8Ye7IAwgceGAHW4oIQNWvf0Pw448B8OTlUXjRBHcDkqTrTPXyOThjFh+EU7hzT3RS91w230uMANcaY1L5yM0FOD30k4CfAD+x1pYDHpxHfpos7WA/D+AkXW+zdirsEH31AbPbWGc5Hcf7EjAc2AfncnIhUAa8jPPc7kOdGL85ZQrOOJ3GDz8k+OGHEA5TMuNSBj7/D3z9+7sdmkhGC375JZW33R5rF5xxhn5vuqGEk64x5jtr7VicwSXOAvbDeQ62AfgIWAHcbYxZnYpAm8VRDZxsrT0Op0c7EhgAhIFPcMYzfgan59eevwEbm22bkkuz0XGSF3Vi/bU4HyDily+n9Ud+MorH56N41izKFiwgUllJeP23lM6aTf8HH8DjzcZRR0XSo/zanxCpcx4U8Q0ZQt6xx7gckaRCp57TjU4A8DAu3jtsFstfgb92YftGYGDyIpImvv79KL7sMipuuAGA+peWUXXPvRTPmO5yZCKZqfYf/6Duny/E2kWTJuHx+drZQrKVuh6SErn77E3+iZtr7ipu/hn1b73lYkQimSlcU0P5tZsHxwsccQQ5w3dxMSJJpUwckep+a23TYKOHGWOWuRlMc9F72AmN3iRQcNaZNP7nPwQ/+ghCIUqnzWDA8//A108Tb4s0qbz9F4S+/hoAT3Exheee63JEkkqZ1NMtwRn8ovlXg6sRfV98fN+2v3rP5vH7KZ49yxlEAwh98w1lc+YSibhe7yWSERr/8x+qlvw61i48/3y8xUUuRiSpljE9XWNMxg+5YowZ7nYM2ca31VYUXzqDiptuBqDuhReoum8JxVOnuByZiLsi4TBlC6+KDafqHzGCwKFdmpNEskAm9XSlm8rdbz/yj49NbUzFjTfRsOodFyMScV/N739Pw5vROgefj6JJEzWhQQ+gpCtpUXDOOfh33tlpBIOUTJ9BuKzM3aBEXBIqKaXiuutj7fzx4/Fvt52LEUm6KOlKWsTu70Yn4A599RWlc+fp/q70SBU33ki4tBQA74ABFJymOah7CiVdSRvfwIEUTZ8Wa9f943mqf/s7FyMSSb/6t96m5tHHYu3Ciy7Ck5fnYkSSTkq6klaBAw4g79hjY+3yn15Pw+qUDmImkjEiwaBTPBWVu//+BH60v4sRSbop6UraFZ53Hv5h0UmUGhspmTaDcHm5u0GJpEHVb3/njEsOEAhQeHGrc7JIN6akK2nnyfFTPGc2nvx8AEJffEHp/Mt1f1e6teDX66i89eexdsFpp+IbMMDFiMQNSrriCt/WW7e8v/u3v1G9NFUTPYm4r3zRIiI1NQD4ttuO/PHjO9hCuiMlXXFN4MADyTvqqFi7fPF1NLz3nosRiaRG3f+9SN3f/h5rF02aiMefMWMTSRop6YqrCi84H98O0SmHGxoomTqNcGWlu0GJJFG4tpaya66NtQOHHkrOiBEuRiRuUtIVV3lyc+k1Z87m+7trP6dsge7vSvdRdcedhL74AgBPYSGF553nckTiJiVdcZ1v8CCKpmwei7n2z3+h5iHXp2wW6bLGTz6h8p57Y+3C887F27uXixGJ25R0JSMERh9E3o/HxdpliywN73/gYkQiXROJRCi78ipobATAv8suBA4/3OWoxG1KupIxCi+cgG/IEKdRX+/c362qcjcokS1U+8wfaHjtNafh9VI0eRIer/7k9nT6CZCM4QnkUjxnDgQCAIQ++4yyKxfq/q5knXBZGeWLr4u18449Fn/TB0rp0ZR0JaP4t/kBRVMmx9q1f3iWmscedzEikc6ruPlnhL/7DgBvv34UnHG6yxFJplDSlYyTd8ghLe59lV17LY1NQ+eJZLiGd9+lulkhYOFFE/BGq/NFlHQlIxVdfBG+pvlF6+opmTqdcHW1u0GJdCASDDrFU9FbIjn77EPuyJEuRyWZRElXMpInEKB47ub7u8FPPqHsqmtcjkqkfdUPPEjj++87jZwcii65GI/H425QklGUdCVj+bfdlqKJl8TatU89RfUTT7oYkUjbQuvXU/GzW2LtglNPxbf11i5GJJlISVcyWt6hhxIYOzbWLr/6Gho//tjFiERaV24XE4k+4ub7wQ/IP+F4lyOSTKSkKxmvaOIl+LbZBoBIba3z/G5trctRiWxWt2IFtX/6c6xdOHEinpwcFyOSTKWkKxnPk5fn3N/NzQUg+NHHlDcbQF7ETZG6OsoWXh1rBw45mNw9dncxIslkSrqSFfzbb0/RxRfH2jWPP0HN08+4GJGIo/LuewitXQuAp6CAwgsucDcgyWhKupI1AocfRuCQg2PtsisX0vjJJy5GJD1d8NPPqLzrV7F2wTnn4O3Tx8WIJNMp6UrW8Hg8FE6ahG/wYAAiNTWUTJ1GRPd3xQWRSISyq6+G+noA/MOGkTduXAdbSU+npCtZxZuf79zfjRapBD/8D2XGuhyV9ES1f/oz9StWOg2Px5nQwKc/qdI+/YRI1vEPHUrhRRNi7ZpHHqHmj390LyDpccKVlZTbzR/28o4+Cv+OO7oYkWQLJV3JSnnjxpF70EGxdtmCKwh++pmLEUlPUnHLrYS/3QCAp08fCs48y+WIJFso6UpW8ng8FE2ZjHfQIAAi1dXO/d26Opcjk+6u4b33qL5/aaxdNOFCvIUF7gUkWUVJV7KWt6CAXnPngN8PQOMHH7SYw1Qk2SKhEGVXLoRwGICcPfdsccVFpCNKupLV/DvsQOGFm5+LrH7gQWr/8lcXI5LurPrhR2hcvcZp5ORQNPESTWggnaKkK1kv76ijyD3wwFi7dP4CgtHBCkSSJbRxIxU33Rxr5590YuzxNZFEKelK1vN4PBRNnYo3OqNLpLKSkmnTiUSfnxRJhvLFPyVSUQGAd9AgCk46yeWIJBsp6Uq34C0soHjObPD5AGj813uUX3+Dy1FJd1H/yqvUPrN52NGiiZfgiY4FLtIZfrcDEEmWnGHDKLzg/FhlafVvf0dg1IHkH3OMu4FJVos0NFB21eYJDXJHjSJ3r71cjKjz6t98k8pbbgWc4q/e117T5roNH3xAxaKOB5zxDRlC31s3zx9c99Iyqu6+O9Yunj+PwMiRbW4frqigZPIUCIUACIwdS/GlMzo8brZTT1e6lbxjjiH3gANi7dJ5Cwh++aWLEUm2q7r3PoLRMb49+fkUTrjQ5Yg6r37Z8ti/G997j9CmTQlt5ykuxtO7d6tf3l692j/m8uXtv//yy7GE25OopyvdisfjoWjaVMo++4zwxo1EysspmTadAc88rcuB0mnBzz+n4pe/jLULzjoTX79+LkbUeeHKShreeQcCAQI/+hH1L79M/YqVFJzc8T3pPjfdiG/gwE4dz1NYCOEwDe+8S7iyEm9xcavr1S9fAYB3wADCGzd26hjZTD1d6Xa8RUUt7+++u5qKG29yOSrJNpFIhLJrfgJ1TkGeb4cdyDvqKJej6rymHmVg//3J+7EzIUNHvdAu8fudpwlCIepfeaXVVYJffUXw00/xDhhAzvDhqYslAynpSreUs/POFJ57bqxdteTX1D7/TxcjkmwQXLuWsoVXsW74CNZtuz31L74Ye69o0iQ80Q9y2aTp0nLgkEPwjxiBd6utCH39NY3/Td20mHljxzrHjvZm24xpzBjoYY85K+lKt5U3/jhy99sv1i6dM4fg11+7GJFksroXX2LDuCOpfvQxIlVVLd/0eolUVboTWBcEv/yS4Kef4ikuJmevPfF4PARGjwagfvmylB3X/8MReAcMIPjJJwS/XtfivUg47PS+gbyxY1IWQ6ZS0pVuy+PxUDRjBt7+/QGIlJVTMnU6kcZGlyOTTBNcu5aSyVOcuZkj3puOAAAgAElEQVSDwe+vEA5T8fPbCK1fn/7guiDWoxw1Ck90uNTAIYc4773yKpHGVr7XJPB4PJuPs6Jlb7fx/fcJb9qEf+ede+TgIkq60q15i6P3d73Oj3rjO+9QcfPPXI5KMk3VfUs6/jAWDFKTRUOMRkJh6lc68/0GDj44ttw/ZHt8229PpKqKhlVvt7uPsisXsmnipFa/wjU17W7b1IutX7mSSCQSW950yTkQvQTd06h6OcWstf2Bk4HjgD2AbYAG4D3gfuB+Y0y4E/vbFlgMHA30B74BngWsMaY0udF3DznDh1NwztnUPPwIAFX33EvgwAPJG3eEy5FJpqh55g+t93CbC4VoWLECJl6SnqC6qPFfawiXluIdMAD/ri2LlQKHHEzNI49Sv2w5gWZDqMaLVLZzSb1ZIm2N7wc/wL/zzgT/+18a//1vcnfbjUhdHfVvvAF+P4EeOlGEerqpdzrwa2Ak8AbwC+BpYHfgN8CT1tqESgmstcOAVcBFwJvA7cCnwCzgtWiCl1bkH388OfvsE2uXzp5DaN03LkYkmSRSXZ3Yelk0dWRd06Xl0aO/NylDYPTB4PHQsHo14fKKNvfR91d3sdXvn2z1y1tY2GEMgabebrRauv6NN6C+ntz99sVbXLSl31pWU9JNvY+BE4BtjTHnGmMWGmMuBnYFvgROBU5JcF93AwOBmcaYk4wxVxpjDsdJvsOB65Mffvfg8XopvnQG3ugzluHSUkpmzCDSUe9GegRPAgkEwJOXl+JIkiNcXUPDW28BLS8tN/EN2Ar/rrs6j/VEi5pSIXDQaPD7aXj9DSL1DT3+0jIo6aacMeZFY8yf4y8hG2PWA/dGm4d2tB9r7Y7AkcBa4FfxhwGqgfOttYn99eiBvL16UTx7Vuz+bsObb1ERHRpPerbAoYd2vJLPR+6Y7Ki2bXj1VYjeoy6bP5/vTj/je1/BDz8EoC6Fz+x6i4vI3XdfIrW11D73HI3vv4+nuJjcZledeholXXc1VW4k0t06PPr6fCsJvBJ4BSgA2r5BI+SMGEHBmWfE2lV3/Yq6ZcvcC0hcFy4ro+GdVR2v6PdTMP641AeUBJ1JpKHPPiP4+RcpiyUQ/aBS89hjEIkQOOigWCV1T9Rzv3OXWWv9QNPs688lsElTJcTHbbz/X5ye8C7A/7VyvAnAhFa22zuBY3cr+SedROO/P6RxjTMZeenM2Qx8/jl8gwa5HJmkWyQcpuSyWYSb39/3eiHc7HOtzwd+P73mzc2Kn5HQN+sJfvQRAH1u+RneAQPaXLfqzrtoWLWK+uXL8F9wQZvrdUXuvvviKS6OFWX15EvLoKTrpptwiqn+Zoz5RwLr946+lrfxftPyPm28PxTo2T/tUR6vl+LLLqVsweWES0sJb9pEyaWXsdXjj/XoT+A9UeUvftli1KnCiZcQ/PIrGlasIFJXhycvj9wxYygYf1xWJFyAuuigF74hQ/APHdruurmjRtGwahV1K1+m4Nzz8PiSf/HTk+OncMKFhNauhUAeOTvvlPRjZBP9hXGBtXYmMA/4D3B+knbbVJ7YVh3/WqC1a057szmh9xje3r0pmjWTCrsYIhEaXnudytt/Qa8F890OTdKk7v9epPK222Pt/BNPJL9pbOUseSwoXiQSoX5F9NncdqbVa5K7/37g8xEpK6NxzWpy9903JXHljRkDWXI/PNWUdNPMWjsD+CXwb+AIY0xJgps29WTbSpC94tZrwRizFFjaSjzL6KE94NzddqPg9NOpefJJACp/eQe5I0eSN+YQlyOTVAt+/jkll82MPWuas/vuFJx9lstRdV3jBx/EZuzJPbDjpOstLCRn991pXLOGumXLU5Z0ZTMVUqWRtXY2cBfwPnBYtII5UR9FX3dp4/2do69t3fOVVuSfcgo5u+/uNCIRSmfOIrRhg7tBSUqFa2spmTiZSLnz+dTbvz/Fs2dn5WQG8ZqGffQNHox/u+0S2iYQTc4Nb79NOMHnlWXLeSIdjCoiyWGtvQLnPu5q4MfGmO86uf0w4BOcy8TDmlcwW2uLcUam8gIDjDEJ/+Y09XSHDBnChAkTOhMSkcZGGt5qfxi5bBAuLaN0wYLYH+HA6NH0f+yRbvFHWFqKRCKUzppD7dNPOwv8fnovXtzj7zP2VDkjdsXbt29XdtHpOZLU000Da+21OAl3Fc4l5TYTrrU2x1q7azTJxhhj/gc8j1MQNSN+M6AQeLAzCVcc3r59KJ41E6Kj9tS/8gqVd9zpclSSCtUPPLg54QJFF1+shCtppXu6KWatvRBnrOQQsBKYaa2NX21t9J4rOGMzfwh8jpNgm5sOvArcYa09IrreSOAwnMvKVyf/O+gZcvfYg/xTTon9Qa687XYCI0cSOGiUy5FJstS/vYryRZt/9wKHHUpA429Lmqmnm3o7RF99wGyc0aPivyYksqNob3d/nIKokTgV0MOAO4BRxphNSYy7xyk4/XT8P/yh0wiHKbn0UkLfdeougGSo0MaNlEyZEhulybfDDhRdMvF7YxKLpJru6fZwuqfbUqikhLIFlxOpcAaBD4wdQ/+HH8Lj1efTbBUJBvnurLNpeO11ADxFRfS5+SZ8Awe6HJm4Tfd0RVzm69eP4ssujbXrl6+g6q74oa4lm1TccGMs4eLxUDx7lhKuuEZJVyRO7t57k3/ySbF2xS23OlOSSdap/fNfqLpvSaxdcOaZ5O61l4sRSU+npCvSioIzz3SmPgPn/u70SwmVJDqOiWSCxo8/pnTuvFg7d7/9WnyYEnGDkq5IKzw+H8WzZ+EpLgYgvH49pbNmEwmHO9hSMkG4stIZAKOmBgDvoEEUXXap7s2L6/QTKNIGX//+FF+6+ZHo+hdfoure+1yMSBIRiUQonTuP4P/+5ywIBOg1fz7eBCeqF0klJV2RduTuuy/5J5wQa1fcdDP13axiu7upuvse6v7291i7eOoU/EO2dzEikc2UdEU6UHD2Wfh3iQ55HQpROn0GoZJSd4OSVtWtfJmKm26OtfOOOYbAwQe7GJFIS0q6Ih3w+P3OgPjRy5OhdesomzsXPeOeWYJff03p9BmxCej9w4dTeEGyZs4USQ4lXZEE+AZsRdGMzfd36/75AlVLfu1iRNJcpL6ekslTCEcrzD19+tBr3lw8fo10K5lFSVckQYEf7U/eccfF2hU33EjDO++6GJE0KbvW0Lh6jdPw+eg1d25XRxoSSQklXZFOKDz3XPw7RWelCQYpmTadcFmZu0H1cNWPP07NI4/E2oXnn0/OiF1djEikbUq6Ip3gyYne3y0oACD01VeUzpuv+7suafjXvyi76ppYOzB6NHnHHuNiRCLtU9IV6STf1gMpmj491q577h9U/+5+FyPqmUIlpZRMmgL19QD4ttuOoqlTNHOQZDQlXZEtEBh5AHnHHB1rl1/3UxrWrHExop4lEgpReumlhL76CgBPfj69FszHk5fncmQi7VPSFdlCheefj3/HHZ1GY6Nzfzc6JaCkVuXPb6N++YpYu+iyy/ANHuxiRCKJUdIV2UKenByK58zGk58PQOjzLyidf7nu76ZY7fPPU/nLO2Lt/FNOIfCj/V2MSCRxSroiXeAbNIiiaVNj7bq//pXqBx50MaLuLfjpZ5TOnB1r5+y1FwVnnOFiRCKdo6Qr0kWBUaPIO/LIWLvcLqbhvfdcjKh7CtfUsGnSJCKVlQB4BwygeNZMPD79GZPsoZ9WkSQovPACfEOHOo2GBkqmTiMcTQ7SdZFIhLLLryD4n4+cBTk59Jo3D2906kWRbKGkK5IEntxces2dE6ueDa39nLLLr9D93SSp/t391P7h2Vi7aOIl+Ift6GJEIltGSVckSXyDB1M0dUqsXfunP1Pz8CPtbCGJqH/zTcoXXxdr540bR97hh7sYkciWU9IVSaLA6NHkjRsXa5eZRTR+8G8XI8puoW+/pWTKNAgGAfAPG0bhxRe5HJXIllPSFUmywgkT8A0Z4jTq6537u1VV7gaVhSKNjc6527ABAE9xMcXz5uHJyXE5MpEtp6QrkmSeQC7Fc+ZAIABA8NNP2XD0sawbPoKvt92edcNHULbwKoJr17obaIYrv+56Gt58y2l4PBTPmY1vwFbuBiXSRUq6Iing3+YHFE2eFGuHPvuMSFUVRCJEqqqofvQxNow7kroXX3IxysxV8+yzVP/2t7F2wTlnk7vHHi5GJJIcSroiKZKzyy7gbeNXLBgkUltLyeQp6vHGafzwQ8rmXx5r5x5wAPknnuhiRCLJo6QrkiI1f/4LdDDjTaSxkaolv0lTRJkvXF7OpomTidTWAtGK8BnTNXOQdBtKuiIp0rByJYRC7a8UDFLzzNPpCSjDRcJhSmfNJtTU8w8EKF6wAG907mKR7kBJVyRFInV1ia1XVZ3iSLJD1Z13UffPF2Lt4unT8G+3rYsRiSSfkq5IiiQ6t6unsDDFkWS+uuXLqbjl1lg7b/x4Agcd5GJEIqmhpCuSIrmHHAI+X4freXr1IlxamoaIMlPwyy8pmX4pRIfM9P/whxSed67LUYmkhpKuSIoUHD8e/P4O1wuvW8eGY8f3yJGrInV1lEyaQqSsDABv3770mjMbTwIfVkSyUcd/EUQyXP2bb1IZvTSZs+ee9L72mjbXbfjgAyoW2Q736RsyhL633hJr1720jKq77461i+fPIzByZJvbhysqKJ09Z3MhlccT68k5B4gmlej7oS++YOMJJ9Lnlp9RcMrJHcbXHUQiEcquvobGpmkQfT6K583D26ePu4GJpJB6upL16pctj/278b33CG3alNB2nuJiPL17t/rl7dWr/WMuX97++y+/3KJy2Tt4MJ78fPB48OTnExg3jr6/uJ3i+fOd5Ti9vtLLZlL2k0VEGhsT+h6yWc2jj1Hz+BOxduGEC8kZvouLEYmknnq6ktXClZU0vPMOBAIEfvQj6l9+mfoVKyk4+aQOt+1z0434Bg7s1PE8hYUQDtPwzruEKyvbnM+1fvkKwJloPbxxIzk770zxpTO+t55v0CB8225D5S23Evr6awCqf/tbGj94n3733oNvwIBOxZctGt59l7Jrro21A2PGkHfUUS5GJJIe6ulKVmvqUQb235+8Hzuz+3TUC+0Sv5/cAw+EUIj6V15pdZXgV18R/PRTvAMGkDN8eMe73GYbet94A7kjD4gta3j9DTYcfQwNq95JWuiZIrRpEyWTp0JDA+Bcyi+aPEkDYEiPoKQrWa3p0nLgkEPwjxiBd6utCH39NY3//SRlx8wbO9Y5drQ322ZMY8ZAgnnEm59P8bx5FJxzdmwUq/D6b9l46mlUP/Qwkeb3g7NYJBikdNoMQuvWAc6Vg17z5+GJTg4h0t0p6UrWCn75JcFPP8VTXEzOXnvi8XgIjB4NQP3yZSk7rv+HI/AOGEDwk08Ifr2uxXuRcNjpfQN5Y8d0ar8ej4eCk0+m19VX4SkqchY2NlJ25ULKFlye8GAbmaziZ7e0uEJQPPMyfIMGuRiRSHop6UrWivUoR43CE300J3DIIc57r7xKpDGYkuN6PJ7Nx1nRsrfb+P77hDdtwr/zzvgGD96i/efutRd9broJ39ChsWU1jz3OxlNP+16Szya1f/s7Vb/aXAGef/pp5O67r4sRiaSfCqkkK0VCYepXrgQgcPDBseX+Idvj2357Ql98QcOqtwkceGCb+yi7cmGbswD1veOX7Y75mzd2DLXPPEP9ypUUnHVm7H5k0yXnQPQS9JbybT2QPj+9jqr7lsS+z8bVa9h4zLH0u+duAqOza7Smxk8+oXTO3Fg7Z599KDjtNBcjEnGHerqSlRr/tYZwaSneAQPw79qyWClwiJOEmz9K1JpIZSWR8vJWv+jgHqrvBz/Av/POhDdupPHfzqAWkbo66t94A/z+pAxh6AkEKLrsUgovvij2XG940ya+O/scKu9bkjX3ecPV1ZRMnOzMJwx4Bw6k+LLL8LQ17aFIN6aermSluqZLy6NHf6/qNTD6YGoefYyG1asJl1fg7d36M7d9f3VXpx8ZanGcsWMI/ve/1C9fTu5uuzkJt76e3JEH4C0u2uL9NufxeMg/5hj8Q4dS8fPbnA8EoRAVi6+jcc0a+tx6S0bPwhOJRCibO5/gf//rLMjJodf8+Uk7PyLZRh81JeuEq2toeOstoOWl5Sa+AVvh33VX57GeaFFTKgQOGg1+Pw2vv0GkviFpl5ZbkzNiBH1+djP+XTYPHlH7xz+x8fgTCH72WdKPlyxVS35N7V/+EmsXTZmMf4ehrsUj4jb1dCXrNLz6KkRHbCqbP7/ddeuWLyf/uGNTEoe3uIjcffel4c03qX3uORrffx9PcTG5++yTkuP5+vWj96JFVN9/P3X//CcAwf98xIZjx9PvzjvIG3dESo67pepffY2K62+ItfOOOjL2uJVIT6WermSduk4MfhH67DOCn3+RslgCY5zHgmoeewwiEQIHHRSrpE4FT46fosmTKJo2FXJyAIhUVLBpwkVU3P4LIuFwyo7dGaFvvqFk2vTYUJj+nXem8MIJ7gYlkgHU05WsEvpmPcGPPgKgzy0/w9vOMIlVd95Fw6pV1C9fhv+CC1IST+6+++IpLiZSWQmk5tJya/IOPxzfkCFU3nIr4U2bIBKh8taf07hmjVN53cHY0akUaWhg0+SphL/7DgBP794Uz5uLJ0d/bkTU05WsUhcd9MI3ZAj+oUPxFha2+ZU7apSzzcqXiYRS0wP05PgpnHAh+cePJ/+008jZeaeUHKc1OcOG0efmm8nZfffYsrp/vuBMExj9YOKGcruYxneiw1d6vRTPmY2vf3/X4hHJJEq6kjUikQj1K6LP5rYzrV6T3P33A5+PSFkZjWtWpyyuvDFjKLzgAgrPPCNlx2iLt3cvel1zNfnHHx9bFvrsMzaOP4HaP/+lnS1To+app6le+kCsXXDeueTutlva4xDJVLrekwbW2tOAscDewF5AMfCIMea8Tu5nLTCkjbe/NcZ06/H0Gj/4gPDGjQDkHthx0vUWFpKz++40rllD3bLl3Xb0I4/PR+EF5+PfaRiVd98D9fVEamoomTqNojVr6HXlFSm9z9yk4f0PKL3iilg7d9SB5I8fn/LjimQTJd30uAYn2VYBXwG7dmFf5cAvWlle1YV9ZoWmwS58gwfj3267hLYJHDiSxjVraHj7bcLV1akMz3WBgw7Ct+22VNxyK+H16wGouudeGt97n773/Apfv34pO3a4rIySyZOhrh4A3zbbUDRtmmYOEomjpJsec3CS7Sc4Pd6XurCvMmPMomQElW2KL53R6py07ckbN468ceNi7dzddmOr3z/Z6WPnHXYoeYcd2untimfOpHjmzE5vt6X8229Pn5tupPLOO2mMTgtY//LLbDz6WPr9Zgm5e+6Z9GNGwmFKLptFKFol7snPp3jBfLz5+Uk/lki20z3dNDDGvGSM+a8xJjvG7ZOs5i0spNfll1NwxhmxaQJDX3/NxpNOofqJzn/g6EjlL35J/YsvxtpFM6bj32abpB9HpDtQTzf7BKy15wHbA9XAv4AVxpiQu2FJJvF4vRScfhr+HXek8o47iNTUQH09ZXPn0bh6Nb3tIjy5uV0+Tt3/vUjlbbfH2vknnpBQkZtIT6Wkm30GAQ/FLfvMWnuRMabNUSOstROACa28tXfyQpNMk7vfvvS56SYqbrmF0JdfAlD94EM0fvBv+i25t0tz2QY//5ySy2bGJofI2X13Cs4+Oylxi3RXurycXe4HjsBJvIXAHsB9wFDg79bavdrZdijO/eT4r96pC1cygW/wIPpcfz25zWY+ali1ig3HHEf9m29u0T7DtbXOzEHl5QB4+/enePZsPNHZkESkderpZhFjjI1b9D4w1VpbBcwDFgEnt7H5WqC1nvDeKPF2e578PIpnz6Jup52ofvhhCIcJb9jAd6efSe9FhsIJFyZcaRyJRCi7YmFsSkP8fornzWtzNicR2UxJt3u4FyfpjmlrBWPMUmBp/HJr7TKcHq90cx6Ph/zjx+PbYSiVt93uDF0ZDFJ+zbU0rF5D35tuwJNAxXH1Aw9S+/TTsXbRxRendSQukWymy8vdw4boa6GrUUhWyN19d/rcfDP+YcNiy2qfeoqNJ51CMHrfty31b6+ifNHmCy6Bww4lkGGzG4lkMiXd7mFU9PVTV6OQrOEbsBW9F1sChx0WW9b4/vtsOPpY6lasaHWb0MaNlEyZEptW0bfDDhRdMlEDYIh0gi4vZxhrbQ4wDGg0xvyv2fLdgG+MMSVx6w8B7oo2H05boJL1PLm5FE2bSs7OO1P1299CKESkrIxN555PryuvIO/YY6he8mtqnvkDkepq8HpjU/V5ioroNX8enkDXHzsS6UmUdNPAWnsScFK02fSMxihr7dLov78zxjTNxr4N8CHwOU7FcZPTgSuttS8BnwGVOMn5OCAP+Btwa4q+BemmPB4PeT8eh2/I9lTe+nPCpaUQDlNxw41U3PwzZ3CNYNBZObT5UfC8447DN3CgS1GLZC8l3fTYG7gwbtmO0S9wEux82vcSMBzYB+dyciFQBryM89zuQxrxSrZUzi670Ofmm6m4/XaCH37oLAy1Pd5K7bPPknfw6C495yvSE3kiEf2d7smaqpeHDBnChAkTOrVtpLGRhrfeTkVY4pJIMEjZFVcS+uKL9lf0+QiMG0fxxEvSE5hICuSM2BVv375d2UWnCxrU05Wu8akWrzvx+HJj0ye2KxSiYcUKmDIp9UGJpIoLRYBKurLFPDk5Gme3G4rU1SW8nv7/RTpH3RQRacFTmNjj3p4iPRYu0llKuiLSQsEpJ4O/g4tgfj8Fp5yanoBEuhElXRFpoWjKZDw5Oe2u48nJoWjyxDRFJNJ9KOmKSAv+oUPpt+Q+Zxzm+B6v348nP59+S+7DP3SoK/GJZDMlXRH5nrzDD2PgC89TeO65eIqLwOPBU1xE4bnnMvCF58k7/LCOdyIi36PqZRFplX/oUPrc8FP63PBTt0MR6TbU0xUREUkTJV0REZE0UdIVERFJEyVdERGRNFEhlewEsH79epYuXepyKCIi2ePzzz9fBqw2xsxOdBslXSkCqK+v5/PPP3c7FhGRbDK2sxso6cpnwA5AFfBJJ7fdG+gNlAOrkxxXd6Tz1Tk6X52j89U5yTpfndpW8+nKFmuaixdYbow51N1oMp/OV+fofHWOzlfnuHW+VEglIiKSJkq6IiIiaaKkKyIikiZKuiIiImmi6mXpiqXAMmCtq1Fkj6XofHXGUnS+OmMpOl+dsRQXzpeql0VERNJEl5dFRETSRElXREQkTZR0RURE0kSFVNKCtfYg4BrgQCAPZ2jI3wF3GmNCndhPe8UCbxhjDmxju/HAfGAfwAd8ANxtjHkg0WOnUzLOl7V2G+AU4FhgBDAYZ1jOd4B7jDHPtLLNocBL7ez2ZmPMlYl/J8ljrd0WWAwcDfQHvgGeBawxprQT++kH/AQ4CeecbAKeA35ijPkqlcdOp67GbK0txDlHxwH7AtsBYeAj4DGcn8WGVrbbot9RtyXj/7jZaFRtyTfG1LWy3Q+BRcChQC/gc+Bx4CZjTG0ix1ZPV2KstScCK4AxwB+AXwG5wO04P1id9TlgW/n6TRvHvxT4M7A78DDwa+AHwFJr7a1bcPyUSuL5ugy4AxiOk0hvA/4BHAI8ba29rZ1tl9P6OX6hM99LslhrhwGrgIuAN3HOxafALOA1a23/BPfTH3gtut3/ovt5M7rfVdbaHVN17HRKUsyH4Py+HAW8D9yJk2y3AW4FXrLW5rWxbad+R92Wgv/j1r53CwRbOfZI4C2cDzgvAL8EKnA+GP7TWhtI5IDq6QoA1tpeOEkuBBxqjHk7uvxa4EXgNGvtWcaYziSTtcaYRQkefyjOH4gSYH9jzNro8sU4P+jzrLVPG2Ne68TxUybJ5+vN6D6Wxx1jBPA6MMda+4gxZlUr2y5L9Bynyd3AQGCmMebOpoXRDw5zgOuBqQns5wZgF+B2Y8zcZvuZifPH7m6cnk4qjp1OyYh5PXAe8PvmPVprbTHOIzEHATOAn7eybcK/oxkiqf/Hnfj75APuBwqAE40xf4ou9wJPAqdGj39TR/tST1eanAYMAB5vSiAA0Uss10Sb01J4/IuBAHBXU8KNHr8U5w8wZNYfzKSdL2PMM/EJN7r8Q+CJaPPQLkWbBtHe55E4zz3+Ku5tA1QD50cvh7a3n0Lg/Oj6Ju7tu6L7P6p5bzdZx06nZMVsjFltjHkk/hKyMaaSzYn20GTE7CaX/4/H4tz6WdGUcAGMMWHg8mhzqrXW09GO1NOVJodHX59r5b0VQA1wkLU2YIypT3Cffay1FwODcKbPWmWMeX0Ljv/3uHUyQSrOV2sao6/fu9wVtVP0snwvnB7PSmPMf7twvK5oOifPR/8YxRhjKq21r+D80TwQ+L929jMKyI/upzJuP2Fr7fPAZOAwnEuLyTx2OqUj5o5+fjrzO+q2pJ8va+2ZOFObNgAfAi+28fva5u+7MeZTa+3HOFdmdsS5HdIm9XSlyfDo68fxbxhjgjjz7vpxfqgStRfwW5xLPnfh3HNZba3do5PH/wbnU+y21tqCThw/lVJxvlqIXsI+FYgAz7ex2rk49/CuxznXH1trn7LW9t3S43ZBm+ckqunDwC4p2E+yjp1O6Yj54uhrax8OoXO/o25Lxfl6HLgR54rA34AvrLWnpfLYSrrSpHf0tbyN95uW90lwf7cBo3EuwRYDPwKewvklfzFasbslx+/dxvvpluzz1UL0MtVvgK1xKpg/jFtlI3AlsAfO+R0AHAO8i5Oo/xy935ROyTonW7KflP5/pEiqf4YuxbnvvRqnoj5eZ39H3ZbM8/VH4HhgW5yrKrviJN8+wBPW2mNSdWxdXu5GrLVrgSGd2OQRY8x5Ca7bdK8ioXFDjTHz4ha9DZxurX0KJynMxyk8SFSnjp+ITDpfrfg5cDqwEpgb/6Yx5gOcx6maVKsQ5zMAAAnpSURBVAHPWWtfxfkjOxrnj8oft/D4qZCs/8Mt2U/Sf37SYItjttaeAvwC55bDqcaYxvh1UvA76raEz5cx5va4RR8BV1lr1+FcObqBzbe1knps9XS7l//h/PAk+rWu2bYd9SR7xa23pe6Nvo6JW57o8Su6ePzmMvJ8WWtvwfljtwI4tjP3hI0xFcCj0Wb8OU61ZJ2TLdlPun5+kyklMVtrT8K5bLoBpyr+0w42idfW76jb0vF//Buc+997R6u/k35s9XS7EWPMEV3Y/CNgf5x7Ei0eTbHW+nGKDYJsLlzZUhujr/EVhh8BW0WP3+KxIGvt4Oj6Xxljarp4/JhMPF/W2tuB2TjP647fwu+3rXOcah9FX9u6r7Vz9LWt+2Jd2U+yjp1OSY/ZWns6zoeu9cDhW1hU59bPT0dS/n9sjKmz1lYCfXG+/6ZCvqQdWz1dafJi9DX+2UdwPvEWAK92sRIXnMpC+H4yau/4x8StkwmSer6stR5r7a9wEu4/geO68AGjrXOcak0jZB0Zfz852msYDdTiPHvcntej642O6200PRd5ZNzxknnsdEpqzNbac3AGxVgHjO1CFbtbPz8dSfn/sbV2OE7CrQS+a/ZWm7/v0UeZdsEZaKTDc6akK02ewvkhO8tau3/TwuhINj+NNu9pvoG1tsBau6u1dvu45fu29qyctXZPnCpJcEbQae5+oB64NDpQRtM2fYGros17yRzJPF8eYAkwHec+0gkdDSlnrR3dWqGUtfY84EycRyCe7PR31QXGmP/hVFkPxRmMoUVoOD2HB40x1bGFzvnYNW4/VcBD0fUXxe3n0uj+/9H8sumWHNttyTpf0eUX4pyzL4AxHV1S3sLfUVcl63xZa3dsrUjMWrsVzt8hcJ6/b/6Y1XKcR4rGWGtPaLaNF7g52rzXGNPhPV1dXhbAuRdorZ2Ek0yWWWsfxxkd6gSccvmn2DxQQ5MDcD59Lqflw/czgVOstS8CX+Ik011xPiX6cEZyeizu+J9ZaxfgDIf4trX2CZzEcRpOheHPM2U0Kkj6+foJMBHnU/pq4EprbfwhVxtjnm3WfgTwRgunvsIZ9/lH0WMEgSnNBxlJo+nAq8Ad1tojcP5QjcR5pvZj4Oq49ZuqsuMHFbgK5xzNtdbujTNq1wjgRJx7lfF/dLfk2Jmgy+fLWnsYTnWyF+fn66JWfn7KjDG/aNbu9O9ohkjGz9cY4DfW2uU4dR0lwPY4Y5/3xikou7z5TowxIWvtRTg93qeixWZfAEfg3GZ6BWdIyg6ppysx0T/qY3EKeE7FGRO4Ead69qxEPsVFPYszNunuwIU4v+D74fTiTjTGTG5tX9Fh3U7Aqcq9AGcAhPXABGPM/C58aymRxPO1Q/Q1H1iIM7pO/NdJcdvcg3OfaTROApqIc098Kc4wmku35HvqqmhvZP9oHCOBecAwnA9To4wxmxLczyacQTLuAHaK7mckTk9kv+hxUnLsdEpSzEPY/Lf8Ylr/+Zkdt80W/Y66LUnnaxVOL34gzu/tPJwPG+/hnIfRxpiyVo79Bs4H2z/i3OKYg5OkFwM/TvRWkicSybjzKiIi0i2ppysiIpImSroiIiJpoqQrIiKSJkq6IiIiaaKkKyIikiZKuiIiImmipCsiIpIm/9/evYVYVcVxHP+aUTYpZhRmWUQGZhoW3cRexqKoh7ALWQ+jYBIF2UN0gwj+/F+6vVgU9NRlUKmeHIuojMynCjPKbhaFShcaYyYR0WJGnR7WWjOnPXufOTl77zNMvw8M+6yz115nPc3//NfZ+78UdEVERGqioCsiIlIT1V4Wkdq5e14Z0Gz95bZx9x5CnedGy8xsWxumI5OIgq6ItFMfcLSswdy9m1C3e5eZXdziNfcDLxKK/p8V6+7uB/bFLmeiVUEpiYKuiLTTlSXvhvQaIegucPcrzGxHC9esisfNqdC9ma1OJ919L2FTAZFx07c3EZlMthE2E4eRYFooblp+VWx2VzQnkWEKuiIyacTt6NbH5l3uPtZqXgrMvcD7lU1MJNLysogUalhavdHMRgUld58BHCBsEj7XzH6rYA6LCHsULwPmAH8T9lxeD7xsZoOZS7qBJwi/xd4EvF0w7hSgKzY3mllpvy2LFFGmKyK53P00Rn7L/LKg22JCwO2vKOCuBXYCq4HzgSPAdGAp8BKwxd07Gq8xs5+Aj2Oz2RJzJ3BefK2lZamFgq6IFFkcj71mtq+gz6XxuLPsD3f35cALwF/A48BsM5sOnALcAPxACJzrci5PQfTm+OUhTwrIX5jZ12XNW6QZBV0RKZICalGW29in1KDr7lOB52NzpZk9ZWZ/AJjZoJl9QFg6PgTc7e5zMkO8SViGPhlYkTN+B3B7bCrLldoo6IpIkZTpNgu6qU/ZmW4nYWl7r5ltyutgZnuATwn3pnRmzh0ANsdm3hLzrcAMwnL166XMWKQFupFKRIo0zXRjNrooNssOukvj8Wx3723Sb2Y8nptzrhu4E7jG3S8ws90N51Igfjdl0CJ1UKYrIqPER21SRaeiTPciYBowCHxX8hTScvFJwOwmf9Niv47sAMAW4Pf4emV6My5FXxebWlqWWinTFZE8Cwi/hx4Cfizok5aWd5nZQMmfnxKCTWZ22/EMYGZH3X0D8Agh6Ho81QVMBf6k4HEikaoo0xWRPGlp+RszO1bQZ0k8ln7nMiN1j1uqn9xEymTnuXtask5Z7xsVfFkQaUpBV0TypCw291GhuPx8S2xWEXQ/icf57r7weAcxs2+Bz2NzlbtfBlwS21paltop6IpInpTpzis4/xAjNy99VcHnfwj8HF+vizdt5XL3WWOMlYLrCuCe+Pp7M9s+vimK/HcKuiKSJ2W6C939WXc/HcDd57r7M8CTDX0H3f2cMj88lnZ8ABgCridUnro6lm7E3U9098vd/Wlgd5OhIDwSNAjMAu6N7ynLlbZQ0BWRf4kB9AxCwHuPcCNSv7sPAL8AjxJKMCZbgfvKnoeZvQWsAQaAawnP5B529z5C4YsdwGNAUcWpNE4f8E5sngAcAzaUPV+RVijoikhWWlreQ1iSfQXoJ2SL24E7zGwtsBE4DHwG5BawGC8zexWYDzxH2OTgCOHZ3H7gI+BhQk3msTRmtlvN7NdyZyrSGj0yJCJZw1WmzOwgIdtck+1kZl3Z96oQN7l/cJxj9BA2ZhBpK2W6IpJV2SYGIv93ynRFJKuqesp59riHmhVmNmEyUXfvAZa3ex4y+Sjoisgwdz8VuDA2qwy6RVsFThT7GT1HFdKQcZsyNDTU7jmIyATh7ksIhSkOAjPNTP8gREqkoCsiIlIT3UglIiJSEwVdERGRmijoioiI1ERBV0REpCYKuiIiIjVR0BUREamJgq6IiEhNFHRFRERq8g8PN0ihmdl7zwAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "\n", + "ax_pd = fig.add_subplot(111)\n", + "\n", + "ax_pd.plot(mus, U_cs, \"o\", ls=\"-\")\n", + "ax_pd.fill_between(mus,[min(U_cs)]*len(U_cs),U_cs, alpha=0.25)\n", + "\n", + "ax_pd.set_ylabel('U [eV]', rotation=0, ha='right')\n", + "ax_pd.set_xlabel('$\\mu$ [eV]')\n", + "\n", + "ax_pd.text(0.725, 0.3, \"AFM\", transform = ax_pd.transAxes, size=24, color='C0')\n", + "ax_pd.text(0.125, 0.1, \"AFM\", transform = ax_pd.transAxes, size=24, color='C0')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Semi particle-hole transformation\n", + "\n", + "If we use the PHT only on one spin specices it is called a semi particle-hole transformation (SPHT).\n", + "This means\n", + "\n", + "$$\n", + "c_{j \\uparrow}^{\\dagger} \\xrightarrow{\\mathrm{SPHT}} d_{j \\uparrow}^{\\dagger}\\quad\\mathrm{and}\\quad\n", + "c_{j \\uparrow} \\xrightarrow{\\mathrm{SPHT}} d_{j \\uparrow}\\\\\n", + "c_{j \\downarrow}^{\\dagger} \\xrightarrow{\\mathrm{SPHT}} (-1)^j d_{j \\downarrow}\\quad\\mathrm{and}\\quad\n", + "c_{j \\downarrow} \\xrightarrow{\\mathrm{SPHT}} (-1)^j d_{j \\downarrow}^{\\dagger}\\,.\n", + "$$\n", + "\n", + "Lets remember the Hubbard Hamiltonian that is invariant under a PHT\n", + "\n", + "$$\n", + "H=-t \\sum_{\\langle j, l\\rangle \\sigma}\\left(c_{j \\sigma}^{\\dagger} c_{l \\sigma}+c_{l \\sigma}^{\\dagger} c_{j \\sigma}\\right)+U \\sum_{j}\\left(n_{j \\uparrow}-\\frac{1}{2}\\right)\\left(n_{j \\downarrow}-\\frac{1}{2}\\right)-\\mu \\sum_{j}\\left(n_{j \\uparrow}+n_{j \\downarrow}\\right)\\,.\n", + "$$\n", + "\n", + "The kinetic term only consist of operators with the same spin and is therefore invariant under SPHT as it was under PHT.\n", + "The interaction term on the underhand has to be treated with more care\n", + "\n", + "$$\n", + "\\left(n_{j \\uparrow}-\\frac{1}{2}\\right)\\left(n_{j \\downarrow}-\\frac{1}{2}\\right) \\xrightarrow{\\mathrm{SPHT}}\n", + "\\left(\\tilde{n}_{j \\uparrow}-\\frac{1}{2}\\right)\\left(1-\\tilde{n}_{j \\downarrow}-\\frac{1}{2}\\right) = \n", + "\\left(\\tilde{n}_{j \\uparrow} - \\frac{1}{2}\\right)\\left(\\frac{1}{2}-\\tilde{n}_{j \\downarrow}\\right) = \\\\\n", + "-\\left(\\tilde{n}_{j \\uparrow} - \\frac{1}{2}\\right)\\left(\\tilde{n}_{j \\downarrow}-\\frac{1}{2}\\right)\\,.\n", + "$$\n", + "\n", + "Under a SPHT we map the repulsive Hubbard model with $U$ to the attractive one with $-U$.\n", + "The chemical potential term is also not invariant under a SPHT\n", + "\n", + "$$\n", + "n_{j \\uparrow}+n_{j \\downarrow} \\xrightarrow{\\mathrm{SPHT}}\n", + "\\tilde{n}_{j \\uparrow}+1-\\tilde{n}_{j \\downarrow} = \n", + "1 + \\left(\\tilde{n}_{j \\uparrow}-\\tilde{n}_{j \\downarrow}\\right)\\,,\n", + "$$\n", + "\n", + "and transforms into a Zeeman term.\n", + "\n", + "To summarize the SPHT maps the Hubbard Hamiltonian with interaction strength $U$ and chemical potential $\\mu$ to a Hubbard Hamiltonian with interaction strength $-U$, a chemical potential of $0$ and an additional Zeeman term of strength $\\mu$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Lets start again with the spin operator in $z$-direction,\n", + "\n", + "$$\n", + "S^z_j = n_{j \\uparrow} - n_{j \\downarrow} \\xrightarrow{\\mathrm{SPHT}} \\tilde{n}_{j \\uparrow} - (1 - \\tilde{n}_{j \\downarrow}) = -1 + \\tilde{n}_{j \\uparrow} + \\tilde{n}_{j \\downarrow}\\,.\n", + "$$\n", + "\n", + "which is just the density operator \n", + "\n", + "$$\n", + "\\tilde{n}_{j}= \\tilde{n}_{j \\uparrow} + \\tilde{n}_{j \\downarrow}\n", + "$$\n", + "\n", + "with a constant.\n", + "If one calculates a susceptibility one is only interested in the change of the expectation value of an obserable $A$ when going from an unperturbed system to one which is perturbed by a field coupling to operator $B$.\n", + "Therefore a constant factor in an observable is unimportant when calculating susceptibilites.\n", + "\n", + "If we consider a Hubbard model at half-filling, i.e. $\\mu=0.0$ the $T-U$ phase diagram is symmetric for $U=0$\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [], + "source": [ + "def get_charge_phase_transistion(p):\n", + " \"\"\"Return U at which model p transitions to charge order via root search\n", + " \"\"\"\n", + " p.copy()\n", + "\n", + " chi0_wk = get_chi0(p)\n", + " \n", + " def one_over_charge(U):\n", + " \n", + " p.U = U\n", + " chi_c_wk, _ = get_chiRPA(p, chi0_wk)\n", + " \n", + " # -- If any value is below zero we are already in an ordered phase\n", + " if np.any(chi_c_wk.data[np.abs(chi_c_wk.data) > 1e-3] < 0.0 ):\n", + " return -1\n", + " \n", + " chi_at_critical_k = np.max(chi_c_wk.data)\n", + " return 1./chi_at_critical_k\n", + " \n", + " U_c = brentq(one_over_charge, -10, 0.0)\n", + " \n", + " return U_c" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "%%capture\n", + "\n", + "Ts = [1000, 750, 500, 250]\n", + "hubbard_models = parameter_scan(hubbard, T=Ts)\n", + "\n", + "U_spin_cs = []\n", + "U_charge_cs = []\n", + "\n", + "for hubbard_model in hubbard_models:\n", + " \n", + " U_spin_c = get_spin_phase_transistion(hubbard_model)\n", + " U_charge_c = get_charge_phase_transistion(hubbard_model) \n", + "\n", + " U_spin_cs.append(U_spin_c)\n", + " U_charge_cs.append(U_charge_c)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.07,0.15,'CDW')" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "\n", + "ax_pd = fig.add_subplot(111)\n", + "\n", + "ax_pd.plot(U_spin_cs, Ts, \"o\", ls=\"-\")\n", + "ax_pd.fill_between(U_spin_cs, Ts, [Ts[-1]]*len(Ts), alpha=0.25)\n", + "\n", + "ax_pd.plot(U_charge_cs, Ts, \"o\", ls=\"-\")\n", + "ax_pd.fill_between(U_charge_cs, Ts, [Ts[-1]]*len(Ts), alpha=0.25)\n", + "\n", + "\n", + "ax_pd.set_ylabel('Temperature\\n[Kelvin]', rotation=0, ha='right', multialignment='center')\n", + "ax_pd.set_xlabel('U [eV]')\n", + "\n", + "ax_pd.set_yticks(Ts)\n", + "ax_pd.set_xticks([np.round(ele,2) for ele in U_spin_cs+U_charge_cs])\n", + "ax_pd.set_xticklabels([np.round(ele,2) for ele in U_spin_cs+U_charge_cs], rotation=45)\n", + "\n", + "ax_pd.spines['left'].set_bounds(Ts[-1], Ts[0])\n", + "ax_pd.spines['bottom'].set_bounds(min(ax_pd.get_xticks()), max(ax_pd.get_xticks()))\n", + "\n", + "ax_pd.text(0.78, 0.15, \"AFM\", transform = ax_pd.transAxes, size=22, color='C0')\n", + "ax_pd.text(0.07, 0.15, \"CDW\", transform = ax_pd.transAxes, size=22, color='C1')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The SPHT also gives information about the superconducting phase of the attractive Hubbard model, this can be seen by transforming the ladder operators of the spin\n", + "\n", + "$$\n", + "S^+_j = S^x_j + iS^y_j = c_{j \\uparrow}^{\\dagger}c_{j \\downarrow} \\xrightarrow{\\mathrm{SPHT}} d_{j \\uparrow}^{\\dagger}d_{j \\downarrow}^{\\dagger} = \\tilde{\\Delta}^{\\dagger}\\,,\\\\\n", + "S^-_j = S^x_j - iS^y_j = c_{j \\downarrow}^{\\dagger}c_{j \\uparrow} \\xrightarrow{\\mathrm{SPHT}} d_{j \\downarrow}d_{j \\uparrow} = \\tilde{\\Delta}\\,.\n", + "$$\n", + "\n", + "The x- and y-components of the spin operator are transformed to the complex superconducting oder parameter.\n", + "We wil focus on $S^x$, because even if we apply a Zeeman term the x- and y-components will be degenerate.\n", + "This means, that if we find a diverging $\\langle S^xS^x \\rangle$ in the repulsive model at some $U$ we will see a superconducting phase at $-U$.\n", + "\n", + "To calculate $\\langle S^xS^x \\rangle$ we need the spin dependent general susceptibility tensor.\n", + "We can obtain this from $\\chi^{(c)}$ and $\\chi^{(s)}$ if our system is $\\mathrm{SU(2)}$ symmetric.\n", + "This can be done via the `general_susceptibility_from_charge_and_spin` function from the module `triqs_tprf.rpa_tensor`." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.6045250062\n", + "nk = 256\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.00 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n" + ] + } + ], + "source": [ + "from triqs_tprf.rpa_tensor import general_susceptibility_from_charge_and_spin\n", + "\n", + "chi_c_wk, chi_s_wk = get_chiRPA(hubbard)\n", + "\n", + "chi_rpa_general_wk = general_susceptibility_from_charge_and_spin(chi_c_wk, chi_s_wk)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can then use the matrix representation of $S^x$ to do the contraction." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [], + "source": [ + "S_x = 0.5 * np.array([[0,1], [1,0]])\n", + "\n", + "def chi_contraction(chi, op1, op2):\n", + " chi_op1op2 = chi[:1,:1,:1,:1].copy()\n", + " chi_op1op2.data[:,:,0,0,0,0] = np.einsum('wqabcd,ab,cd->wq', chi.data, op1, op2)\n", + " return chi_op1op2\n", + "\n", + "chi_sxsx = chi_contraction(chi_rpa_general_wk, S_x, S_x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But for a $\\mathrm{SU(2)}$ symmetric system doing this is unnecessary, because\n", + "\n", + "$$\n", + "\\langle S^z S^z \\rangle = \\langle S^x S^x \\rangle\\,,\n", + "$$\n", + "\n", + "and we therefore already know where the superconducting phase in the attractive model lies, it is degenerate with the CDW.\n", + "\n", + "We will now use the implementation of the linearized Eliashberg equation to confirm this superconducting phase.\n", + "To do this we will construct the pairing vertex $\\Gamma$ in the singlet channel via the spin- and charge susceptibilites by using the `gamma_PP_singlet` function of the `triqs_tprf.lattice` module.\n", + "We can then use the `solve_eliashberg` function of the `triqs_tprf.eliashberg` module to solve the linearized eliashberg equation for the specifc $\\Gamma$ to obtain the $\\lambda$ as an indicator for the strength of the superconducting phase.\n", + "If\n", + "\n", + "$$\n", + "\\lambda = 1\n", + "$$\n", + "\n", + "we encounter a phase transition to the superconducting phase.\n", + "To find this phase transition we use the same procedure as for the susceptibilites and search when\n", + "\n", + "$$\n", + "\\lambda - 1 \\approx 0\\,.\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [], + "source": [ + "from triqs_tprf.lattice import gamma_PP_singlet\n", + "from triqs_tprf.eliashberg import solve_eliashberg\n", + "\n", + "def get_lambda_delta(p):\n", + " \"\"\"Solve the linearized eliashberg equation for model parameters in a ParameterCollection\n", + " \"\"\"\n", + "\n", + " e_k = get_disperion_relation(p)\n", + "\n", + " wmesh = MeshImFreq(beta=temperature_to_beta(p.T), S='Fermion', n_max=p.nw)\n", + " g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh)\n", + " \n", + " chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw)\n", + "\n", + " U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norb, p.U, 0.0, 0.0, 0.0)\n", + "\n", + " chi_c_wk = solve_rpa_PH(chi0_wk, -U_c)\n", + " chi_s_wk = solve_rpa_PH(chi0_wk, U_s)\n", + "\n", + " gamma_singlet_wk = gamma_PP_singlet(chi_c_wk, chi_s_wk, U_c, U_s)\n", + "\n", + " Es, eigen_modes = solve_eliashberg(gamma_singlet_wk, g0_wk,\n", + " solver='IRAM', tol=1e-5)\n", + "\n", + " return Es[0], eigen_modes[0]\n", + "\n", + "def get_sc_phase_transistion(p, guess=None):\n", + " \"\"\"Return U at which model p transitions to superconducting order via root search\n", + " \"\"\"\n", + " \n", + " e_k = get_disperion_relation(p)\n", + "\n", + " wmesh = MeshImFreq(beta=temperature_to_beta(p.T), S='Fermion', n_max=p.nw)\n", + " g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh)\n", + " \n", + " chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw)\n", + " \n", + " def lambda_minus_1(U):\n", + "\n", + " U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norb, U, 0.0, 0.0, 0.0)\n", + " \n", + " chi_c_wk = solve_rpa_PH(chi0_wk, -U_c)\n", + " chi_s_wk = solve_rpa_PH(chi0_wk, U_s)\n", + "\n", + " gamma_singlet_wk = gamma_PP_singlet(chi_c_wk, chi_s_wk, U_c, U_s)\n", + "\n", + " Es, eigen_modes = solve_eliashberg(gamma_singlet_wk, g0_wk,\n", + " solver='IRAM', tol=1e-5)\n", + " lamb = max(Es)\n", + " \n", + " print(lamb, U)\n", + " \n", + " return lamb - 1.0\n", + " \n", + " upper = guess\n", + " lower = 0.5*guess\n", + " \n", + " U_c = brentq(lambda_minus_1, lower, upper, xtol=1e-4)\n", + "\n", + " return U_c" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "%%capture\n", + "\n", + "Ts = [1000, 750, 500, 250]\n", + "hubbard_models = parameter_scan(hubbard, T=Ts)\n", + "guesses = [-ele for ele in U_spin_cs]\n", + "\n", + "U_sc_cs = []\n", + "\n", + "for hubbard_model, guess in zip(hubbard_models, guesses):\n", + " \n", + " U_sc_c = get_sc_phase_transistion(hubbard_model, guess)\n", + "\n", + " U_sc_cs.append(U_sc_c)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.07,0.15,'SC')" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "\n", + "ax_pd = fig.add_subplot(111)\n", + "\n", + "ax_pd.plot(U_spin_cs, Ts, \"o\", ls=\"-\")\n", + "ax_pd.fill_between(U_spin_cs, Ts, [Ts[-1]]*len(Ts), alpha=0.25)\n", + "\n", + "ax_pd.plot(U_sc_cs, Ts, \"o\", ls=\"-\", color='grey')\n", + "ax_pd.fill_between(U_sc_cs, Ts, [Ts[-1]]*len(Ts), alpha=0.25, color='grey')\n", + "\n", + "\n", + "ax_pd.set_ylabel('Temperature\\n[Kelvin]', rotation=0, ha='right', multialignment='center')\n", + "ax_pd.set_xlabel('U [eV]')\n", + "\n", + "ax_pd.set_yticks(Ts)\n", + "ax_pd.set_xticks([np.round(ele,2) for ele in U_spin_cs+U_sc_cs])\n", + "ax_pd.set_xticklabels([np.round(ele,2) for ele in U_spin_cs+U_sc_cs], rotation=45)\n", + "\n", + "ax_pd.spines['left'].set_bounds(Ts[-1], Ts[0])\n", + "ax_pd.spines['bottom'].set_bounds(min(ax_pd.get_xticks()), max(ax_pd.get_xticks()))\n", + "\n", + "ax_pd.text(0.78, 0.15, \"AFM\", transform = ax_pd.transAxes, size=22, color='C0')\n", + "ax_pd.text(0.07, 0.15, \"SC\", transform = ax_pd.transAxes, size=22, color='grey')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The superconducting phase gets correctly predicted by the linearized Eliashberg equation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Not at half-filling\n", + "\n", + "If we are not at half-filling in the repulsive Hubbard model we have to take the Zeeman term into account in the attractive model.\n", + "Because the implementation of the linearized Eliashberg equation is right now limited to $\\mathrm{SU(2)}$ symmetric systems and the Zeeman term breaks this symmetry we will apply the Zeeman term in the repulsive model.\n", + "This means, that \n", + "\n", + "$$\n", + "\\langle S^z S^z \\rangle \\neq \\langle S^x S^x \\rangle\\,,\n", + "$$\n", + "\n", + "and the CDW will therefore no longer be degenerate with the superconducting phase.\n", + "\n", + "To add the Zeeman term in the repulsive model we will introduce a new function for the disperison relation and use a Hubbard model with explicitly carries spin as an index, i.e. two orbitals instead of one." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [], + "source": [ + "def get_disperion_relation_spin_dependent(p):\n", + " \"\"\"Return the disperion relation for model parameters in a ParameterCollection\n", + " \"\"\"\n", + " \n", + " try:\n", + " zeeman = p.zeeman * np.array([[1,0], [0,-1]])\n", + " except AttributeError:\n", + " zeeman = 0.0 * np.array([[1,0], [0,-1]])\n", + " \n", + " t = -p.t * np.eye(p.norb)\n", + " \n", + " # next-nearest neighbour hopping only if p has `tp` attribute\n", + " try:\n", + " tp = -p.tp * np.eye(p.norb)\n", + " except AttributeError:\n", + " tp = 0 * np.eye(p.norb)\n", + " \n", + " H = TBLattice(\n", + " units = [(1, 0, 0), (0, 1, 0)],\n", + " hopping = {\n", + " # Zeeman term\n", + " ( 0, 0): zeeman,\n", + " \n", + " # nearest neighbour hopping\n", + " ( 0,+1): t,\n", + " ( 0,-1): t,\n", + " (+1, 0): t,\n", + " (-1, 0): t,\n", + " \n", + " # next-nearest neighbour hopping\n", + " ( +1,+1): tp,\n", + " ( -1,-1): tp,\n", + " (+1, -1): tp,\n", + " (-1, +1): tp,\n", + " },\n", + " orbital_positions = [(0,0,0)]*p.norb,\n", + " )\n", + " \n", + " e_k = H.on_mesh_brillouin_zone(n_k = (p.nk, p.nk, 1))\n", + "\n", + " return e_k\n", + "\n", + "hubbard_spin_dependent = hubbard.copy(norb=2)\n", + "\n", + "e_k = get_disperion_relation_spin_dependent(hubbard_spin_dependent.copy(zeeman=1.0))" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.54,0.65,'$\\\\downarrow$')" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "\n", + "# -- Bandstructure\n", + "ax_bs = fig.add_subplot(111)\n", + "\n", + "lower_limit = np.min(e_k.data.real)\n", + "upper_limit = np.max(e_k.data.real)\n", + "\n", + "path = 'G-X-M-G'\n", + "\n", + "ax_bs.bsplot(e_k[:1,:1], path)\n", + "ax_bs.bsplot(e_k[1:2,1:2], path)\n", + "\n", + "ax_bs.spines['left'].set_bounds(lower_limit, upper_limit)\n", + "ax_bs.spines['bottom'].set_bounds(ax_bs.get_xticks()[0], ax_bs.get_xticks()[-1])\n", + "\n", + "ax_bs.set_ylabel('$\\epsilon(\\mathbf{k})$')\n", + "\n", + "ax_bs.text(0.54, 1., \"$\\uparrow$\", transform = ax_bs.transAxes, size=22, color='C0')\n", + "ax_bs.text(0.54, 0.65, \"$\\downarrow$\", transform = ax_bs.transAxes, size=22, color='C1')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will introduce versions of the functions we defined before, i.e. `get_chi0`, `get_chiRPA`, as a spin dependent version.\n", + "Also we introduce the function `get_sus` to get the interacting susceptibility for any two operators and `get_phase_transition` to find the phase transition for any order defined by any two operators." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [], + "source": [ + "def get_chi0_spin_dependent(p, e_k=None):\n", + " \"\"\"Return the non-interaction susceptibility for model parameters in a ParameterCollection\n", + " \"\"\"\n", + " \n", + " if not e_k:\n", + " e_k = get_disperion_relation_spin_dependent(p)\n", + "\n", + " wmesh = MeshImFreq(beta=temperature_to_beta(p.T), S='Fermion', n_max=p.nw)\n", + " g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh)\n", + " \n", + " chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw)\n", + " \n", + " return chi0_wk\n", + "\n", + "from triqs_tprf.rpa_tensor import quartic_tensor_from_charge_and_spin\n", + "\n", + "def get_chiRPA_spin_dependent(p, chi0_wk=None):\n", + " \n", + " if not chi0_wk:\n", + " chi0_wk = get_chi0_spin_dependent(p)\n", + " \n", + " U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(1, p.U, 0.0, 0.0, 0.0)\n", + " U_abcd = quartic_tensor_from_charge_and_spin(U_c, U_s)\n", + " \n", + " chi_rpa_wk = solve_rpa_PH(chi0_wk, U_abcd)\n", + " \n", + " return chi_rpa_wk\n", + "\n", + "def get_sus(p, op1, op2, chi0_wk=None):\n", + " \n", + " chi_rpa_wk = get_chiRPA_spin_dependent(p, chi0_wk)\n", + " chi_op1op2 = chi_contraction(chi_rpa_wk, op1, op2)\n", + " \n", + " return chi_op1op2\n", + "\n", + "def get_phase_transition(p, op1, op2, lower=0.0, upper=10):\n", + " \"\"\"Return U at which model p transitions to any order of op1 and op2 via root search\n", + " \"\"\"\n", + " # Make copy\n", + " p = p.copy()\n", + " \n", + " chi0_wk = get_chi0_spin_dependent(p)\n", + " \n", + " def one_over_chi(U):\n", + " \n", + " p.U = U\n", + " chi = get_sus(p, op1, op2, chi0_wk)\n", + " \n", + " # -- If any value is below zero we are already in an ordered phase\n", + " if np.any(chi.data[np.abs(chi.data) > 1e-3] < 0.0 ):\n", + " return -1\n", + " \n", + " chi_at_critical_k = np.max(chi.data)\n", + " \n", + " return 1./chi_at_critical_k\n", + " \n", + " U_c = brentq(one_over_chi, lower, upper)\n", + " \n", + " return U_c" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can then scan the phase space of the repulsive Hubbard model with a Zeeman term of strength $\\xi$ and an attractive model which is doped by $\\mu=\\xi$.\n", + "And as we know the AFM and CDW phases should be symmetric for $U=0.$" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [], + "source": [ + "%%capture\n", + "\n", + "# Density operator\n", + "n = np.eye(2)\n", + "# Spin operator\n", + "S_z = 0.5 * np.array([[1,0], [0,-1]])\n", + "\n", + "\n", + "xi = 0.1\n", + "\n", + "Ts = [1000, 750, 500]\n", + "hubbard_models_doped = parameter_scan(hubbard_spin_dependent.copy(mu=xi), T=Ts)\n", + "hubbard_models_zeeman = parameter_scan(hubbard_spin_dependent.copy(zeeman=xi), T=Ts)\n", + "\n", + "U_spin_cs = []\n", + "U_charge_cs = []\n", + "\n", + "for hubbard_model_doped, hubbard_model_zeeman in zip(hubbard_models_doped, hubbard_models_zeeman):\n", + " \n", + " U_spin_c = get_phase_transition(hubbard_model_zeeman, S_z, S_z, 0, 10)\n", + " U_charge_c = get_phase_transition(hubbard_model_doped, n, n, -10, 0) \n", + "\n", + " U_spin_cs.append(U_spin_c)\n", + " U_charge_cs.append(U_charge_c)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.4,0.5,'AFM')" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "\n", + "ax_pd_spin = fig.add_subplot(122)\n", + "\n", + "ax_pd_spin.plot(U_spin_cs, Ts, \"o\", ls=\"-\")\n", + "ax_pd_spin.fill_betweenx(Ts, U_spin_cs, [max(U_spin_cs)]*len(U_spin_cs) , alpha=0.25)\n", + "\n", + "ax_pd_charge = fig.add_subplot(121)\n", + "\n", + "\n", + "ax_pd_charge.plot(U_charge_cs, Ts, \"o\", ls=\"-\", color='C1')\n", + "ax_pd_charge.fill_betweenx(Ts, U_charge_cs, [min(U_charge_cs)]*len(U_charge_cs), alpha=0.25, color='C1')\n", + "\n", + "\n", + "ax_pd_charge.set_ylabel('Temperature\\n[Kelvin]', rotation=0, ha='right', multialignment='center')\n", + "ax_pd_charge.set_xlabel('U [eV]')\n", + "ax_pd_spin.set_xlabel('U [eV]')\n", + "\n", + "ax_pd_charge.set_yticks(Ts)\n", + "ax_pd_spin.set_yticks([])\n", + "\n", + "ax_pd_charge.set_xticks([np.round(ele,3) for ele in U_charge_cs])\n", + "ax_pd_charge.set_xticklabels([np.round(ele,3) for ele in U_charge_cs], rotation=45)\n", + "ax_pd_spin.set_xticks([np.round(ele,3) for ele in U_spin_cs])\n", + "ax_pd_spin.set_xticklabels([np.round(ele,3) for ele in U_spin_cs], rotation=45)\n", + "\n", + "ax_pd_charge.spines['left'].set_bounds(Ts[-1], Ts[0])\n", + "ax_pd_spin.spines['left'].set_visible(False)\n", + "\n", + "ax_pd_charge.text(0.2, 0.5, \"CDW\", transform = ax_pd_charge.transAxes, size=22, color='C1')\n", + "ax_pd_spin.text(0.4, 0.5, \"AFM\", transform = ax_pd_spin.transAxes, size=22, color='C0')" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [], + "source": [ + "%%capture\n", + "\n", + "xi = 0.1\n", + "\n", + "Ts = [1000, 750, 500]\n", + "hubbard_models_doped = parameter_scan(hubbard.copy(mu=xi), T=Ts)\n", + "hubbard_models_zeeman = parameter_scan(hubbard_spin_dependent.copy(zeeman=xi), T=Ts)\n", + "\n", + "U_sx_cs = []\n", + "U_sc_cs = []\n", + "\n", + "for hubbard_model_doped, hubbard_model_zeeman in zip(hubbard_models_doped, hubbard_models_zeeman):\n", + " \n", + " U_sx_c = get_phase_transition(hubbard_model_zeeman, S_x, S_x)\n", + " U_sc_c = get_sc_phase_transistion(hubbard_model_doped, guess=-1.2*U_sx_c) \n", + "\n", + " U_sx_cs.append(U_sx_c)\n", + " U_sc_cs.append(U_sc_c)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.6,0.35,'prediction')" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "\n", + "ax_pd_sc = fig.add_subplot(111)\n", + "\n", + "negative_U_sx_cs = [-ele for ele in U_sx_cs]\n", + "\n", + "ax_pd_sc.plot(negative_U_sx_cs, Ts, \"o\", ls=\"-\")\n", + "ax_pd_sc.fill_betweenx(Ts, negative_U_sx_cs, [min(U_sc_cs)]*len(negative_U_sx_cs) , alpha=0.15)\n", + "\n", + "ax_pd_sc.plot(U_sc_cs, Ts, \"o\", ls=\"-\", color='grey')\n", + "ax_pd_sc.fill_betweenx(Ts, U_sc_cs, [min(U_sc_cs)]*len(U_sc_cs), alpha=0.35, color='grey')\n", + "\n", + "ax_pd_sc.set_ylabel('Temperature\\n[Kelvin]', rotation=0, ha='right', multialignment='center')\n", + "ax_pd_sc.set_xlabel('U [eV]')\n", + "\n", + "ax_pd_sc.set_yticks(Ts)\n", + "\n", + "ax_pd_sc.set_xticks([np.round(ele,3) for ele in U_sc_cs+negative_U_sx_cs])\n", + "ax_pd_sc.set_xticklabels([np.round(ele,3) for ele in U_sc_cs+negative_U_sx_cs], rotation=45)\n", + "\n", + "ax_pd_sc.spines['left'].set_bounds(Ts[-1], Ts[0])\n", + "ax_pd_sc.spines['bottom'].set_bounds(min(ax_pd_sc.get_xticks()), max(ax_pd_sc.get_xticks()))\n", + "\n", + "\n", + "ax_pd_sc.text(0.2, 0.3, \"SC\", transform = ax_pd_sc.transAxes, size=22, color='Grey')\n", + "ax_pd_sc.text(0.6, 0.35, \"prediction\", transform = ax_pd_sc.transAxes, size=22, color='C0', rotation=-45)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.6045250062\n", + "nk = 256\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.00 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "_, delta_1 = get_lambda_delta(hubbard.copy(mu=xi, U=U_sc_cs[0]))\n", + "\n", + "plt.imshow(delta_1[Idx(0), :].data.reshape(hubbard.nk, hubbard.nk).real)" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [], + "source": [ + "%%capture\n", + "\n", + "xi = 0.3\n", + "\n", + "Ts = [1000, 750, 500]\n", + "hubbard_models_doped = parameter_scan(hubbard.copy(mu=xi), T=Ts)\n", + "hubbard_models_zeeman = parameter_scan(hubbard_spin_dependent.copy(zeeman=xi), T=Ts)\n", + "\n", + "U_sx_cs = []\n", + "U_sc_cs = []\n", + "\n", + "for hubbard_model_doped, hubbard_model_zeeman in zip(hubbard_models_doped, hubbard_models_zeeman):\n", + " \n", + " U_sx_c = get_phase_transition(hubbard_model_zeeman, S_x, S_x)\n", + " U_sc_c = get_sc_phase_transistion(hubbard_model_doped, guess=-1.2*U_sx_c) \n", + "\n", + " U_sx_cs.append(U_sx_c)\n", + " U_sc_cs.append(U_sc_c)" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.6,0.35,'prediction')" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "\n", + "ax_pd_sc = fig.add_subplot(111)\n", + "\n", + "negative_U_sx_cs = [-ele for ele in U_sx_cs]\n", + "\n", + "ax_pd_sc.plot(negative_U_sx_cs, Ts, \"o\", ls=\"-\")\n", + "ax_pd_sc.fill_betweenx(Ts, negative_U_sx_cs, [min(U_sc_cs)]*len(negative_U_sx_cs) , alpha=0.15)\n", + "\n", + "ax_pd_sc.plot(U_sc_cs, Ts, \"o\", ls=\"-\", color='grey')\n", + "ax_pd_sc.fill_betweenx(Ts, U_sc_cs, [min(U_sc_cs)]*len(U_sc_cs), alpha=0.35, color='grey')\n", + "\n", + "ax_pd_sc.set_ylabel('Temperature\\n[Kelvin]', rotation=0, ha='right', multialignment='center')\n", + "ax_pd_sc.set_xlabel('U [eV]')\n", + "\n", + "ax_pd_sc.set_yticks(Ts)\n", + "\n", + "ax_pd_sc.set_xticks([np.round(ele,3) for ele in U_sc_cs+negative_U_sx_cs])\n", + "ax_pd_sc.set_xticklabels([np.round(ele,3) for ele in U_sc_cs+negative_U_sx_cs], rotation=45)\n", + "\n", + "ax_pd_sc.spines['left'].set_bounds(Ts[-1], Ts[0])\n", + "ax_pd_sc.spines['bottom'].set_bounds(min(ax_pd_sc.get_xticks()), max(ax_pd_sc.get_xticks()))\n", + "\n", + "\n", + "ax_pd_sc.text(0.2, 0.3, \"SC\", transform = ax_pd_sc.transAxes, size=22, color='Grey')\n", + "ax_pd_sc.text(0.6, 0.35, \"prediction\", transform = ax_pd_sc.transAxes, size=22, color='C0', rotation=-45)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.6045250062\n", + "nk = 256\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.00 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "_, delta_1 = get_lambda_delta(hubbard.copy(mu=xi, U=U_sc_cs[0]))\n", + "\n", + "plt.imshow(delta_1[Idx(0), :].data.reshape(hubbard.nk, hubbard.nk).real)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/doc/user_guide/notebook.mplstyle b/doc/user_guide/notebook.mplstyle new file mode 100644 index 000000000..9205141a2 --- /dev/null +++ b/doc/user_guide/notebook.mplstyle @@ -0,0 +1,39 @@ +# Style for jupyter-notebooks + +figure.figsize : 6,5 + +axes.titlesize : 26 +axes.labelsize : 24 +axes.linewidth : 2.5 + +axes.edgecolor : grey +axes.labelcolor : grey + +axes.spines.left : True +axes.spines.bottom : True +axes.spines.top : False +axes.spines.right : False + + +lines.linewidth : 3 +lines.markersize : 10 + + +xtick.color : grey +ytick.color : grey + +xtick.labelsize : 20 +ytick.labelsize : 20 + +xtick.major.size : 7 +xtick.major.width : 2.5 +ytick.major.size : 7 +ytick.major.width : 2.5 + + +axes.prop_cycle : cycler('color', ['e41a1c','377eb8','4daf4a','984ea3', 'ff7f00','ffff33','a65628','f781bf'] ) + +figure.subplot.wspace : 0.3 +figure.subplot.hspace : 0.3 + +legend.fontsize : 20 diff --git a/doc/user_guide/plotting_tools.py b/doc/user_guide/plotting_tools.py new file mode 100644 index 000000000..8cfea0dc4 --- /dev/null +++ b/doc/user_guide/plotting_tools.py @@ -0,0 +1,64 @@ +import itertools +import types + +import numpy as np + +import matplotlib as mpl +from pytriqs.plot.mpl_interface import plt + +from triqs_tprf.lattice_utils import k_space_path + +hs_to_k = { + 'G' : np.array([0.0, 0.0, 0.0]), + 'X' : np.array([0.5, 0.0, 0.0]), + 'Y' : np.array([0.0, 0.5, 0.0]), + 'Z' : np.array([0.0, 0.0, 0.5]), + 'M' : np.array([0.5, 0.5, 0.0]), + 'R' : np.array([0.5, 0.5, 0.5]), + } + +hs_to_latex = { + 'G' : r'$\Gamma$', + 'X' : r'$X$', + 'Y' : r'$Y$', + 'Z' : r'$Z$', + 'M' : r'$M$', + 'R' : r'$R$', + } + +def bsplot(obj, path, *opt_list, **opt_dict): + """ + Plot stuff like bs lol + """ + __bsplot_impl(plt, obj, path, plt.xticks, plt.xticks, *opt_list, **opt_dict) + + +def __bsplot_impl(top, obj, path, xticks_fct, xticklabels_fct, *opt_list, **opt_dict): + + hs_points = path.split('-') + hs_labels = [hs_to_latex[hs_point] for hs_point in hs_points] + hs_k = [hs_to_k[hs_point] for hs_point in hs_points] + + k_paths = zip(hs_k, hs_k[1:]) + k_vecs, k_plot, K_plot = k_space_path(k_paths, bz=obj.mesh.domain) + kx, ky, kz = k_vecs.T + + get_gf_on_path = np.vectorize(lambda kx, ky, kz : obj([kx, ky, kz])[(0,0)].real) + gf_on_path = get_gf_on_path(kx, ky, kz) + + plot_min, plot_max = np.min(gf_on_path), np.max(gf_on_path) + y_ticks = [plot_min, plot_max] + + plt_fct = getattr(top, 'plot') + + plt_fct(k_plot, gf_on_path, *opt_list, **opt_dict) + + if isinstance(top, types.ModuleType): + xticks_fct(K_plot, hs_labels) + else: + xticks_fct(K_plot) + xticklabels_fct(hs_labels) + +mpl.axes.Axes.bsplot = lambda self, obj, path, *opt_list, **opt_dict: __bsplot_impl(self, obj, path, self.set_xticks, self.set_xticklabels, *opt_list, **opt_dict) + + From c5feec3e64962ea8b70e21970c9c4f27a3f3d4b2 Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 3 May 2019 14:59:00 +0200 Subject: [PATCH 008/121] [utl] add converter between Kelvin and 1/eV --- python/triqs_tprf/utilities.py | 23 +++++++++++++++++++++++ 1 file changed, 23 insertions(+) diff --git a/python/triqs_tprf/utilities.py b/python/triqs_tprf/utilities.py index 6a179e86a..bd479464a 100644 --- a/python/triqs_tprf/utilities.py +++ b/python/triqs_tprf/utilities.py @@ -154,3 +154,26 @@ def G2_loc_fixed_fermionic_window_python(g2, nwf): g2_out.data[:] = g2.data[:, s:e, s:e] return g2_out + +# ---------------------------------------------------------------------- +def beta_to_temperature(beta): + """Convert beta in 1/eV to Temperature in Kelvin + """ + + def eV_to_Kelvin(ev): + return 11604.5250061657 * ev + + T = 1. / beta + return eV_to_Kelvin(T) + +# ---------------------------------------------------------------------- +def temperature_to_beta(T): + """Convert Temperature in Kelvin to beta in 1/eV + """ + + def Kelvin_to_eV(K): + return K / 11604.5250061657 + + T = Kelvin_to_eV(T) + beta = 1./ T + return beta From 5592a3fa3b81c7a0a8169f315ae243067a595074 Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 3 May 2019 15:41:50 +0200 Subject: [PATCH 009/121] [paramcoll] add function to scan parameters --- python/triqs_tprf/ParameterCollection.py | 50 ++++++++++++++++++++++++ 1 file changed, 50 insertions(+) diff --git a/python/triqs_tprf/ParameterCollection.py b/python/triqs_tprf/ParameterCollection.py index bc79ad407..5a37efed9 100644 --- a/python/triqs_tprf/ParameterCollection.py +++ b/python/triqs_tprf/ParameterCollection.py @@ -21,6 +21,7 @@ ################################################################################ import inspect +import itertools import numpy as np # ---------------------------------------------------------------------- @@ -243,3 +244,52 @@ def __str__(self): from pytriqs.archive.hdf_archive_schemes import register_class register_class(ParameterCollections) + +# ---------------------------------------------------------------------- + +def parameter_scan(p, **kwargs): + """Return ParameterCollections with copies of ParameterCollection for different parameters + + Uses a given ParameterCollection as a template to create copies of it with one or more + parameters changing. Stores all of these copies in a ParameterCollections for easy access. + + Parameters + ---------- + p : ParameterCollection, + The ParameterCollection that shall be used as a template for all the others + **kwargs : Sequence, + The keyword gives the parameter name and the Sequence the values that shall + be scanned through. + + Returns + ------- + ParameterCollections + + Examples + -------- + >>> p = ParameterCollection(beta=10., U=1.0, t=1.0) + >>> ps = parameter_scan(p, U=[1.0, 1.5, 2.0]) + >>> print ps[0] + U = 1.0 + beta = 10.0 + t = 1.0 + >>> print ps[1] + U = 1.5 + beta = 10.0 + t = 1.0 + >>> print ps[2] + U = 2.0 + beta = 10.0 + t = 1.0 + """ + parameter_values = [] + + for key, value in kwargs.iteritems(): + parameter_values.append(zip([key]*len(value), value)) + + ps = [] + + for parameter_value in itertools.product(*parameter_values): + ps.append(p.copy(**dict(parameter_value))) + + return ParameterCollections(ps) From 7e7772cee30491008dbdc24356ff78d0a622926d Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 6 May 2019 17:21:42 +0200 Subject: [PATCH 010/121] [latutil] add contraction of chi with operators --- python/triqs_tprf/lattice_utils.py | 27 +++++++++++++++++++++++++++ 1 file changed, 27 insertions(+) diff --git a/python/triqs_tprf/lattice_utils.py b/python/triqs_tprf/lattice_utils.py index 1fd4d55a1..4c13c58b8 100644 --- a/python/triqs_tprf/lattice_utils.py +++ b/python/triqs_tprf/lattice_utils.py @@ -215,6 +215,33 @@ def imtime_bubble_chi0_wk(g_wk, nw=1): return chi0_wk +# ---------------------------------------------------------------------- +def chi_contraction(chi, op1, op2): + """Contract a susceptibility with two operators + + Parameters + ---------- + chi : Gf, + Susceptibility :math:`\chi(i\omega_n, \mathbf{k})`. The mesh attribute of + the Gf must be a MeshProduct with the components (MeshImFreq, MeshBrillouinZone) + and its target_rank 4. + op1, op2 : np.ndarray, + Operators in matrix representation. + + Returns + ------- + Gf, + Susceptibility :math:`\chi(i\omega_n, \mathbf{k})`. With a target_rank of 0. + """ + if chi.target_shape[:2] != op1.shape or chi.target_shape[2:] != op2.shape: + raise ValueError('The shape of the operators %s and %s'%(op1.shape, op2.shape) + + ' must fit the shape of chi %s.'%(chi.target_shape,)) + + chi_op1op2 = chi[0, 0, 0, 0].copy() + chi_op1op2.data[:] = np.einsum('wqabcd,ab,cd->wq', chi.data, op1, op2) + + return chi_op1op2 + # ---------------------------------------------------------------------- def chi0_w0k_tau_bubble(beta, mu, tb_lattice, nk, nw, sigma_w=None): From 479fb0e85576e2c9dbc3257f5f21c99d508a7ee5 Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 8 May 2019 14:01:30 +0200 Subject: [PATCH 011/121] [eli] add eliashberg product for constant term If the dynamic part of the pairing vertex is zero the solving of the eliashberg equation will only be done with the constant part reducing the computational cost. --- c++/triqs_tprf/lattice/eliashberg.cpp | 31 +++++++++++++++++++++++++++ c++/triqs_tprf/lattice/eliashberg.hpp | 1 + python/triqs_tprf/eliashberg.py | 28 ++++++++++++++---------- python/triqs_tprf/lattice_desc.py | 6 ++++-- 4 files changed, 53 insertions(+), 13 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index c8f40d189..de731d0ea 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -154,6 +154,37 @@ gk_iw_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_cons return delta_wk_out; } + +// optimized version if there is only a constant term +gk_iw_t eliashberg_product_fft_constant(chi_r_vt Gamma_pp_const_r, + gk_iw_vt g_wk, gk_iw_vt delta_wk) { + + auto _ = all_t{}; + + auto F_wk = eliashberg_g_delta_g_product(g_wk, delta_wk); + auto F_tr = make_gf_from_fourier<0, 1>(F_wk); + + auto rmesh = std::get<1>(F_tr.mesh()); + + auto delta_r_out = make_gf(std::get<1>(F_tr.mesh()), delta_wk.target()); + delta_r_out *= 0.; + + for (const auto r : rmesh) { + auto F_t = F_tr[_, r]; + for (auto [A, a, B, b] : Gamma_pp_const_r.target_indices()) + delta_r_out[r](a, b) += -Gamma_pp_const_r[r](A, a, B, b) * F_t(0)(A, B); + } + + auto delta_k_out = make_gf_from_fourier<0>(delta_r_out); + + auto delta_wk_out = make_gf(F_wk.mesh(), delta_wk.target()); + delta_wk_out *= 0.; + + for (const auto [w , k]: delta_wk_out.mesh()) + delta_wk_out[w, k] += delta_k_out[k]; + + return delta_wk_out; +} chi_wk_t gamma_PP_singlet(chi_wk_vt chi_c, chi_wk_vt chi_s, \ array_view, 4> U_c, array_view, 4> U_s) { diff --git a/c++/triqs_tprf/lattice/eliashberg.hpp b/c++/triqs_tprf/lattice/eliashberg.hpp index ce6ffd053..16d04e15e 100644 --- a/c++/triqs_tprf/lattice/eliashberg.hpp +++ b/c++/triqs_tprf/lattice/eliashberg.hpp @@ -91,6 +91,7 @@ namespace triqs_tprf { */ gk_iw_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const_r, gk_iw_vt g_wk, gk_iw_vt delta_wk); + gk_iw_t eliashberg_product_fft_constant(chi_r_vt Gamma_pp_const_r, gk_iw_vt g_wk, gk_iw_vt delta_wk); gk_iw_t eliashberg_g_delta_g_product(gk_iw_vt g_wk, gk_iw_vt delta_wk); std::tuple split_into_dynamic_wk_and_constant_k(chi_wk_vt Gamma_pp); std::tuple dynamic_and_constant_to_tr(chi_wk_vt Gamma_pp_dyn_wk, chi_k_vt Gamma_pp_const_k); diff --git a/python/triqs_tprf/eliashberg.py b/python/triqs_tprf/eliashberg.py index 48a100af9..17a0d3fe8 100644 --- a/python/triqs_tprf/eliashberg.py +++ b/python/triqs_tprf/eliashberg.py @@ -22,6 +22,7 @@ # ################################################################################ +import functools import numpy as np from scipy.sparse.linalg import LinearOperator from scipy.sparse.linalg import eigs @@ -30,7 +31,7 @@ from pytriqs.gf import Gf from lattice import eliashberg_product -from lattice import eliashberg_product_fft +from lattice import eliashberg_product_fft, eliashberg_product_fft_constant from lattice import split_into_dynamic_wk_and_constant_k, dynamic_and_constant_to_tr # ---------------------------------------------------------------------- @@ -192,23 +193,28 @@ def from_wk_to_x(delta_wk): Gamma_pp_dyn_tr, Gamma_pp_const_r = preprocess_gamma_for_fft(Gamma_pp_wk, Gamma_pp_const_k) - def matvec(delta_x): - delta_wk = from_x_to_wk(delta_x) - delta_out_wk = eliashberg_product_fft(Gamma_pp_dyn_tr, Gamma_pp_const_r, g_wk, delta_wk) - delta_out_x = from_wk_to_x(delta_out_wk) - return delta_out_x + if np.allclose(Gamma_pp_dyn_tr.data, 0): # -- If dynamic part is zero reduced calculation + eliashberg_product = functools.partial(eliashberg_product_fft_constant, + Gamma_pp_const_r, g_wk) + + else: + eliashberg_product = functools.partial(eliashberg_product_fft, + Gamma_pp_dyn_tr, Gamma_pp_const_r, g_wk) elif product == 'SUM': + eliashberg_product = functools.partial(eliashberg_product, Gamma_pp_wk, g_wk) - def matvec(delta_x): - delta_wk = from_x_to_wk(delta_x) - delta_out_wk = eliashberg_product(Gamma_pp_wk, g_wk, delta_wk) - delta_out_x = from_wk_to_x(delta_out_wk) - return delta_out_x else: raise NotImplementedError('There is no implementation of the eliashberg product' ' called %s.'%product) + + def matvec(delta_x): + delta_wk = from_x_to_wk(delta_x) + delta_out_wk = eliashberg_product(delta_wk) + delta_out_x = from_wk_to_x(delta_out_wk) + return delta_out_x + if not initial_delta: initial_delta = semi_random_initial_delta(g_wk) initial_delta = from_wk_to_x(initial_delta) diff --git a/python/triqs_tprf/lattice_desc.py b/python/triqs_tprf/lattice_desc.py index a2686a7e9..0eafb52b9 100644 --- a/python/triqs_tprf/lattice_desc.py +++ b/python/triqs_tprf/lattice_desc.py @@ -1,5 +1,5 @@ # Generated automatically using the command : -# c++2py ../../c++/triqs_tprf/lattice.hpp --members_read_only -N triqs_tprf -a triqs_tprf -m lattice -o lattice -C pytriqs --moduledoc="Lattice functionality" --cxxflags="-std=c++17" --target_file_only +# c++2py ../../c++/triqs_tprf/lattice.hpp --members_read_only -N triqs_tprf -a triqs_tprf -m lattice -o lattice -C pytriqs --moduledoc="Lattice functionality" --cxxflags="-std=c++17" from cpp2py.wrap_generator import * # The module @@ -494,6 +494,8 @@ out Gives the result of the product :math:`\Delta^{(out)} \sim \Gamma^{(pp)}GG \Delta`""") +module.add_function ("triqs_tprf::gk_iw_t triqs_tprf::eliashberg_product_fft_constant (triqs_tprf::chi_r_vt Gamma_pp_const_r, triqs_tprf::gk_iw_vt g_wk, triqs_tprf::gk_iw_vt delta_wk)", doc = r"""""") + module.add_function ("triqs_tprf::gk_iw_t triqs_tprf::eliashberg_g_delta_g_product (triqs_tprf::gk_iw_vt g_wk, triqs_tprf::gk_iw_vt delta_wk)", doc = r"""""") module.add_function ("std::tuple triqs_tprf::split_into_dynamic_wk_and_constant_k (triqs_tprf::chi_wk_vt Gamma_pp)", doc = r"""""") @@ -934,4 +936,4 @@ -module.generate_code() +module.generate_code() \ No newline at end of file From 923f9a3df8623142f9099e1eddecaee10e58ea3a Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 8 May 2019 14:03:21 +0200 Subject: [PATCH 012/121] [tb] add model class --- python/triqs_tprf/tight_binding.py | 85 ++++++++++++++++++++++++++++++ 1 file changed, 85 insertions(+) diff --git a/python/triqs_tprf/tight_binding.py b/python/triqs_tprf/tight_binding.py index d2f2f1e55..19f03ee74 100644 --- a/python/triqs_tprf/tight_binding.py +++ b/python/triqs_tprf/tight_binding.py @@ -21,6 +21,9 @@ # ################################################################################ +import numbers +from collections import namedtuple + import numpy as np from pytriqs.lattice.lattice_tools import BrillouinZone as BrillouinZone @@ -129,3 +132,85 @@ def on_mesh_brillouin_zone(self, n_k): e_k.data[:] = self.hopping(k_vec_rel.T).transpose(2, 0, 1) return e_k + +# ---------------------------------------------------------------------- + +Parameter = namedtuple('Parameter', ['name', 'type', 'default']) +Parameter.__new__.__defaults__ = (None,) + +class Model(object): + """Base class for models to check for characterizing parameters + """ + mandatory_parameters = [Parameter('norb', int)] + optional_parameters = [Parameter('spin', bool, True)] + + def __init__(self, **kwargs): + + for key, value in kwargs.iteritems(): + self.__setattr__(key, value) + + for parameter in self.mandatory_parameters: + + if not hasattr(self, parameter.name): + raise AttributeError('The parameter %s has to be given.'%parameter.name) + + if not isinstance(getattr(self, parameter.name), parameter.type): + raise TypeError('The parameter %s needs to be of %s type.'%(parameter.name, + parameter.type)) + for parameter in self.optional_parameters: + + if hasattr(self, parameter.name): + continue + + # -- If the default is the name of another parameter set it to its value + if isinstance(parameter.default, str) and hasattr(self, parameter.default): + setattr(self, parameter.name, getattr(self, parameter.default)) + + else: + setattr(self, parameter.name, parameter.default) + + if self.spin: + self.norb = 2*self.norb + +class SquareLattice(Model, TBLattice): + """Square lattice with nearest neighbor and next-nearest neighbor hopping + """ + mandatory_parameters = [Parameter('t', numbers.Number)] + mandatory_parameters += Model.mandatory_parameters + + optional_parameters = [Parameter('tp', numbers.Number, 0.0), + Parameter('zeeman', numbers.Number, 0.0)] + optional_parameters += Model.optional_parameters + + def __init__(self, **kwargs): + + Model.__init__(self, **kwargs) + + if self.zeeman != 0.0 and not self.spin: + raise AttributeError('There can not be a zeeman term in a spinless model.') + + t_matrix = -self.t * np.eye(self.norb) + tp_matrix = -self.tp * np.eye(self.norb) + zeeman_matrix = self.zeeman * np.diag([(-1)**orb for orb in range(self.norb)]) + + hopping = { + # Zeeman term + ( 0, 0): zeeman_matrix, + + # nearest neighbour hopping + ( 0,+1): t_matrix, + ( 0,-1): t_matrix, + (+1, 0): t_matrix, + (-1, 0): t_matrix, + + # next-nearest neighbour hopping + ( +1,+1): tp_matrix, + ( -1,-1): tp_matrix, + (+1, -1): tp_matrix, + (-1, +1): tp_matrix, + } + + units = [(1, 0, 0), (0, 1, 0)] + orbital_positions = [(0, 0, 0)] * self.norb + TBLattice.__init__(self, units, hopping, orbital_positions) + From 18c22679a9fab4334e2dc7095ac738388bfc003d Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 8 May 2019 17:41:42 +0200 Subject: [PATCH 013/121] [eli] fix minor bugs test: - the eigenvectors can differ in sign depending on when the eigenvaluesolver stops. Therefore check for sign flip. - missing parenthesis eliashberg.py: - stopped using variable `eliashberg_product` or multiple things --- python/triqs_tprf/eliashberg.py | 12 +++++------- test/python/eliashberg/eigenvalue_solver.py | 8 ++++++-- 2 files changed, 11 insertions(+), 9 deletions(-) diff --git a/python/triqs_tprf/eliashberg.py b/python/triqs_tprf/eliashberg.py index 17a0d3fe8..8cc0d18f7 100644 --- a/python/triqs_tprf/eliashberg.py +++ b/python/triqs_tprf/eliashberg.py @@ -194,16 +194,14 @@ def from_wk_to_x(delta_wk): Gamma_pp_dyn_tr, Gamma_pp_const_r = preprocess_gamma_for_fft(Gamma_pp_wk, Gamma_pp_const_k) if np.allclose(Gamma_pp_dyn_tr.data, 0): # -- If dynamic part is zero reduced calculation - eliashberg_product = functools.partial(eliashberg_product_fft_constant, - Gamma_pp_const_r, g_wk) + eli_prod = functools.partial(eliashberg_product_fft_constant, Gamma_pp_const_r, g_wk) else: - eliashberg_product = functools.partial(eliashberg_product_fft, - Gamma_pp_dyn_tr, Gamma_pp_const_r, g_wk) + eli_prod = functools.partial(eliashberg_product_fft, + Gamma_pp_dyn_tr, Gamma_pp_const_r, g_wk) elif product == 'SUM': - eliashberg_product = functools.partial(eliashberg_product, Gamma_pp_wk, g_wk) - + eli_prod = functools.partial(eliashberg_product, Gamma_pp_wk, g_wk) else: raise NotImplementedError('There is no implementation of the eliashberg product' @@ -211,7 +209,7 @@ def from_wk_to_x(delta_wk): def matvec(delta_x): delta_wk = from_x_to_wk(delta_x) - delta_out_wk = eliashberg_product(delta_wk) + delta_out_wk = eli_prod(delta_wk) delta_out_x = from_wk_to_x(delta_out_wk) return delta_out_x diff --git a/test/python/eliashberg/eigenvalue_solver.py b/test/python/eliashberg/eigenvalue_solver.py index a20c953db..446a4836d 100644 --- a/test/python/eliashberg/eigenvalue_solver.py +++ b/test/python/eliashberg/eigenvalue_solver.py @@ -103,12 +103,16 @@ def run_solve_eliashberg(p): Es_pm, eigen_modes_pm = run_solve_eliashberg(p) - Es_iram, eigen_modes_iram = run_solve_eliashberg(p.copy(solver='IRAM') + Es_iram, eigen_modes_iram = run_solve_eliashberg(p.copy(solver='IRAM')) print(Es_pm[0], Es_iram[0]) np.testing.assert_allclose(Es_pm[0], Es_iram[0]) - np.testing.assert_allclose(eigen_modes_pm[0].data, eigen_modes_iram[0].data, atol=1e-8) + + try: + np.testing.assert_allclose(eigen_modes_pm[0].data, eigen_modes_iram[0].data, atol=1e-8) + except AssertionError: + np.testing.assert_allclose(-eigen_modes_pm[0].data, eigen_modes_iram[0].data, atol=1e-8) print('Both solvers yield the same results.') From ef3fd0e23c4722a9850fa3861228ad2d8e23c885 Mon Sep 17 00:00:00 2001 From: Stefan Date: Thu, 9 May 2019 10:07:36 +0200 Subject: [PATCH 014/121] [doc] place eliashberg doc in proper place --- doc/reference/eliashberg.rst | 12 ------------ doc/reference/python_reference.rst | 10 +++++++++- 2 files changed, 9 insertions(+), 13 deletions(-) delete mode 100644 doc/reference/eliashberg.rst diff --git a/doc/reference/eliashberg.rst b/doc/reference/eliashberg.rst deleted file mode 100644 index a1dc194d1..000000000 --- a/doc/reference/eliashberg.rst +++ /dev/null @@ -1,12 +0,0 @@ -.. highlight:: python - -.. _eliashberg_functions: - -Eliashberg -========== - -.. autofunction:: triqs_tprf.eliashberg.solve_eliashberg -.. autofunction:: triqs_tprf.eliashberg.semi_random_initial_delta -.. autofunction:: triqs_tprf.eliashberg.power_method_LR -.. autofunction:: triqs_tprf.eliashberg.implicitly_restarted_arnoldi_method -.. autofunction:: triqs_tprf.eliashberg.preprocess_gamma_for_fft diff --git a/doc/reference/python_reference.rst b/doc/reference/python_reference.rst index 2cfa35687..af64a2940 100644 --- a/doc/reference/python_reference.rst +++ b/doc/reference/python_reference.rst @@ -46,7 +46,15 @@ GW approximation Linearized Eliashberg equation ============================== -.. autofunction:: triqs_tprf.eliashberg.solve_eliashberg_fft +.. autofunction:: triqs_tprf.eliashberg.solve_eliashberg +.. autofunction:: triqs_tprf.eliashberg.semi_random_initial_delta +.. autofunction:: triqs_tprf.eliashberg.power_method_LR +.. autofunction:: triqs_tprf.eliashberg.implicitly_restarted_arnoldi_method +.. autofunction:: triqs_tprf.eliashberg.preprocess_gamma_for_fft +.. autofunction:: triqs_tprf.eliashberg.eliashberg_product +.. autofunction:: triqs_tprf.eliashberg.eliashberg_product_fft +.. autofunction:: triqs_tprf.eliashberg.gamma_PP_singlet +.. autofunction:: triqs_tprf.eliashberg.gamma_PP_triplet Hubbard atom analytic response functions ======================================== From 45bc8628ae8715c807ea2fbcf9539bce7fcc057f Mon Sep 17 00:00:00 2001 From: Stefan Date: Thu, 9 May 2019 10:49:59 +0200 Subject: [PATCH 015/121] [rpa] add kanamori tensor creation function --- doc/reference/python_reference.rst | 1 + python/triqs_tprf/rpa_tensor.py | 31 ++++++++++++++++++++++++++++++ 2 files changed, 32 insertions(+) diff --git a/doc/reference/python_reference.rst b/doc/reference/python_reference.rst index af64a2940..8b28293a1 100644 --- a/doc/reference/python_reference.rst +++ b/doc/reference/python_reference.rst @@ -18,6 +18,7 @@ Random Phase Approximation ========================== .. autofunction:: triqs_tprf.lattice.solve_rpa_PH +.. autofunction:: triqs_tprf.rpa_tensor.kanamori_quartic_tensor Impurity susceptibility and Bethe-Salpeter Equation =================================================== diff --git a/python/triqs_tprf/rpa_tensor.py b/python/triqs_tprf/rpa_tensor.py index edaf1e77d..4070bda83 100644 --- a/python/triqs_tprf/rpa_tensor.py +++ b/python/triqs_tprf/rpa_tensor.py @@ -190,6 +190,37 @@ def quartic_tensor_from_charge_and_spin(U_c, U_s): return U_4 +# ---------------------------------------------------------------------- +def kanamori_quartic_tensor(norb, U, Up, J, Jp): + r"""Return Kanamori interaction as a quartic tensor + + .. math:: + + \hat{U}_{\text { Kanamori }} = U \sum_{i} \hat{n}_{i, \uparrow} \hat{n}_{i, \downarrow}+\sum_{i>j, s, s^{\prime}}\left(U^{\prime}-J \delta_{\sigma, \sigma^{\prime}}\right) \hat{n}_{i, \sigma} \hat{n}_{j, \sigma^{\prime}} - \\ J \sum_{i \neq j}\left(\hat{c}_{i, \downarrow}^{\dagger} \hat{c}_{j, \uparrow}^{\dagger} \hat{c}_{j, \downarrow} \hat{c}_{i, \uparrow}+\hat{c}_{j, \uparrow}^{\dagger} \hat{c}_{j, \downarrow}^{\dagger} \hat{c}_{i, \uparrow} \hat{c}_{i, \downarrow}+\mathrm{h.c.}\right) + + Parameters + ---------- + norb : int, + Number of orbitals including spin up and down as seperate orbs. + U : complex, + Strength of intra-orbital interaction. + Up : complex, + Strength of inter-orbital interaction. + J : complex, + Strength of Hound's coupling. + Jp : complex, + Strength pair hopping and spin-flip. + + Returns + ------- + np.ndarray + """ + + U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(int(norb/2), U, Up, J, Jp) + U = quartic_tensor_from_charge_and_spin(U_c, U_s) + + return U + # ---------------------------------------------------------------------- def lose_spin_degree_of_freedom(gf, spin_fast=True): """Only keep the up spin elements of a Greens function From 9291694b357cb8916ac25091d25c5398bf5b4243 Mon Sep 17 00:00:00 2001 From: Stefan Date: Thu, 9 May 2019 14:31:51 +0200 Subject: [PATCH 016/121] [eli/doc] improve use_guide WIP - minor change in plotting_tools.py so it does not access the [0,0] of the Gf, object --- doc/user_guide/PHT_Hubbard_Model.ipynb | 989 ++++++++----------------- doc/user_guide/plotting_tools.py | 11 +- 2 files changed, 298 insertions(+), 702 deletions(-) diff --git a/doc/user_guide/PHT_Hubbard_Model.ipynb b/doc/user_guide/PHT_Hubbard_Model.ipynb index 46b081581..8a0608f2a 100644 --- a/doc/user_guide/PHT_Hubbard_Model.ipynb +++ b/doc/user_guide/PHT_Hubbard_Model.ipynb @@ -47,29 +47,22 @@ "The Hamiltonian of the Hubbard model on a square lattice is given by\n", "\n", "$$\n", - "H=-t \\sum_{\\langle j, 1\\rangle \\sigma}\\left(c_{j \\sigma}^{\\dagger} c_{1 \\sigma}+c_{1 \\sigma}^{\\dagger} c_{j \\sigma}\\right)+U \\sum_{j} n_{j \\uparrow} n_{j \\downarrow}-\\mu \\sum_{j}\\left(n_{j \\uparrow}+n_{j \\downarrow}\\right)\\,.\n", + "H=-t \\sum_{\\langle j, 1\\rangle \\sigma}\\left(c_{j \\sigma}^{\\dagger} c_{1 \\sigma}+c_{1 \\sigma}^{\\dagger} c_{j \\sigma}\\right)+U \\sum_{j} n_{j \\uparrow} n_{j \\downarrow}-\\mu \\sum_{j}\\left(n_{j \\uparrow}+n_{j \\downarrow}\\right)\\,,\n", "$$\n", "\n", - "The first term describes the kinetic energy in terms of hopping processes between adjoining lattice sites, indicated by the angular brakets.\n", - "The second term desribes the onsite interaction.\n", - "The third term determines the filling via the chemical potential." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here $c_{j\\sigma}^{\\dagger}$ creates an electron on site $j$ with spin $\\sigma$ while $c_{j\\sigma}$ destroys such an electron, further the operator $n_{j\\sigma}$ count the number of electrons on site $j$ with spin $\\sigma$.\n", + "here $c_{j\\sigma}^{\\dagger}$ creates an electron on site $j$ with spin $\\sigma$ while $c_{j\\sigma}$ destroys such an electron, further the operator $n_{j\\sigma}$ count the number of electrons on site $j$ with spin $\\sigma$.\n", + "\n", "The first term describes the kinetic energy of the electrons, which can be interpreted as an electron with spin $\\sigma$ *hopping* from site $l$ to site $j$ and vice versa.\n", - "Here the angular braket under the sum means that we only take *hopping* terms between neighboring lattice sites into account.\n", + "Here the angular braket under the sum means that we only take *hopping* terms between neighboring lattice sites into account and the energy that is gained by such a *hopping* process is given by $t$.\n", "This is the most basic version of the kinetic part of the Hubbard model which can, and will be, extended later.\n", "\n", "The second term describes the repulsive interaction between the electrons.\n", - "This repulsion is crudely approximated in the Hubbard model in the sense, that electrons only *see* each other if the occupy the same lattice site.\n", + "This repulsion is crudely approximated in the Hubbard model in the sense, that electrons only *see* each other if they occupy the same lattice site.\n", + "The energy that is needed to have a lattice site doubly occupied is given by $U$.\n", "\n", "The last term describes the filling of the lattice via an energy offset by the chemical potential $\\mu$.\n", "\n", - "The Hubbard model is therefore defined by the parameters $t$, $U$ and $mu$, but we also need to know the temperature $T$ at which we shal observe the Hubbard model.\n", + "The Hubbard model is therefore defined by the parameters $t$, $U$ and $\\mu$, but we also need to know the temperature $T$ at which we shall observe the Hubbard model.\n", "We will record these parameters using the `ParameterCollection` class in `triqs_tprf.ParameterCollection`." ] }, @@ -84,9 +77,10 @@ "T = 1000\n", "U = 1.0\n", "mu = 0.0\n", - "nk = 16\n", + "nk = 32\n", "norb = 1\n", "nw = 50\n", + "spin = False\n", "t = 1.0" ] }, @@ -104,9 +98,10 @@ " U=1.0, # Strength of the on-site interaction\n", " mu=0.0, # Chemical potential determining the filling.\n", " T=1000, # Temperature.\n", + " spin=False, # Treat indices only for orbital character.\n", " \n", " # -- Technical parameter\n", - " nk=16, # Number of points in one dimension considered in the Brillouin zone.\n", + " nk=32, # Number of points in one dimension considered in the Brillouin zone.\n", " nw=50, # Number of Matsubara points in positive dimension.\n", " )\n", "hubbard" @@ -116,76 +111,34 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "A representation of the kinetic part of the Hubbard model can be constructed using the `TBLattice` class in `triqs_tprf.tight_binding` where the hoppings are given as a dictionary with relative coordinate vectors as keys and hopping matrices as values. The unit vectors of the lattice, the position of the site local orbitals and names also needs to be setup, see below.\n", - "Here we also added the functionality for next-nearest neighbor hopping, which will be used later.\n", + "A representation of the kinetic part of the Hubbard model can be constructed using the `SquareLattice` class in `triqs_tprf.tight_binding`.\n", + "This class needs information about the number of orbitals `norb` and the hopping energy `t`, so we can construct it with the parameters stored in `hubbard`. \n", + "From this `SquareLattice` object we can then obtain the dispersion relation as a mesh over the Brillouin zone via its member function `on_mesh_brillouin_zone`.\n", "\n", - "From this `TBLattice` object we can obtain the dispersion relation as a mesh over the Brillouin zone via its member function `on_mesh_brillouin_zone`.\n", - "All of this is condensed in the `get_disperion_relation` which only cares about the Hubbard model parameters.\n", - "Also lets plot the bandstructure and density of states.\n", - "There we can see, that the system has a particle hole symmetric density of states." + "The dispersion relation is stored in a `Gf` object and we can plot its bandstructure via the `bplot` function in `plotting_tools`." ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 43, "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Starting run with 1 MPI threads at : 2019-04-29 18:54:47.073302\n" - ] - } - ], + "outputs": [], "source": [ - "from triqs_tprf.tight_binding import TBLattice\n", + "from triqs_tprf.tight_binding import SquareLattice\n", "\n", - "def get_disperion_relation(p):\n", - " \"\"\"Return the disperion relation for model parameters in a ParameterCollection\n", - " \"\"\"\n", - " \n", - " t = -p.t * np.eye(p.norb)\n", - " \n", - " # next-nearest neighbour hopping only if p has `tp` attribute\n", - " try:\n", - " tp = -p.tp * np.eye(p.norb)\n", - " except AttributeError:\n", - " tp = 0 * np.eye(p.norb)\n", - " \n", - " H = TBLattice(\n", - " units = [(1, 0, 0), (0, 1, 0)],\n", - " hopping = {\n", - " # nearest neighbour hopping\n", - " ( 0,+1): t,\n", - " ( 0,-1): t,\n", - " (+1, 0): t,\n", - " (-1, 0): t,\n", - " \n", - " # next-nearest neighbour hopping\n", - " ( +1,+1): tp,\n", - " ( -1,-1): tp,\n", - " (+1, -1): tp,\n", - " (-1, +1): tp,\n", - " },\n", - " orbital_positions = [(0,0,0)]*p.norb,\n", - " )\n", - " \n", - " e_k = H.on_mesh_brillouin_zone(n_k = (p.nk, p.nk, 1))\n", + "H = SquareLattice(**hubbard)\n", "\n", - " return e_k\n", - "\n", - "e_k = get_disperion_relation(hubbard)" + "e_k = H.on_mesh_brillouin_zone(n_k=(hubbard.nk, hubbard.nk, 1))" ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 44, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -199,8 +152,6 @@ "from scipy.stats import gaussian_kde\n", "from plotting_tools import bsplot\n", "\n", - "fig = plt.figure()\n", - "\n", "gs = gridspec.GridSpec(1, 2, width_ratios=[3, 1]) \n", "gs.update(wspace=0.025, hspace=0.05)\n", "\n", @@ -216,7 +167,8 @@ "ax_bs.spines['left'].set_bounds(lower_limit, upper_limit)\n", "ax_bs.spines['bottom'].set_bounds(ax_bs.get_xticks()[0], ax_bs.get_xticks()[-1])\n", "\n", - "ax_bs.set_ylabel('$\\epsilon(\\mathbf{k})$')\n", + "ax_bs.set_ylabel('$\\epsilon(\\mathbf{k})$', rotation=0, ha='right')\n", + "\n", "# -- Density of states\n", "ax_dos = plt.subplot(gs[1])\n", "\n", @@ -227,64 +179,34 @@ "\n", "ax_dos.plot(dos(xs).real, xs)\n", "ax_dos.fill_betweenx(xs, dos(xs).real, [0]*len(xs), alpha=0.25)\n", - "#ax_dos.set_xlim()\n", - "\n", - "#ax_dos.spines['left'].set_visible(False)\n", "ax_dos.set_xlabel('DOS')\n", "\n", "ax_dos.set_yticklabels([''])\n", "ax_dos.set_xticks([])\n", "\n", - "ax_dos.spines['left'].set_bounds(lower_limit, upper_limit)\n" + "ax_dos.spines['left'].set_bounds(lower_limit, upper_limit)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Spin and charge susceptibility\n", + "## Charge- and spin-susceptibility\n", "\n", - "Lets first introduce some helper function to convert between temperature in Kelvin and beta in 1/eV." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [], - "source": [ - "def beta_to_temperature(beta):\n", - " \"\"\"Convert beta in 1/eV to Temperature in Kelvin\n", - " \"\"\"\n", - " \n", - " def eV_to_Kelvin(ev):\n", - " return 11604.5250061657 * ev\n", + "To get physical information about the Hubbard model we will calculate the spin and charge susceptibilites in the random phase approximation (RPA) limit to see at which parameters they diverge and a phase transition occurs.\n", "\n", - " T = 1. / beta\n", - " return eV_to_Kelvin(T)\n", - "\n", - "def temperature_to_beta(T):\n", - " \"\"\"Convert Temperature in Kelvin to beta in 1/eV\n", - " \"\"\"\n", - " \n", - " def Kelvin_to_eV(K):\n", - " return K / 11604.5250061657\n", + "To use the RPA we need the non-interaction particle-hole bubble which is contstructed via the non-interaction Green's function.\n", + "We therefore first construct a Matsubara frequency mesh object by using `MeshImFreq` from `pytriqs.gf`.\n", + "This constructor needs to know the inverse temperature `beta` in $1/\\mathrm{eV}$, which we can get from the temperature in $\\mathrm{Kelvin}$ by using the converter function `temperature_to_beta` from `triqs_tprf.utilities`, the statistic of our particle `S`, in our case a Fermion, and the number of points to use `n_max` in one dimension.\n", + "With this mesh object and the dispersion relation `e_k` we can then use `lattice_dyson_g0_wk` from `triqs_tprf.lattice` to construct the non-interaction Green's function for a specific filling given by `mu`.\n", + "The non-interaction particle-hole bubble is then constructed from this `Gf` object by using `imtime_bubble_chi0_wk` from `triqs_tprf.lattice_utils`.\n", "\n", - " T = Kelvin_to_eV(T)\n", - " beta = 1./ T\n", - " return beta" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We will then calculate the non-interacting susceptibiliy as previous and wrap it in a function that only cares about the Hubbard model parameters." + "We wraped all of this in the function `get_chi0` which uses a `ParameterCollection` as an input to get all the parameters." ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -298,11 +220,11 @@ "Two-Particle Response Function tool-box \n", "\n", "beta = 11.6045250062\n", - "nk = 256\n", + "nk = 1024\n", "nw = 100\n", "norb = 1\n", "\n", - "Approx. Memory Utilization: 0.00 GB\n", + "Approx. Memory Utilization: 0.01 GB\n", "\n", "--> fourier_wk_to_wr\n", "--> fourier_wr_to_tr\n", @@ -316,13 +238,14 @@ "from pytriqs.gf import MeshImFreq\n", "from triqs_tprf.lattice import lattice_dyson_g0_wk\n", "from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk\n", - "\n", + "from triqs_tprf.utilities import temperature_to_beta\n", "\n", "def get_chi0(p, e_k=None):\n", " \"\"\"Return the non-interaction susceptibility for model parameters in a ParameterCollection\n", " \"\"\"\n", " if not e_k:\n", - " e_k = get_disperion_relation(p)\n", + " H = SquareLattice(**p)\n", + " e_k = H.on_mesh_brillouin_zone(n_k=(p.nk, p.nk, 1))\n", "\n", " wmesh = MeshImFreq(beta=temperature_to_beta(p.T), S='Fermion', n_max=p.nw)\n", " g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh)\n", @@ -338,52 +261,49 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We then calculate the spin and charge susceptibiliy in the RPA limit with the know equations.\n", + "We can now calculate the spin and charge susceptibiliy in the RPA limit with the known equations.\n", "\n", "$$\n", - "EQ here lol\n", + "\\chi^{(\\mathrm{c})}=\\frac{\\chi^{(0)}}{1+\\chi^{(0)} U}\n", + "\\quad\n", + "\\mathrm{and}\n", + "\\quad\n", + "\\chi^{(\\mathrm{s})}=\\frac{\\chi^{(0)}}{1-\\chi^{(0)} U}\\,.\n", "$$\n", "\n", - "We also wrap this is a small function that only cares about the Hubbard model parameters." + "These kind of equation is implemented as `solve_rpa_PH` in `triqs_tprf.lattice` and we wrapped it in the function `get_chiRPA` to immediately obtain the charge- and spin-susceptibilites in RPA from given parameters.\n", + "We can plot them for $\\nu=0$, using the `Idx` object from `from pytriqs.gf`, in the same fashion as the bandstructure.\n", + "There we can see, that the spin-susceptibiliy has a peak at the M-point, which will lead to an antiferromagnetic (AFM) state for large enough $U$." ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [ - "from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors\n", "from triqs_tprf.lattice import solve_rpa_PH\n", "\n", "def get_chiRPA(p, chi0_wk=None):\n", - " \"\"\"Return the spin and charge susceptibility in the RPA limit for model parameters in a ParameterCollection\n", + " \"\"\"Return the charge- and spin-susceptibility in the RPA limit for model parameters in a ParameterCollection\n", " \"\"\"\n", " \n", " if not chi0_wk:\n", " chi0_wk = get_chi0(p)\n", " \n", - " U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norb, p.U, 0.0, 0.0, 0.0)\n", + " U = p.U * np.ones(shape=(1,1,1,1), dtype=complex)\n", "\n", - " chi_c_wk = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation\n", - " chi_s_wk = solve_rpa_PH(chi0_wk, U_s)\n", + " chi_c_wk = solve_rpa_PH(chi0_wk, -U) # Minus for correct charge rpa equation\n", + " chi_s_wk = solve_rpa_PH(chi0_wk, U)\n", " \n", " return chi_c_wk, chi_s_wk\n", "\n", "chi_c_wk, chi_s_wk = get_chiRPA(hubbard, chi0_wk)" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We cann now easily acces the spin and charge susceptibility and have a look at it.\n", - "Again we see the the peak of the spin susceptibiliy at the M-point telling us, that the system will order antiferromagnetically." - ] - }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -392,13 +312,13 @@ "Text(0.55,0.18,'$\\\\chi^{(c)}$')" ] }, - "execution_count": 9, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] @@ -410,18 +330,15 @@ "source": [ "from pytriqs.gf import Idx\n", "\n", - "chi_c_k = chi_c_wk[Idx(0), :]\n", - "chi_s_k = chi_s_wk[Idx(0), :]\n", - "\n", "fig = plt.figure()\n", "\n", "ax_bs = fig.add_subplot(111)\n", "\n", - "ax_bs.bsplot(chi_s_k, path)\n", - "ax_bs.bsplot(chi_c_k, path)\n", + "ax_bs.bsplot(chi_s_wk[Idx(0), :], path)\n", + "ax_bs.bsplot(chi_c_wk[Idx(0), :], path)\n", "\n", - "lower_limit = np.round(np.min(chi_c_k.data.real), 2)\n", - "upper_limit = np.round(np.max(chi_s_k.data.real), 2)\n", + "lower_limit = np.round(np.min(chi_s_wk.data.real), 2)\n", + "upper_limit = np.round(np.max(chi_s_wk.data.real), 2)\n", "\n", "ax_bs.set_yticks([lower_limit, upper_limit])\n", "\n", @@ -437,7 +354,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We will now introduce a small function that will find $U_\\mathrm{c}$, the interaction strength at which the Hubbard model goes into a spin ordered phase.\n", + "We will now introduce a small function `get_spin_phase_transistion` that will find $U_\\mathrm{c}$, the interaction strength at which the Hubbard model goes into a spin ordered phase.\n", "This is done by searching for the $U$ at which \n", "\n", "$$\n", @@ -449,7 +366,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 9, "metadata": {}, "outputs": [], "source": [ @@ -457,15 +374,12 @@ "\n", "def get_spin_phase_transistion(p):\n", " \"\"\"Return U at which model p transitions to spin order via root search\n", - " \"\"\"\n", - " p = p.copy()\n", - " \n", + " \"\"\" \n", " chi0_wk = get_chi0(p)\n", " \n", " def one_over_spin(U):\n", - " \n", - " p.U = U\n", - " _, chi_s_wk = get_chiRPA(p, chi0_wk)\n", + "\n", + " _, chi_s_wk = get_chiRPA(p.copy(U=U), chi0_wk)\n", " \n", " # -- If any value is below zero we are already in an ordered phase\n", " if np.any(chi_s_wk.data[np.abs(chi_s_wk.data) > 1e-3] < 0.0 ):\n", @@ -485,49 +399,23 @@ "source": [ "To scan through some parameters we will copy our base model `hubbard`, which parameters are stored as a `ParameterCollection`, and only change the specific parameters.\n", "We do this with the function `parameter_scan` which outputs us a `ParameterCollections` objects which is a container for multiple `ParameterCollection`.\n", - "We can then loop over the `ParameterCollections` object." - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [], - "source": [ - "import itertools\n", - "from triqs_tprf.ParameterCollection import ParameterCollections\n", - "\n", - "def parameter_scan(p, **kwargs):\n", - " parameter_values = []\n", - "\n", - " for key, value in kwargs.iteritems():\n", - " parameter_values.append(zip([key]*len(value), value))\n", - " \n", - " ps = []\n", - " \n", - " for parameter_value in itertools.product(*parameter_values):\n", - " ps.append(p.copy(**dict(parameter_value)))\n", + "We can then loop over the `ParameterCollections` object to access the individual `ParameterCollection` objects.\n", "\n", - " return ParameterCollections(ps)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can now do a crude scan of a $T-U$ phase diagram to map out the antiferromagnetic (AFM) phase." + "To show this off we will do a crude scan of a $T-U$ phase diagram to map out the AFM phase." ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "%%capture\n", "\n", + "from triqs_tprf.ParameterCollection import parameter_scan\n", + "\n", "Ts = [1000, 750, 500, 250]\n", - "# -- Use the hubbard model as a base for the parameters and only change T\n", + "# -- Use the hubbard model as a template for the parameters and only change T\n", "hubbard_models = parameter_scan(hubbard, T=Ts)\n", "\n", "U_cs = []\n", @@ -540,7 +428,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 11, "metadata": {}, "outputs": [ { @@ -549,13 +437,13 @@ "Text(0.625,0.3,'AFM')" ] }, - "execution_count": 13, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -565,9 +453,7 @@ } ], "source": [ - "fig = plt.figure()\n", - "\n", - "ax_pd = fig.add_subplot(111)\n", + "ax_pd = plt.subplot()\n", "\n", "ax_pd.plot(U_cs, Ts, \"o\", ls=\"-\")\n", "ax_pd.fill_between(U_cs, Ts, [Ts[-1]]*len(Ts), alpha=0.25)\n", @@ -636,13 +522,15 @@ "\n", "which leads to additional terms.\n", "But those terms only consist of a shift in chemical potential and an constant energy.\n", - "We can therfore write a new Hamiltonian for the Hubbard model which is also invariant in the interaction term for a PHT.\n", + "We can therfore write a new Hamiltonian for the Hubbard model which is also invariant in the interaction term for a PHT\n", "\n", "$$\n", - "H=-t \\sum_{\\langle j, l\\rangle \\sigma}\\left(c_{j \\sigma}^{\\dagger} c_{l \\sigma}+c_{l \\sigma}^{\\dagger} c_{j \\sigma}\\right)+U \\sum_{j}\\left(n_{j \\uparrow}-\\frac{1}{2}\\right)\\left(n_{j \\downarrow}-\\frac{1}{2}\\right)-\\mu \\sum_{j}\\left(n_{j \\uparrow}+n_{j \\downarrow}\\right)\n", + "H=-t \\sum_{\\langle j, l\\rangle \\sigma}\\left(c_{j \\sigma}^{\\dagger} c_{l \\sigma}+c_{l \\sigma}^{\\dagger} c_{j \\sigma}\\right)+U \\sum_{j}\\left(n_{j \\uparrow}-\\frac{1}{2}\\right)\\left(n_{j \\downarrow}-\\frac{1}{2}\\right)-\\mu \\sum_{j}\\left(n_{j \\uparrow}+n_{j \\downarrow}\\right)\\,,\n", "$$\n", "\n", - "Doing the PHT here yields\n", + "we will cal this the particle-hole symmetric form of the Hubbard model.\n", + "\n", + "Doing the PHT on its interaction term yields\n", "\n", "$$\n", "\\left(n_{j \\uparrow}-\\frac{1}{2}\\right)\\left(n_{j \\downarrow}-\\frac{1}{2}\\right) \\xrightarrow{\\mathrm{PHT}}\n", @@ -662,7 +550,7 @@ "\n", "and therefore an unimportant constant term, but also a sign change.\n", "\n", - "The Hubbard hamiltonian in equation REFHERE can therfore be mapped via a PHT to an identical Hubbard model with only a negative chemical potential.\n", + "The particle-hole symmetric form of the Hubbard model can therefore be mapped via a PHT to an identical Hubbard model with only a negative chemical potential.\n", "\n", "To use this knowledge let us now see how the spin operator in $z$-direction changes under a PHT\n", "\n", @@ -670,7 +558,7 @@ "S^z_j = n_{j \\uparrow} - n_{j \\downarrow} \\xrightarrow{\\mathrm{PHT}} (1 - \\tilde{n}_{j \\uparrow}) - (1 - \\tilde{n}_{j \\downarrow}) = \\tilde{n}_{j \\downarrow} - \\tilde{n}_{j \\uparrow} = \\tilde{S}^z_j\\,.\n", "$$\n", "\n", - "This sign change for the direction of the spin is unimportant for the calculation of suscpeitbilites and therefore the spin susceptibility is invariant under PHT\n", + "This sign change for the direction of the spin is unimportant for the calculation of susceptibilites and therefore the spin susceptibility is invariant under PHT\n", "\n", "$$\n", "\\langle S^z_jS^z_j \\rangle = \\langle \\tilde{S}^z_j\\tilde{S}^z_j \\rangle\\,.\n", @@ -682,7 +570,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ @@ -702,7 +590,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 13, "metadata": {}, "outputs": [ { @@ -711,13 +599,13 @@ "Text(0.125,0.3,'AFM')" ] }, - "execution_count": 15, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -727,9 +615,7 @@ } ], "source": [ - "fig = plt.figure()\n", - "\n", - "ax_pd = fig.add_subplot(111)\n", + "ax_pd = plt.subplot(111)\n", "\n", "ax_pd.plot(mus, U_cs, \"o\", ls=\"-\")\n", "ax_pd.fill_between(mus,[min(U_cs)]*len(U_cs),U_cs, alpha=0.25)\n", @@ -744,7 +630,6 @@ "ax_pd.spines['left'].set_bounds(min(U_cs), max(U_cs))\n", "ax_pd.spines['bottom'].set_bounds(min(mus), max(mus))\n", "\n", - "\n", "ax_pd.text(0.725, 0.3, \"AFM\", transform = ax_pd.transAxes, size=24, color='C0')\n", "ax_pd.text(0.125, 0.3, \"AFM\", transform = ax_pd.transAxes, size=24, color='C0')" ] @@ -755,7 +640,7 @@ "source": [ "Here we see that the AFM phase is indeed symmetric for $\\mu=0$.\n", "\n", - "If we now introduce a next-nearest neighbor hopping we introduce hopping between sublattices of the same type.\n", + "If we now introduce next-nearest neighbor hopping we introduce hopping between sublattices of the same type.\n", "The kinetic term of the Hubbard model does then contain terms of the form $c_{1 \\sigma}^{\\dagger} c_{l \\sigma}$, which are not invariant under PHT\n", "\n", "$$\n", @@ -763,28 +648,38 @@ "d_{l \\sigma} d_{l \\sigma}^{\\dagger}= -d_{l \\sigma}^{\\dagger} d_{l \\sigma}\\,.\n", "$$\n", "\n", - "Such a model is therefore not symmetric for $\\mu=0$, which we can test." + "Such a model is therefore not symmetric in its AFM phase for $\\mu=0$, which we can test.\n", + "\n", + "We make a copy of our `ParameterCollection` `hubbard` where we have stored the parameters of our Hubbard model and give this copy the additional parameter `tp`.\n", + "This parameter stands for the energy gain of next-nearest neighbor hopping processes.\n", + "The `SquareLattice` class knows about this parameter and we can proceed as before to obatin the dispersion relation.\n", + "Plotting it, we already see, that the density of states is no longer symmetric.\n", + "We preceed as before and obtain a $\\mu-U$ phase diagram.\n", + "There we can observe that the symmetry is destroyed." ] }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 54, "metadata": {}, "outputs": [], "source": [ "hubbard_next_nearest_neighbor_hopping = hubbard.copy(tp=-0.05)\n", "\n", - "e_k = get_disperion_relation(hubbard_next_nearest_neighbor_hopping)" + "H = SquareLattice(**hubbard_next_nearest_neighbor_hopping)\n", + "\n", + "e_k_nn = H.on_mesh_brillouin_zone(n_k=(hubbard_next_nearest_neighbor_hopping.nk,\n", + " hubbard_next_nearest_neighbor_hopping.nk, 1))" ] }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 55, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -794,52 +689,49 @@ } ], "source": [ - "from matplotlib import gridspec\n", - "from scipy.stats import gaussian_kde\n", - "from plotting_tools import bsplot\n", - "\n", - "fig = plt.figure()\n", - "\n", - "gs = gridspec.GridSpec(1, 2, width_ratios=[3, 1]) \n", - "gs.update(wspace=0.025, hspace=0.05)\n", - "\n", "# -- Bandstructure\n", "ax_bs = plt.subplot(gs[0])\n", "\n", - "lower_limit = np.min(e_k.data.real)\n", - "upper_limit = np.max(e_k.data.real)\n", + "lower_limit = np.min(e_k_nn.data.real)\n", + "upper_limit = np.max(e_k_nn.data.real)\n", "\n", - "path = 'G-X-M-G'\n", - "ax_bs.bsplot(e_k, path)\n", + "ax_bs.bsplot(e_k, path, color='grey', ls=\"dotted\", alpha=0.5)\n", + "ax_bs.bsplot(e_k_nn, path)\n", "\n", "ax_bs.spines['left'].set_bounds(lower_limit, upper_limit)\n", "ax_bs.spines['bottom'].set_bounds(ax_bs.get_xticks()[0], ax_bs.get_xticks()[-1])\n", "\n", - "ax_bs.set_ylabel('$\\epsilon(\\mathbf{k})$')\n", + "ax_bs.set_yticks([lower_limit, upper_limit])\n", + "\n", + "ax_bs.set_ylabel('$\\epsilon(\\mathbf{k})$', rotation=0, ha='right')\n", + "\n", "# -- Density of states\n", "ax_dos = plt.subplot(gs[1])\n", "\n", - "dos = gaussian_kde(e_k.data[:,0,0].real)\n", - "xs = np.linspace(lower_limit, upper_limit , 500)\n", - "dos.covariance_factor = lambda : .1\n", - "dos._compute_covariance()\n", + "dos_nn = gaussian_kde(e_k_nn[0,0].data.real)\n", + "xs_nn = np.linspace(lower_limit, upper_limit , 500)\n", + "dos_nn.covariance_factor = lambda : .1\n", + "dos_nn._compute_covariance()\n", + "\n", + "ax_dos.plot(dos(xs).real, xs, color='grey', ls=\"dotted\", alpha=0.5)\n", + "\n", + "ax_dos.plot(dos_nn(xs_nn).real, xs_nn)\n", + "ax_dos.fill_betweenx(xs_nn, dos_nn(xs_nn).real, [0]*len(xs), alpha=0.25)\n", + "\n", "\n", - "ax_dos.plot(dos(xs).real, xs)\n", - "ax_dos.fill_betweenx(xs, dos(xs).real, [0]*len(xs), alpha=0.25)\n", - "#ax_dos.set_xlim()\n", "\n", - "#ax_dos.spines['left'].set_visible(False)\n", "ax_dos.set_xlabel('DOS')\n", "\n", + "ax_dos.set_yticks([lower_limit, upper_limit])\n", "ax_dos.set_yticklabels([''])\n", "ax_dos.set_xticks([])\n", "\n", - "ax_dos.spines['left'].set_bounds(lower_limit, upper_limit)\n" + "ax_dos.spines['left'].set_bounds(lower_limit, upper_limit)" ] }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 56, "metadata": {}, "outputs": [], "source": [ @@ -859,22 +751,22 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "Text(0.125,0.1,'AFM')" + "Text(0.08,0.1,'AFM')" ] }, - "execution_count": 19, + "execution_count": 60, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -884,9 +776,7 @@ } ], "source": [ - "fig = plt.figure()\n", - "\n", - "ax_pd = fig.add_subplot(111)\n", + "ax_pd = plt.subplot(111)\n", "\n", "ax_pd.plot(mus, U_cs, \"o\", ls=\"-\")\n", "ax_pd.fill_between(mus,[min(U_cs)]*len(U_cs),U_cs, alpha=0.25)\n", @@ -894,8 +784,15 @@ "ax_pd.set_ylabel('U [eV]', rotation=0, ha='right')\n", "ax_pd.set_xlabel('$\\mu$ [eV]')\n", "\n", + "ax_pd.set_yticks([min(U_cs), max(U_cs)])\n", + "ax_pd.set_xticks(mus)\n", + "ax_pd.set_xticklabels(mus, rotation=25)\n", + "\n", + "ax_pd.spines['left'].set_bounds(min(U_cs), max(U_cs))\n", + "ax_pd.spines['bottom'].set_bounds(min(mus), max(mus))\n", + "\n", "ax_pd.text(0.725, 0.3, \"AFM\", transform = ax_pd.transAxes, size=24, color='C0')\n", - "ax_pd.text(0.125, 0.1, \"AFM\", transform = ax_pd.transAxes, size=24, color='C0')" + "ax_pd.text(0.08, 0.1, \"AFM\", transform = ax_pd.transAxes, size=24, color='C0')" ] }, { @@ -914,7 +811,7 @@ "c_{j \\downarrow} \\xrightarrow{\\mathrm{SPHT}} (-1)^j d_{j \\downarrow}^{\\dagger}\\,.\n", "$$\n", "\n", - "Lets remember the Hubbard Hamiltonian that is invariant under a PHT\n", + "Lets remember the particle-hole symmetric Hubbard model that is invariant under a PHT\n", "\n", "$$\n", "H=-t \\sum_{\\langle j, l\\rangle \\sigma}\\left(c_{j \\sigma}^{\\dagger} c_{l \\sigma}+c_{l \\sigma}^{\\dagger} c_{j \\sigma}\\right)+U \\sum_{j}\\left(n_{j \\uparrow}-\\frac{1}{2}\\right)\\left(n_{j \\downarrow}-\\frac{1}{2}\\right)-\\mu \\sum_{j}\\left(n_{j \\uparrow}+n_{j \\downarrow}\\right)\\,.\n", @@ -964,27 +861,25 @@ "If one calculates a susceptibility one is only interested in the change of the expectation value of an obserable $A$ when going from an unperturbed system to one which is perturbed by a field coupling to operator $B$.\n", "Therefore a constant factor in an observable is unimportant when calculating susceptibilites.\n", "\n", - "If we consider a Hubbard model at half-filling, i.e. $\\mu=0.0$ the $T-U$ phase diagram is symmetric for $U=0$\n", - "\n" + "If we consider a Hubbard model at half-filling, i.e. $\\mu=0.0$ the $T-U$, this means, that the spin-susceptibility in the repulsive Hubbard model is equal to the charge-suscpeitbility in the attractive one.\n", + "We already see this in the RPA equations for the susceptibilites were they only differ by a sign, but we will test it anyways.\n", + "To study the transition to a charge density wave we will the function `get_charge_phase_transistion`, were we scan for divergences is the range of negative $U$." ] }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 61, "metadata": {}, "outputs": [], "source": [ "def get_charge_phase_transistion(p):\n", " \"\"\"Return U at which model p transitions to charge order via root search\n", " \"\"\"\n", - " p.copy()\n", - "\n", " chi0_wk = get_chi0(p)\n", " \n", " def one_over_charge(U):\n", - " \n", - " p.U = U\n", - " chi_c_wk, _ = get_chiRPA(p, chi0_wk)\n", + "\n", + " chi_c_wk, _ = get_chiRPA(p.copy(U=U), chi0_wk)\n", " \n", " # -- If any value is below zero we are already in an ordered phase\n", " if np.any(chi_c_wk.data[np.abs(chi_c_wk.data) > 1e-3] < 0.0 ):\n", @@ -1000,7 +895,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 62, "metadata": {}, "outputs": [], "source": [ @@ -1023,7 +918,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 67, "metadata": {}, "outputs": [ { @@ -1032,15 +927,15 @@ "Text(0.07,0.15,'CDW')" ] }, - "execution_count": 22, + "execution_count": 67, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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t359yRJIk1Z5Ssdi3KH2lSYikKSyTyfRdqtcpWZIkjbnC5s0U9yT/x2ZmzCC7eFHKEY09kxBJo1I5JWu9+4VIkjTm+o6CnEQmk0kxmvFhEiJpVE7st0JWqWRdiCRJY6mjsh6kBovSwSRE0igtnN1MS0MWgD0HO3lsV1vKEUmSVFs6bz+0U3otrowFJiGSRqmuX12IS/VKkjR2Ctu20f3kk0mjsZHc8cenG9A4MQmRNGqVU7IsTpckaez0qQdZsYJMNptiNOPHJETSqC07yuJ0SZLGQ61vUtjDJETSqC2Z10JDLvn18eSednbszacckSRJtaHWNynsYRIiadRy2TqWzp/W23Y0RJKkI9e9axeFTZuSRjZL/bLl6QY0jkxCJB2WPlOyrAuRJOmI9RkFOfFEMo0NKUYzvkxCJB0Wd06XJGls9a0HWZliJOPPJETSYTl+/jTqyju4PrzjAHvbOlOOSJKk6lY5ElLLRelgEiLpMDXWZzl2Xktv+97Hnk0xGkmSqlvxwAG6fnt/0shkyJ10UroBjTOTEEmHzSlZkiSNjc6774ZiEYDsscdSN336MD2qm0mIpMO2rGLTQlfIkiTp8PXZpHBlbdeDgEmIpCNwQsUKWRue3Ed7ZyHFaCRJql4dU6geBExCJB2B6U05Fs5uBqC7WOKBbXtTjkiSpOpT6uig8557etu5Gl8ZC0xCJB2hyilZ91gXIknSqHXedx/kOwCoO/posnPnphzR+DMJkXREllmcLknSEelTDzIFpmKBSYikI1S5Qtb92/ZS6C6mGI0kSdVnKm1S2MMkRNIRmTOtgXnTGwDId3Wz4al9KUckSVL1KHV307luXW/bkRBJGqHKKVnrtzolS5Kkkep6cAOlfckXeJnZs6lbsCDliCaGSYikI1Y5Jcv9QiRJGrnOO/tOxcpkMilGM3FMQiQdscoVsu57bA/FYinFaCRJqh5TsSgdTEIkjYGjZjYxoykHwL72Alt2Hkg5IkmSJr9SqdR3k8KVJiGSNGKZTKbPlCz3C5EkaXjdW7ZS3LEDgExzM9ljj005ooljEiJpTFROyXK/EEmShtdx5x29z3MrV5LJTp2P5lPnnUoaV/2L00sl60IkSRrKVK0HAZMQSWNk8ZwWmuqTXyk793Xw1LPtKUckSdLk1nHn1NuksIdJiKQxUVeX4fj5h6ZkrXdKliRJg+revp3urY8mjfp6cieemG5AE8wkRNKYWWZxuiRJI9JRMRUrt2wZmfr6FKOZeCYhksbMsgWHkhCL0yVJGlyfTQpPnlr1IGASImkMHTdvGrm6ZKfXx3a1setAR8oRSZI0OXVM4aJ0MAmRNIbqc3Uc97xpve17H3M0RJKk/orPPkthw4akkcmQW7Ei3YBSYBIiaUz1Wap3q0mIJEn9ddy1DspL2eeOP5665uaUI5p4JiGSxtSyfvuFSJKkvirrQXJTcCoWmIRIGmMnHDWdTFIWwubt+zmYL6QbkCRJk8xU3qSwh0mIpDHV3JBl8ZwWAIoluO9xR0MkSepRam+n8777etv1K6fWJoU9TEIkjbkTj67ctPDZFCORJGly6bxnPXR1AZBdtIi6WTNTjigdJiGSxlyf4vRHd6cYiSRJk0vHHXf0Ps9N0VEQMAmRNA4qi9N/98ReOrq6U4xGkqTJo089yBTcpLCHSYikMTezuZ6jZjYB0NVd4sEn96UckSRJ6SsVCnTefXdve6oWpYNJiKRxsqxPXYjF6ZIkdd1/P6W2NgDq5s0jO39+yhGlJ5d2ANJ4iDFeCFw5zGXFEEK2fP1SYMsQ134rhPD2QV7rXcBfACcD3cA9wKdCCD8ZXdS15cSjZ3DrpmeAnrqQE9INSJKklHXcfqgeZCqPgoBJiGrXeiAOcu73gVcBPxvg3L3ADwY4fv9AN4oxfgr4ELAN+BLQALwd+HGM8f0hhMtGGXfNqBwJuX3zLl4arqW5Icu5LzyGd65ZyuK5LSlGJ0nSxCls3cqBy6/g4Ne/0Xuse9cuurdvJ7tgQYqRpcckRDUphLCeJBF5jhjjbeWnVwxwen0I4WMjeY0Y4xqSBORh4MwQwp7y8X8G7gY+FWP8SQhh6+iirw3bn833aZeAts5ufnT3Nn66/gkufduprFk+dYehJUlTQ/6Xv2L3xe+m1NUF3YcWails3MieD/81Mz/0QRpOOy3FCNNhTYimlBjjC4CXAE8A/3WEt3tP+fGTPQkIQDnp+BzQCPzZEb5GVdq5L89Xbnp4wHOFYol8V5FLvrWebbvbJjgySZImTmHr1iQBaW+HQqHvyWIROjrY9y//Svf27ekEmCJHQjTVvLv8+JUQwkDrxh4TY3w3MA/YBdwWQrhvgOsgmdIF8PMBzv0M+Gj5mnAE8ValGx7YTqG7OOQ1he4S37x1K3993skTFJUkSRPrwOVXJCMgQykUaPvJfzHjov8+MUFNEiYhmjJijM3AHwNF4MuDXPaa8p/KfjcC7wohPFZxbBqwCDgQQnhqgPtsKj+uGCKeC4ELBzh16mB9qsVdj+yiWBr6mkKxxM/ve8okRJJUs9q+9/3njoD0191N59q1MMWSEKdjaSr5b8Bs4GchhMf7nWsDPg6sBuaU/7wC+BVwFnBDOfHoMav8uHeQ1+o5PnuIeJaWX6P/n1lD9KkK+a6hR0F6tHUO84tZkqQqVjp4cGTX5fPDX1RjHAnRVHJx+fHy/idCCDuAv+93eG2M8bXALcCLgYuA/zfK1xxqPGArcNMAx0+lyhORpvq6ESUiLQ3+CpIk1a7MtGmUDhwY/rqmpgmIZnLxE4CmhBjjycAakqV0fzrSfiGEQozxyyRJyMs5lIT0jHQMliwMN1JCCOEq4KoBYr2RZESkap15wjx+/dDOIadk5eoynNu6cOKCkiRpgrW8+QIOfuObQ0/JymZpePnLJy6oScLpWJoqhitIH8rO8mPvdKwQwkGSFbamxxgH+iS9vPz40ChfqyacfcoCctmhf73kshnesWbpxAQkSVIKpr/7YjL19UNflMvRct7rJyagScQkRDUvxtgE/AlJQfpXDuMWLyk/PtLv+C/Lj+cO0Od1/a6ZUubPbOKis06kIVdHXabvubpMMl3r0red6oaFkqSallu6lJkf+9jAJ7NZaGxk5oc+OCU3LDQJ0VTwhySF5j8doCAdgBjji2OMDQMcfxXwgXLza/1Of7H8+JEY45yKPkuBvwA6gCuPKPIqdsri2VzyxlP4vRVHkcseykSeN6ORr73vZW5UKEmaEkr79x1q1NVBJkOmuZnGV7+aOZ/65ym5USFYE6KpoacgfaAd0nv8X+CUcj3GtvKxVg7tBfLREMKtlR1CCLfGGP8V+CBwX4zxu0AD8DZgLvD+qbpbeo/5M5t420uP47WtC/m779wLwO6DncxuGWZoWpKkGpG/9he9z6e/5900vfKVKUYzeTgSopoWY3w+8HsMX5D+VeAO4EzgfwDvI6nr+Dbw8hDCJwbqFEL4EMleH9tJkp0/BR4A3hBCuGxs3kX1mzOtgSXzkqlXhe4St216JuWIJEkaf927dtG5bl3SyGRoOP30dAOaRIYcCYkxDrPd2KBuCiGcdZh9dQRijC8hqVHYEEK4Ju140hZCeBDIjOC6r3B49SKEEK4Grj6cvlNJ65LZPL6rDYCbN+7gNatcGUuSVNvy118PpeTjdG7FCupmVfUK/GNquJGQpwf507P/fH6Q87vHI1iNyEuAALw97UCkSq3H9pbNcOumZyh0j2xDQ0mSqlXlVKyGM89MMZLJZ8iRkBDCgKX6FfsYfCuEcOHYhyWp1iya08zcaQ3sPtjJgXyB32zdw4tOnJd2WJIkjYtiezsdN63tbTeeeUaK0Uw+1oRImhCZTIZVx87uba/dsCPFaCRJGl8dN99CKZ8HIHvMMWSPOSbliCaXCVsdK8b4VuDPgTOA2SRTtm4F/l8I4aYBrv8r4NPAD0MI58cY/xx4L7ASaAN+BVwSQnikfP1xwEdI6iGOArYCXwA+E0Io9bv3qcA9wN4QwuwY46uBvwFWA03Ag+W+/96/b7/7nAH8T5JRoaPLcd1LUh9wdQih2O/6/q97FsnKSi8C5gMfDyF8rHzt6cD5wKuBY8vvaR+wnmSX7a9XxhZjnA3sqXi5Nw1Q03NaCGF9/zgGeW/nA98H7g0hnNrv3LMkO4KfVo7pfwOvBRYCt/avByr/fN8LvBR4XrnPOuCLIYQfDPT6qk2tS+Zw04NJ8nHLxh186A9WkskMW7IjSVLVyf+iciqWoyD9jftISIyxOcb4A+A7JBu4zQfaST60XwDcGGO8ZJh7fJGkaPiF5UNHkSyDekuMcUmMsRW4k2RVo1lAPXAS8G/AgKsaVdz7z4BrgdeQ/DwaSZKRLwNXxxgH/IQUY/xI+TX/GFgCdAIzSRKSfwd+FGMcdB3SGONFwA3AG8qv2X+C/J3AR0k+uB9N8jObB5xNspLTN/rFViSpx9lfbncweC3PWDkN+A1wUTm2QuXJGGNdjPHzwHXAm0mSlHaS5WvPAb4fY7x8jGPSJLZ8wXSa67MAbN+bZ9P2/cP0kCSp+pS6u8lfd31v23qQ55qI6VifB94EbCT5IDothDCLJFn4AMnowSdjjK8bpP9ZwLtIlj+dWf7zIuBRkg+1nwS+CdwPPL/i3v9U7v835VGSgbQAnyP5xn9xCGEOyQfkWD7/JyTf4PcRY3wXSXKzj2Qk43khhBnl+72BZBTm9QyeALUAl5FsftfzutPou7HddeX3vQRoKr+vmSSJ1m6SwvOLei4OIewr1/D8ffnQz0MIC/r9eWCQeA7XZ0j+Xs8IIUwPIbRUxkSSRL0XeJJkFGxW+X1MJ1nK9hng4hjjc37Gqk3ZujpOWXxoZRCnZEmSalHnb+6h+EyyHH1m1ixyy5anHNHkM67TsWKMqzm0h8IrQwhP9ZwLIewD/i3G2AZcTjKV6mcD3GYW8FchhC9VHLsrxvh+4EckicKTJB+E28v3PgD8bXka0OkkSdBnBrh3Pck3+W8LIXRXxPWx8vSm/wl8NMZ4RQihUH5PTcA/l/u/OYTwy4r31AH8JMa4tXzf98cYP1m+Z//X/VkI4V0VfTtJEque9nOSshDCfuDLMcany+/9fcCX+l83gfYD54QQnu05EELYDBBjXAhcQpJkvrYyAQohtAFfLb+Pa4FLYoxfHGrqm2pH67GzWbclWUDv5o07ueiVy1KOSJKksZW/7rre5w2nn04maxl2f+P9E7mw/HhNZQLSzzeBEvCSGOP0Ac4/S1Kf0d8N5X4A/9aTgAxwDcALhojx//YkIP38H5IpTgtINrvr8XqSKWXrKxOQSiGE+4H7gGbgZYO87j8PcnwkriWZWtU6yM9sonypMgHp550ku4f/YrARmBDCL4BdwGKSWh9NAScvmk22LplJuPGpfTy9d6B/upIkVS+X5h3eeBemryk//nmM8R3DXJsFjgEe6nf8ofIoQR8hhLYY40GSqT33D3LPp8uPcwY5D3DjQAdDCNtjjBuB55OMpvRc1/OeVsYYtw9x356C7yUDnCsBtw/RlxhjHckH+XeQ1MI8j6R2pL8FwOah7jWObhviXM/P6TXD/Jx65uYsIVkQQDWuuSHLigUzePDJZIDw5g07eeuLj005KkmSxkbXw49Q2Fz+aNbQQEPrqnQDmqTGOwnp2RK5p5ZjOC0DHBtsBAWge5hres4PViDeHkLYM8g5gCdIkpD5Fcd63lNT+c9wBnpPBwcZuQF6p3z9iKRYvkeepIai5z0dRbIT+LQRxDBedg5xrufnNI2RxTjQz0k1atWS2b1JyNqNO0xCJEk1o8+qWC9sJdM40HfIGu8kpGe617tCCP8xzq81HgZaGavnPV0ZQvjzw7zvQNO/Kn2AJAHZS7J08I/7T2eLMe4nGQVKc33Tod5Hz88phBD+YSKCUfVoPXY2377jMQB+s3U3B/JdTG8adDE5SZKqRp8k5AyX5h3MeNeE9EyHOnmcX+dwNZcL0AfT821+5Tf+E/Ge/rD8+L9CCFcMkIBMI0lADlfPUrpDjeTMGuLcSEz2v3ulaM60RpbMSwa/Ct0lbtv8TMoRSZJ05Lp37aJz3d1JI5OhYfXqdAOaxMY7CempGbhgsP02JoFXDHQwxng0yV4jkKwsJ6uOAAAgAElEQVR01aPnPZ0RYxyvOSSLy4/3DHL+7CH69uw3MtTPu6eYvDHG+LxBrjnSKqqen9M55aRJ6qN1yaH8/2aX6pUk1YD89ddDMfkolluxgrpZR/qdbu0a7ySkZ9+LFcD7h7owxjhU8fh4+tsYY3aA439DUiy/Hbil4viPSVZ0ygKfHiq5OoL3tLf8+JxKphhjI/CxIfr2LAc86AhPCGEbh3ZXf9MAr7GIZBPGI/F1khW8ZgMfH+rCFP/ulaJVSw79td+66RkK3f3365Qkqbq4KtbIjWtNSAjhjhjjv5NsVPdvMcYlwGdCCI8DxBhnkix/eyHJh/q3jGc8A+gCTgW+GWP8QAjhiRjjDJKajA+Wr/l4zx4hACGEgzHGDwD/QbL54o9jjB8NIdwDEGNsINlJ/O3AWxl4dazhXAcsAy6NMT4OXBdCKJZ3hv8MsJxkh/aGAfr2LId7RoxxVQjht4O8xndINoC8NMb4KPArklGUl5Ps23JEnwhDCI/HGD8O/APwgXKi8Y8hhIcAYowtwIuBPyJJtl58JK+n6rN4bjNzpzWw+2AnB/IF7nl0D2eeMC/tsCRJOiyl9nY6blrb27YeZGjjXZgOyYZ6DSTfrH8Y+HCMcR/JMrUzOTRt6AcTEEt/bSQJx5eBt8YYny3H1DMy8lUG2KMkhPDV8ofqfyXZN+T1McZ2oJ2klqKn/2B7aAzn48AbgUXAz4GOGGMnMIMkcXoH8BUGTkLWAfeSLOt7X4zxGeBg+dwfhBB+V37+MeA8kmWRryNZfatIskrVRpKRoCPdCPETJLUrf0OSaF5YXla5k+Tn1DMSt/4IX0dVKJPJsOrY2dz0YDIVa+2GHSYhkqSqlb/5Fkr5PADZY44ht+iYlCOa3MZ9+8YQQkcI4U9IVnu6BnicQ8vbbiX5Rv4dJDufT7gQwpXAOcD15UOdwN3A/yBZ1WvAXbxDCJ8hKbr+HLCB5AP8DJIi9uuA/w845TBjegp4EUmi8RTJ39MB4NvAS0MI/zlE3xJwbrnvYyQf9o8r/2mouO4p4CXAVSRF5HXlx0+VX/uIK4VDCKUQwt+S1JdcCTxSfp1pJLvc/xi4CHj1kb6WqlNrxZSsmzfsoFQa8J+bJEmTXp9Vsc50FGQ4man4n36M8VSSou+9IYShVseSJlyM8UbgFccddxwXXnjhuL3O3Vt2j9u9R6q7WORvv7me9q5ktef/eM9LWbFwJFsKSZI0eZSKRbaftpriM8l3uLM+8XHqTzppmF7jr/75K6mbMyGlt6NegGrcR0IkaTDZujpOWXxo5ZCbN7pKliSp+nT+5p7eBCQzcya5ZctTjmjyMwmRlKrWYw8NRq7dsHOIKyVJmpz6TMVavZpM1o/Yw/EnJClVJy+aRbYuGcXd+NQ+nt7bnnJEkiSNjkvzjp5JiKRUNTfkWL5gRm/7ZkdDJElVpOvhRyhs3pw0GhpoaH3ONm8awEQs0TvphBDWcxgFNJLGR+uS2Wx4Mtln8+aNO3jri49NOSJJkkYmf13FKEhrK5nGxhSjqR6OhEhKXWVdyN1bd3Mg35ViNJIkjVzfqVguzTtSJiGSUjdnWiNL5rUAUOgucdvmI96mRpKkcde9axed6+5OGpkMDatXpxtQFTEJkTQprFpyaDTk5g0u1StJmvzy198AxSIAuRUrqJs1a5ge6lE1NSExxufsqhhCmDR1HTHGbcAi4PdDCLeMwf1yQM+clCUhhG1Hes/yfc8A7up3+IYQgruWK1WtS+bw0/VPAnDrpmcodBfJucShJGkSc5f0w1c1SUiFZ4DugU7EGM8CflVuHh9C2DrIdf8H+Nty8xMhhI+OcYyTWRfwdPl5M+D21JoUFs9tZs60BvYc7ORAvsA9j+7hzBPmpR2WJEkDKrW303HT2t52wxkuzTsa1ZiEnDlYcjESMcZPA39Vbn4khHDpmEQ19krAxvLzMavSDSHcCywAiDFeBHxprO4tHYlMJkPrktncVJ6KtXbDDpMQSdKklb/5Fkrtyd5W2WOOIbfomJQjqi7VmIQclhhjBvg88J7yoQ+GED6dYkhDCiF0AyvTjkOaSK3HHkpCbt6wgw++biWZzKSZdSlJUq/8ddf1Pncq1uhNiQnXMcY64CskCUgJeN9kTkCkqWr5ghk012cB2L43z+an96cckSRJz1UqFslfd31vu+EMk5DRqvmRkHKB99XAO4EicFEI4cph+hwPfAh4LbAYKAAPAd8GLgshtI3wta8C3gV8K4Tw9iGu+yjwD8BdIYQXVcQ9YGF6jPETwEeAr4QQLoox/hnwXuBkknqZdcClIYQbRhKnNFlk6+o4ZfEs1m3ZDSRTspYvsGxJkjS5dP7mHoo7dwKQmTmT3PIVKUdUfWp6JCTGWA9cQ5KAFIA/GUEC8ofAg8BfAMvLhxuB1cD/BW6NMc4fYQjfKD++IcY4fYjr3tHv+hGLMV4J/DtwGkmSNRN4FfCLGOObRns/KW2VS/Wu3bAzxUgkSRpYn1WxVq8m42qOo1bLP7FG4HvAW0hGFN4WQhjyQ36M8SUkiUAW+Efg2BBCC9ACrCEZYXghcNUIY7iBZCWqFmDAhCDG+ELg+SQJxLdGeN8ebwHeBrwbmBVCmAmcCNxC8nd7WYwxO8p7Sqk6ZfEssnVJHcjGp/bx9N72lCOSJKmv/C8q60FcFetw1HIS8k3gPKADuCCE8L0R9Pk0yRS1D4YQLgkhPA5JkXgI4TbgXGA78AcxxlOHu1m5uPzb5eY7B7msZxTkVyGEp0YQY6XZwJ+FEK7omSIWQnikfM8ukqlkLx7lPaVUNTfkWL5gRm/75o2OhkiSJo/CI1sobNqUNBoaaGhdlW5AVaqWk5DTyo9XhxD+a7iLY4wnAS8BDgJXDHRNCGEXcG25+ZoRxtEz+vKaGGOf9UbLK3a9vd91o/FICOE5oyfl+pG7y80XHMZ9pVS1unu6JGmSav/Ftb3PG1pbyTQ2phhN9arlwvQ7SEYBLo4x3htC+Pww168pPzYCj8YYB7uup7ZjyUiCCCHcHmN8mGSa1B8CX+z3mseRjNb850ju18+6Ic49UX6ccxj3lVK1aslsvn3HYwDcvXU3B/JdTG+qTzkqSZL6T8VyVazDVcsjIX8K/Lz8/LIY438f5vqF5ccccPQQf6aVr2sZRSzXlB/f0e94T/unIYS9o7hfj6HWL82XH/3kpqozd3ojS+Ym/8QK3SVu2/xMyhFJkgTdu3fTeVf5O+BMhobVq9MNqIrV8khIJ3AB8BPgbOCKGGM+hPD1Qa7vSch6l8kdQ18nWVL392OMi0MI28oF439YPn84U7Gkmrbq2Nk8vjtZDfvmDTt5zQsWDtNDkqTxlb/ueigWAcitWEHdrFkpR1S9ankkhBBCHngjcDPJe706xvjWQS5/uvx40livKBVCeBC4F6isATkbOArYR5IoSarQuuTQTMLbNu2k0F1MMRpJkvotzetUrCNS00kIQHnVqNcDt5MsvfuNGOMbB7j0tvLjTJIEYaz1jHb0rJLVMxXr++VkSVKFxXObmTOtAYD9+QL3PLon5YgkSVNZqb2djpvW9rYbznBp3iNR80kIQAhhP8nyur8hqZH4dozxnH7X3M+hQu9/ijEOWvMRY2yJMTaMMoxvAiXgtPLeIBeUjzsVSxpAJpPps0rWWlfJkiSlKH/Lrym1J3tXZY85htyiY1KOqLpNiSQEoFz4/RrgPpIVsL4fY3xlv8v+kqSW5IXA2hjjq3qmZsUY62KML4gx/j3wMMlUqtG8/uMkmwhCssP5LJIpYDcc5luSal7rsRVL9W7cQalUSjEaSdJU1mcq1hlOxTpSUyYJAQgh7CZJRB4EmoEfxxhfVnH+DpJdyPcDq0kShLYY4zMkq039FojAApJRjdHqGfU4vfz47fKGhpIGsHzBDJrrkxKt7c/m2fz0UAvCSZI0PkrFYlKUXmY9yJGbUkkIQAhhB0nNxyaS5XZ/GmN8UcX5nwDLgUuBe0iSj9kkBeS/Bj4KrAwhPMHofYdkJ/MeTsWShpCtq+PkxYdWHnFKliQpDV33rKe4cycAmZkzyS1fkXJE1S9TLdMbYow9gR4fQtiaZiy1IsZ4EfAl4IYQwqvTjkeJGOONwCuOO+44LrzwwnF7nbu37B63e4+ldY/s4sq1jwBw0sKZXP2el6YckSRpqtn7j/+HA5d9DoDGV76SGe97b8oRjUz981dSN2dC9q3OjLbDlBsJkVRdTlk8i2xd8rtt41P72LHXxeQkSRMrf61L8461atyscEuMEYAQwqizrqkuxngGcFfacUgj1dyQY/mCGWx4ch8Aazfu4K0vOjblqCRJU0XhkS0UNm1KGg0NNLS2phtQjaimkZCnB/ij0eviuT/H6piXoylrVcVSvTdbFyJJmkDtlatitbaSaWxMMZraUTUjISGEBWnHUAtCCPeSrO4lVY3WJbP5zh2PAXD31t0cyHcxvak+5agkSVOBu6SPj2oaCZE0Rc2d3siSucn+oYXuErdv3pVyRJKkqaB792467yrvZZ3J0HD66UN30IiZhEiqCqvcPV2SNMHy110PxSIAuRUrqJs9e5geGimTEElVoXL39Ns27aTQXUwxGknSVJC/7rre507FGlsmIZKqwuK5LcyZ1gDA/nyBex7dk3JEkqRaVmpvp+PGm3rbDWecmWI0tcckRFJVyGQytLpKliRpguRv+TWl9nYAsgsXklt0TMoR1RaTEElVY1XFlKy1G3dQKpVSjEaSVMv6TsVyFGSsmYRIqhrLj55BU30WgO3P5tn89P6UI5Ik1aJSsZgUpZdZDzL2TEIkVY1cto5TFs/qbbtKliRpPHTds57ijuT/mMzMmeSWr0g5otpjEiKpqvSpC9m4M8VIJEm1qs8u6atPJ5P1I/NY8ycqqaqcvGgWdZkMABue3MeOvfmUI5Ik1Zr8L6wHGW8mIZKqSktjjhULZvS21250SpYkaewUtmyh8NBDSaO+nobW1nQDqlEmIZKqTuUqWbeYhEiSxlD7tRVTsVpbyTQ2phhN7TIJkVR1KutC1m3ZzcF8IcVoJEm1JF9ZD+JUrHFjEiKp6syd3sjiuS0AFLpL3Lb5mZQjkiTVgu7du+m8a13SyGRoWH16ugHVMJMQSVWpcjTEpXolSWMhf/0NUCwCkFuxgrrZs4fpocNlEiKpKrVW1IXctmknhe5iitFIkmpBn6lYZ6xOMZLaZxIiqSotntvCnGkNAOzPF1j/6J6UI5IkVbNSezsdN97U27YeZHyZhEiqSplMhlVOyZIkjZGOX99Kqb0dgOzCheQWLUo5otpmEiKpalVOyVq7cQelUinFaCRJ1azdVbEmlEmIpKq1/OgZNNVnAdj+bJ7NTx9IOSJJUjUqFYvkr7u+t91wxhkpRjM1mIRIqlq5bB2nLJ7V277ZKVmSpMPQtf5eijuS/0MyM2eSW7Ei5Yhqn0mIpKrWZ6led0+XJB2G9muv7X3esPp0Mlk/Io83f8KSqtrJi2ZRl8kAsOHJfezYm085IklStcn/4rre59aDTAyTEElVraUxx4oFM3rbNzsaIkkahcKWLRQeeihp1NfTsGpVugFNESYhkqreqopVskxCJEmj0V45CtLaSqapKcVopg6TEElVr3K/kHVbdnMwX0gxGklSNcm7NG8qTEIkVb150xtZPLcFgEJ3ids2P5NyRJKkatC9ezedd96VNDIZGlafnm5AU4hJiKSaULlKllOyJEkjkb/+BigWAcgtX07d7NnD9NBYMQmRVBMq60JufWgnhe5iitFIkqpB/rrKVbHcoHAimYRIqglL5rYwZ1oDAPvzBdY/uifliCRJk1kpn6fjxpt629aDTCyTEEk1IZPJ9ClQX+vu6ZKkIXTc8mtKbW0AZBcuJLdoUcoRTS0mIZJqRmufpXp3UiqVUoxGkjSZtVeuinWGU7EmmkmIpJqx/OgZNNVnAXjq2XY2P30g5YgkSZNRqVgkf931vW2nYk08kxBJNSOXreOURbN62zc7JUuSNICu9fdS3JH8H5GZOZPcihUpRzT1mIRIqimVU7LWulSvJGkA7dde2/u8YfXpZLJ+JJ5o/sQl1ZSTF82iLpMBYMOT+9ixN59yRJKkySb/i4qlea0HSYVJiKSa0tKYY/mCGb1tNy6UJFUqbNlC4aGHkkZ9PQ2trekGNEWZhEiqOX1XyTIJkSQd0l45CtLaSqapKcVopi6TEEk1p3K/kHVbdnMwX0gxGknSZJKvXJrXVbFSYxIiqebMm97I4rktABS6S9z+8DMpRyRJmgy6d++h8867kkYmQ8Pq09MNaAozCZFUk9w9XZLUX8cNN0CxCEBu+XLqZs8epofGi0mIpJpUWRdy60M7KXQXU4xGkjQZ9Nkl/UxXxUqTSYikmrRkbgtzpjUAsD9fYP2je1KOSJKUplI+T8eNN/W2rQdJl0mIpJqUyWT6TMlylSxJmto6fn0rpbY2AOoWLiR7zDEpRzS1mYRIqlmtfepCdlIqlVKMRpKUpvZrD03FajzjDDLljW2VDpMQSTVr+YIZNNVnAXjq2XY2P30g5YgkSWkoFYvkr6vYH8SpWKkzCZFUs3LZOk5ZNKu3fbOrZEnSlNS1/l6KO5L/AzIzZpBbsSLliGQSIqmmrXL3dEma8vqsirV6NZmsH4HT5t+ApJp2yqJZ1JXn/T745D527MunHJEkaaLlXZp30jEJkVTTWhpzLF8wo7ftlCxJmloKW7dS2PhQ0qivp6G1Nd2ABJiESJoCWp2SJUlTVuWqWA2trWSamlKMRj1yaQcgjZcY41bguEFOPx1CWDBAnzXA3wEvAZqAzcC/A58NIXQP8jrnAR8GTgOywAPA50MIVx/pe9DYWLVkNt+54zEA1m3ZzcF8gWlN/vqTpKmg76pYTsWaLPxfWLVuL/BvAxx/zlqtMcY3Af8J5IFvAbuBNwCfBl4G/OEAff4S+CywC/ga0Am8FbgqxrgqhPDhsXkbOhLzpjdy9MxGnt7XQaG7xNn/eAMtDVnOfeExvHPNUhbPbUk7REnSGCps3cqBy6+g7T+/R+ngwd7j2SVLUoxKlTJu3qVaVR4JIYSwdATXziQZ9ZgFvCyEsK58vAn4JfBS4B0hhGsq+iwFNgAHgdUhhK3l43OAu4ATgTUhhNtGGfeNwCuOO+44LrzwwtF0HZW7t+wet3tPNg9se5bLb9hMd7/fd7m6DLlshkvfdiprls9PKTpJ0ljK//JX7L743ZS6uqBQ6HuysZGZH/ogDaedlk5wE6z++SupmzNnIl5q1Ds/WhMiJd4KzAeu6UlAAEIIeZLpWQDv7dfnz4FG4LKeBKTcZw9wabn5nvEKWCOzc1+eL9/48HMSEIBCsUS+q8gl31rPtt1tKUQnSRpLha1bkwSkvf25CQhARwf7/uVf6d6+feKDUx9Ox1Kta4wx/jFwLMmIxX3A2gHqO15Vfvz5APdYC7QBa2KMjSGEjhH0+Vm/a5SSGx7YTqG7OOQ1he4S37x1K3993skTFJUkaTwcuPyKZARkKIUCbT/5L2Zc9N8nJigNyCREtW4B8NV+x7bEGP8shHBTxbGTyo8P9b9BCKEQY9wCnAKcADw4gj5PxRgPAotjjC0hhOd8zR5jvBC4cICYTx387Wi07npkF8VhZp0WiiV+ft9TJiGSVOXavvf9gUdAKnV307l2LZiEpMrpWKplVwJnkyQi04BVwOXAUuBnMcYXVlw7q/y4d5B79RyfXXFspH1mDXJ+KfCKAf4Mdr0OQ75r6FGQHm2dw/ynJUma9CqL0Ie8Lu/GtWlzJEQ1K4QQ+x26H3hPjPEA8CHgY8AFI7xdT8HVaFZyGK7PVuCmAY6fionImGmqrxtRItLS4K9DSap2mWnTKB14zgKYz73OvUJS5/+6moq+SJKEvLzi2HCjFjP7Xdfz/HnlPruG6LNvoBuGEK4Crup/vGd1rEHi0CidecI8fv3QziGnZOXqMpzbunDigpIkjYuWN1/AwW98c+gpWdksDS9/+eDnNSGcjqWpqGfL7GkVxzaWH1f0vzjGmAOOBwrAIyPss7B8/20D1YNo4px9ygJy2aF/1eWyGd6xZunEBCRJGjfT330x1A3z8TaXo+W8109MQBqUSYimopeWHysTil+WH88d4PqXAy3ArRUrYw3X53X9rlFK5s9s4qKzTqQhV0fdIKuYf+RNL3DDQkmqAbmlS8kdv3Tgk9ls7z4h2QULJjIsDcAkRDUpxnhKjHHuAMePAy4rN79Wceq7wDPA22OMZ1Rc3wR8otz8Qr/bXQl0AH9Z3riwp88c4JJy84uH/y40Vk5ZPJtL3ngKv7fiKJrq68jQd1elR3YMP39YkjT5ddxxB4WNFYtWNjVBJkOmuZnGV7+aOZ/65ymzUeFk547pqkkxxo8B/wv4FbAF2E+yg/nrgSbgp8AFIYTOij7nkyQjeeAaYDfwRpKleL8L/LcQQp9/MDHG9wOfIakJ+RbQSbLx4WLgX0IIHz6M2G/EHdPH3bpHdnHl2mQwbHpTjh984OVMb6pPOSpJ0pF45o/+mI4bkzVfGl95FjPe976UI0qXO6ZLE+9XwPdJajneCXyQpNj7FuBdwHmVCQhACOEH5WvWAm8B3g90lfu+vX8CUu7zWZJE5QHgT4GLge3AhYeTgGjinL50LkfNbATgQL7A9+56POWIJElHovPee3sTEDIZWs4/P92ANCRHQqRJxpGQiXPrpp18/ddbAZgzrYHv/9XLaWrIphuUJOmw7PofF5P/6c8AaFizhpkf+KuUI0qfIyGSNAm96IR5zJnWAMCeg5388DfbUo5IknQ4uh56qDcBgWSpXk1uJiGSpqxcto5Xv+DQCilf//VWugoj22FdkjR57P/s53qfN6xeTe6441KMRiNhEiJpSluzfD4zmpJ9W3fsy/PTe59MOSJJ0mgUHn2U9h/+sLfd/JY3pxiNRsokRNKU1pCr4+xTDo2GfPWWRyh0OxoiSdVi/+e+AN3dANSvWkX98uUpR6SRMAmRNOX9/sqjaCkXpG/b3c4ND2xPOSJJ0kh0P/UUbd/5Tm+72VqQqmESImnKa6rPctbzj+5tX33zFopFVw6UpMlu/xcvh85kxf3cihXUn3JKyhFppExCJAk46+SjacwlvxIf2XGAmzfuSDkiSdJQunftou1rX+9tt7z5zWQyo14pVikxCZEkYFpjjt9feVRv+6q1j+A+SpI0eR340pcp5fMAZJcupf7001KOSKNhEiJJZa86eQG5uuRbtAef3MedD+9KOSJJ0kCKe/dy8Kqre9stb77AUZAqYxIiSWWzWupZs2J+b/uqtY+kGI0kaTAHr7qa0v79AGSPOYaGF7045Yg0WiYhklTh1S9YQF3527R7Ht3D+kf3pByRJKlSsa2NA1/6cm+7+fzzyWT9SFtt/BuTpArzpjfyohPn9bYdDZGkyaXta1+nuCf5gqhu/nwaf//3Uo5Ih8MkRJL6ee2qBfTMLL598zNseHJfqvFIkhKljg72X355b7v5TW8kk8ulGJEOl0mIJPVz9KxmTls6p7d99c2OhkjSZND27e9Q3P40AJnZs2l65StTjkiHyyREkgZwTusxvc9vfPBptuw8kGI0kqRSocD+z3+ht938hvPINDSkGJGOhEmIJA1g8dwWXrB4FgClEvzHzVtSjkiSprb2H/6I7sceAyAzfTrNr3ltyhHpSJiESNIgzq0YDfnFb5/iid1tKUYjSVNXqVhk/2Wf6203/8EfkGluSjEiHSmTEEkaxPFHTWfFwhkAdBdLfO3XjoZIUhryP7+WwkMPAZBpbqbpdeemHJGOlEmIJA2hcjTkJ/c8wY59+RSjkaSpp1Qqsf8zn+1tN732tdRNn55iRBoLJiGSNIQVC2Zw/PxpAHR1l/jGrVvTDUiSppiOG2+k67e/TRr19TSf9/p0A9KYMAmRpCFkMpk+K2X9YN02nj3YmWJEkjS19BkFefXZ1M2enWI0GismIZI0jBcsnsWiOc0A5Lu6ueb2R1OOSJKmho7bb6fzzruSRjZL8xvfmG5AGjMmIZI0jP6jId+98zEO5LtSjEiSpobKUZDGV7yC7POel2I0GksmIZI0AqcdN4ejZybLQR7IF/junY+nHJEk1bbO9evpuGlt0shkaDn//HQD0pgyCZGkEairy/CaVQt729fctpX2zkJ6AUlSjdv/2ct6nzeuWUN24YIUo9FYMwmRpBF60YlzmTOtAYBn27r44d3bUo5IkmpT14YN5H9+bW+7+YILUoxG48EkRJJGKFtXx2tecOibuK/fupXOQjHFiCSpNlXujt5wxhnkjjs2xWg0HkxCJGkUXrp8PjOacgDs3NfBT9c/kXJEklRbClu20P7DH/W2m9/85hSj0XgxCZGkUWjI1XF2xWjIV2/ZQqHb0RBJGiv7P/8FKCa/V+tXraJ++bKUI9J4MAmRpFH6/ZOOoqUhC8ATe9q5/oHtKUckSbWh8MSTtH3nu73t5rc4ClKrTEIkaZSa6rOcdfLRve2r1z5CsVhKMSJJqg0HLr8cupJ9mHInnUT9ySenHJHGi0mIJB2Gs55/NI255Ffolp0HWbtxR8oRSVJ1637mGdq+/o3edsubLyCTyaQYkcaTSYgkHYZpjTlevvKo3vZVax+hVHI0RJIO14EvfZlSPg9A9vjjqT/ttJQj0ngyCZGkw/SqUxZQn02+pdvw5D7ueHhXyhFJUnUq7t3Lwav/o7fdcoGjILXOJESSDtPM5nrWLJ/f275q7SMpRiNJ1evAlVdR2r8fgOyiRTS8+EUpR6TxZhIiSUfg1S9YQF3527r1j+5h/aN7Uo5IkqpL8eBBDn75K73t5gvOJ1PnR9Ra59+wJB2BudMbefGyeb3tq9Y+nGI0klR9Dn7t6xT3JF/g1M2fT+PLXpZyRJoIJiGSdIReu2ohPVOXb9+8iwef2JtuQJJUJUr5fLIsb1nz+W8ik8ulGJEmikmIJB2ho2Y2cf73bJYAACAASURBVPrSub3tq262NkSSRqLt29+h+HSyxHndnDk0nXVWugFpwpiESNIYOKd1Ye/zmx7cwSM7DqQYjSRNfqWuLvZ//gu97eY3vIFMQ0OKEWkimYRI0hhYNKeFVUtm97avdjREkobU/oMf0v344wBkZsyg6TWvTjkiTSSTEEkaI5WjIdf99ime2N2WYjSSNHmVikX2X/a53nbz6/+ATFNTihFpopmESNIYOX7+dE5aOBOAYgm+esuWlCOSpMkp/9OfUdi8GYBMczNN55yTckSaaCYhkjSGzq0YDfmv9U+wY18+xWgkafIplUrs/+xlve2mc86hbvr0FCNSGkxCJGkMLV8wg+PnTwOgq7vEN369Nd2AJGmS6fjlr+i6//6k0dBA83mvTzcgpcIkRJLGUCaT4dzWY3rb37/7cfYc7EwxIkmaPEqlEvs/89nedtPZZ1M3a1aKESktJiGSNMZOWTyLxXNbAOjoKnLNbY+mHJEkTQ6dt91O57p1SSObpflNb0w3IKXGJESSxlgmk/n/27vvOKmq+//jr9m+C0uXJgoWFLBgYkWMDlaisaAxTaPmm8T0Zn7fJJqY4+ebHlPsXYMlRlPVqFFjYcCKBWxYaYpIb7vL9pnfH+fO7mVZtk7dfT8fDx7Dnbkz53Mxufd+7jnnc7aplPX3+e9RVduYxYhERHJDuBekNHoUhcOHZzEaySYlISIiaXDArkMZNciXm6ypb+Lv89/LckQiItnVsGAB9fPm+Y1IhIpTT8tuQJJVSkJERNKgoCDC8aHekLueXU5tQ1MWIxIRya5wRazS6dMpHDM6i9FItikJERFJk4N3H8bwgSUAbN7ayD0vrMhyRCIi2dH4xhvUPfxIy3b5LPWC9HdF2Q5ARPLfays28cKSDSxdW82W2kbi8QQDy4rYeVgF+40bwsF7DKesuBCABxZ8wIMvr9zm+0UFEcpKChlaUcK44RXss/Ng9t91CIUF2z8n+fFfF7JpayNfO2Yi++4yZLvPl66p5ncPvgHAqQeO4/j9xmy3T21DEz/4ywLiCfjprH0ZNbg8Ff8M2yksKODYfcdw97N+YvqdTy/jjEN2paRIz39EpH8Jr45ecvDBFO26a0baTcTjbPz6N4ivX09k0CCGXX8dkaL2b383fP0bxNeu7fD3Kv/3/1F6yCEANLz+OlsusZbPhlz2R4p23rnd78W3bmXDl8+HBl8tceDXv07ZjGgPjqjvUBIiIj1WVdvIzXMW887qKgBGDy5j8thBFBUUsHFrA2+t3MLrKzZz/4IP+MHJUxg+sLTluyMqS9ljpF+cKp5IUNvQzKrNdTzzzjqeeWcdQyqKOXv6bkzeedvSjRNHV/L8kg28vaqq3STknVVV2/y9vSTk3dXVxBMwuLw4bQlI0rQ9R/DQyyvZXNvI2qp6HljwAbMO3iWtbYqI5JKmpUupve/fLdvlZ5yesbYbX36F+Pr1ACS2bKHhxRcpPfTQDr9TPHUqBUO2v74AFI4YscPv1T8xh6Kzz2r3s4ann25JQMRTEiIiPbK1vonfP/gGa6vq2W2nAXx22gR2DsrSJtU1NjPvzTU89MqHbK1vZnhoQdw9Rg7knI/tvt3vrt5cywMLVvLisg1c/ejbfHnGnkzddWjL5xNHD+L5JRt4Z9WWduN6Z3UVBREYM6ScxauraI4nKCyIbLtPkKhMHF3Z08PvsuKiAo7eZzT/euF9AG5/aiknf3RnigrVGyIi/UPV1ddAPA74G/ziPfbIWNt1TzwOQMGwYcQ3bKDu8Sc6TULKZ51GyT77dLmNglGjSFRXUz93LhWf/SyRds7vdU/MgYICCsePp3np0m4dQ1+lq6CI9Mhfn1vO2qp6xo8YwHdOmLRdAgJQVlzIcfuN4YcnT2FQedeeeYwaXM7/RPfg6H1GkUjA7fOWsrW+dUJ3MnFYsWErtQ3N23w3Hk+wZE0V44ZVsO8uQ6hvivPe+prt2kgmMHuNGdTl4+2NI/beiQGlfjjayo21/Pe1VRlpV0Qk25o+WMnWv/+jZbvi9FkZazteVU3DCy9CJELld78LBQU0LlxI84YNKW0nUlJC6eGHE9+4kcZXXtnu8+aVK2l6+23fwzJ0aDu/0D8pCRGRblu7pY4XlvqT+Genjae4kzkOIweVMbiipFttnHbgOAZXFFPb2MzT77SO0R05qIyhA0qIJ2Dx6qptvvPe+hrqGuPsObqSPUf5ZCU8PAt878yKDVuBzPSEgE/GZkxprQJz67wlxOOJjLQtIpJN1dddB41+naSiSZMonjIlY23Xz5sLjY0UT5lC8eRJFE+dCvE49bG5KW+rdMYMAOrmzNnus7on/Hv9fQ5IW0pCRKTbXluxiUQCxg4tZ5fhA9LSRmFBAR+dMAyAN1duO/QqmWC83SbBaBlmNaqS3UcOpCAS2S4JeXd1FfEEDKkoZmSwjkcmHDVpJGXF/pS7bG0NsTfXZKxtEZFsaF67lpo772zZrjg9c3NBoPXmvzS4+U8mAfVPPJHytoon7knhuHE0PP888ZrWHvhEPE793LlEBg6k5KCDUt5uPlMSIiLd9t5635MwfkR6EpCkXYf7IV4fbqrd5v29gh6Md9v0hLyzuooIPkkpKy5kl+EVLFlTtU2vw7sZnA8SVlFaxJGTRrZsz567hERCvSEi0ndV33gT1NUDULjbbhQfMDVjbTctXUrzsmVEysspPewwAEoOOphIZSXNH35I4xtvprzN0mgUGhupf/KplvcaX36F+IYNlE6fTqS4OOVt5jMlISLSbdV1fo5GZVl6a1sMLPMn7Jr6bRf5SyYQ76+vaZkXEo8nWLy6mrFDy6ko9XHtOaqSusZt54Uke0/2Gp2Z+SBhM6aMprjQT5J/68MtPPvuuozHICKSCfFNm6i59baW7YrTZxGJRDr4RmrVPeYnpJdMm0ak1FdmjBQXUXrEdP95MGG9PVsuMdad+ant/oTLDLen7MgjobCQ+tCQrLqg16UsGK4lrZSEiEjOSvYUtL1w7RSeF7LGJxXvb6ihrrGZPUM9HMlkJTkkq66xmffXZ3Y+SNig8mIO32unlu3Zc5dkPAYRkUyo/tNsEtXVABTuvDMlwdoamZBobKT+Kd8b0XYeRjIZaHjmWRK1de1+v3jqVEqPOmq7P8WTJ3XYbsHQIRRPnUrTu+/S9P4K4tXVNLzwAoW77ELRHttXg+zvVKJXRLptYNADUlXX1MmevVMd9IBUlBRu99nE0ZXMX7yed1ZVse+4IdvMB0naY+RAIhHf+3HcfmNYvLqaeCLB0AEl7JTB+SBhx+07miffWktzPMHL721iwbINfCSY+yIi0hfEa2qovunmlu3yWbOItLP4bLo0zJ9PorqagjFjKJ60beJQtNtuFE6YQPOyZdQ/8zRlRx+93fe7W6I3rGxGlMaXXqJ+zhwKRu4EjY3qBdkBJSEi0m27Dq9g/uL1LF+3ffnbVHp/ne+1GDt0+/K/4SQEWns7wj0hFaVFjB1S3jIvJFmaNxu9IElDB5Ry6B7DefodPxRr9twlSkJEpE+puf12Eps2AVAwcmTLEKhMqXvcD4FKbN3Kpp9cvN3nic2bW/ZrLwnpjZIDDyJSWUn9vHm+HG9hIaVHfiylbfQVGo4lIt22z7ghRCJ+zYv321mHIxWamuO8tMyXAZ48dvv5G3uF5oVsrW9i8epqRg8uo7Js24l/E0e3zgtJTmTfK4tJCMBx+40hOcLsucXrWfTB5qzGIyKSKom6Oqqvv7Flu/y0U4kUbt+bnS7N69bR+OqrPpbNm2l6663t/sQ3bgSg6a23aF65MqXtJ+edxDdupGnJEko+8hEKBg9OaRt9hZIQEem2kYPKODB4en/XM8tpbI53uP/aLXVs3trQrTbufWkFm2sbqSgpZNrEnbb7fERlGcOCeSGxN9dQ22Y+SFKynO9rKzazfF1yPkjmJ6WHhf/9AG7V3BAR6SNq7rqb+Bpfgrxg6FDKotGMtl//xBxIJCjebz9G/O2vO/xTMs1XzEr2mqRS2YyjiVRWEqmspPSY1Pa09CVKQkSkRz512HhGVJaybF0NVzz8Fh9s3LrdPvWNzTz2+ip+8+9FbKnt2vyR1ZvruCW2mMdfX01BBM752O6UtzMnBFqHVT3+ul+BPDwfJCmZmMTeWE08kWDYgBJGVJZ2KZZ0OmH/MS1/j725ZruFF0VE8k2isZHqa69r2S4/5eSMlqVNJBLUxWIAnQ6BKj3ySADq584l0cmDtO4q2m0Cw2+5meG33Eyp1gbZIc0JEZEeGVBaxAUfn8TNcxazeE01v7z3dUYPKWP04HIKCyJs2trA8rU1NMUTVJYVMaB020Ri8ZpqbpvnewDiCahtaGLV5jrWVfma8kMHlHD29AlMGrvjbuyJoyt5bvF6tgZletvrCaksK2b04DJWba5r+U4uGDu0gv13GcIr7/tx07fOW8r/fXL/LEclItJzW/91D80rVgAQqayk7NhjM9p+42uvE1+9GkpLKTn00A73LTngACKVlcQ3bqRx4QJKDjwwQ1FKkpIQEemxwRUlXHDiZF59fxMvLF3P0jU1LPpgM/F4goFlRUwaO4j9dx3KQbsNo7R42yRkXVV9S8JRVBChrKSQoRUlHD5xBPuMG8x+uwyhsJNqKuG1PnaqLGVIRUm7++05ujKUhGR3KFbYzKljWpKQR1/7kC/P2CNtK9CLiKRTormZ6tA6GuUnnUSkLLNVCJMroZcedBAF5eUd7hspKqJ0+nTqHnqIusefUBKSBRGt2CuSW8xsDnDU+PHjOe+889LWzotLN6Ttt6XrrnzkLd5c6at2nfLRnbno1H2zHJGISPfV/vt+Nnz1awBEyssZeu01FAzQQ5VsK548yVfpSr9ur0SpOSEiIlk0MzQ35MGXV7J6c20WoxER6b5EIkHVFVe2bJfNnKkERDqlJEREJIv2HFXJ7iMHAtDUnODOp5dlNyARkW6qf+xxGhct8hulpZSfdFJ2A5K8oCRERCSLIpHINr0h97y4gg3V9VmMSESk67brBTn2GAoG587cO8ldSkJERLJsys6D2WW4XxW+vjHO3c8uz3JEIiJd0/D0MzS8+KLfKCqi/ORTshuQ5A0lISIiWRaJRDhhv9bekL/Pf5+q2sYsRiQi0jXb9IJEoxQOH9bB3iKtlISIiOSAqeOHMmqwL2dZU9/E3+a/l+WIREQ61vDSAuqffNJvRCKUn3ZqdgOSvKIkREQkBxS06Q25+9nlbK3v2irzIiLZUHXFFS1/Lz1iOoWjRmUxGsk3SkJERHLEQbsPY/hAv+Di5q2N3PPiiixHJCLSvsZFb1D330dbtstnzcpiNJKPlISIiOSIwoICjtu3tTfkzqeXUd/YnMWIRETaV3Vl61yQkkMOoWiXXbIYjeQjJSEiIjnksD1HMLi8GIB1VfU8sHBlliMSEdlW4+Il1P77/pbtitNPz2I0kq+UhIiI5JDiogKO2Xd0y/btTy6lqTmexYhERLZVffXVkEgAUDx1KkV77J7liCQfKQkREckxR+y1EwNKiwD4cFMtj7z6YZYjEhHxmlasYOs//tmyXXGGekGkZ5SEiIjkmNLiQmZMaa0yc+u8pcTjiSxGJCLiVV93PTT5yn1FkydTPHlyliOSfKUkREQkBx01aSRlxYUALF9Xw5w3Vmc5IhHp75rXrqXmL39p2a44XRWxpOeUhIiI5KCK0iKOnDSyZXv2vCUkEuoNEZHsqb7hRqirB6Bo990pnjo1yxFJPlMSIiKSo47eZxTFhf40/faHVTzz7rosRyQi/VV840Zqbr2tZbv89NOJRCJZjEjynZIQEZEcVVlWzBF77dSyPXuuekNEJDuq/zSbRE0NAIW77ELJwQdlOSLJd0pCRERy2DH7jqawwD9tfOW9TSxYvjHLEYlIfxOvrqb65ptbtstnnUakQLeQ0jv6X5CISA4bOqCEw/Yc0bI9e+6SLEYjIv1Rze13kNi0GYCCUaMoPfzwLEckfYGSEBGRHHfcvqNJDr2ev3g9iz7YnN2ARKTfSNTWUn39DS3bFaedSqSwMIsRSV+hJEREJMftNKiMg3Yb1rKt3hARyZSau+8mvnYtAAXDhlF61FFZjkj6CiUhIiJ54Pj9xrb8fe6ba3h3dVUWoxGR/iDR2Ej1Nde1bJefcgqR4uIsRiR9iZIQEZE8MHZoOVN3HdKyfds89YaISHpt/ec/af7gAwAilZWUHXN0liOSvkRJiIhInjhh/9bekEdfW8X762uyGI2I9GWJ5maqrry6Zbv8EycRKSvLYkTS1ygJERHJE+NHDGDy2EEAxBNw25NLsxyRiPRVtfc/QPNSf46JVFRQdsLMLEckfY2SEBGRPBLuDfnPyytZvbk2i9GISF+USCSouvKqlu2ymTMpGFCRxYikL1ISIiKSRyaOrmSPkQMBaGpOcMdTy7IbkIj0OXX/fZSmN97wG6WllJ90YnYDkj5JSYiISJ4J94bc9+IK1lfXZzEaEelLEokEVVdc2bJdduyxFAwalMWIpK9SEiIikmem7DyIXYf7oRH1TXHuemZ5liMSkb6i4amnaVywwG8UFVF+ysnZDUj6LCUhIiJ5JhKJcML+Y1q2//H8e2ypbcxiRCLSV2zTCzIjSuGwYR3sLdJzSkJERPLQ/rsOZfQQXy5za30zf3/uvSxHJCL5ruHFl6h/6im/UVBA+amnZTcg6dOUhIiI5KGCSIQT9mvtDbnr2eVsrW/KYkQiku/CvSClRxxB4aiRWYxG+rqibAcgkg5mNhyYBZwE7AfsDDQArwJ/Av7knIuH9p8AdLTowt3Ouc/soK1zgW8AU4BmYAHwO+fc/b0+EJEOHLjbcB5YuJJ1VfVsqW3kXy+s4KzpE7IdlojkocbXF1H36KN+IxKhfJZ6QSS91BMifdWZwI3AocBzwGXAP4B9gZuAv5pZpJ3vvQxYO3/+3l4jZvY7YDYwJmjvDnzS828z+2bqDkdke4UFEY7bd3TL9pWPvMU09zBH/+JRfnv/IlZs2JrF6EQk1zUtW8amCy9i5d6TWXP8CS3vF++/P0XjxmUxMukP1BMifdXbwCnAA216PC4C5gNnAKfjE5Owhc65S7rSgJkdDnwfWAwc7JzbGLx/KfAi8Dszu985t6x3hyKyY5XlxdtsJ4CtDc3c9+IKHlz4Ab/89AEcPnGn7AQnIjmr7vEn2HD+V0g0NkLTtkM5GxctomHBAko+8pEsRSf9gXpCpE9yzj3unPt3OAEJ3l8FXBdsRnvZzFeD118kE5CgjWXA1UAp8IVetiGyQ2u31DF77pJ2P2uKJ6hrjHPR3QvVIyIi22hatswnILW12yUgADQ2suX3f6B51arMByf9hnpCpD9K1jJtbxbvWDP7CjAcWA8845x7ZQe/c3Tw+lA7n/0HuDjYx/UiVpEdeuz1VTQ1xzvcp6k5wV+eXsb/fmJKhqISkVxXff0NvgekI01NbL3/ASq/9MXMBCX9jpIQ6VfMrAg4J9hsL3k4LvgT/s4c4Fzn3Huh9wbgJ7tXO+c+bOd33gle9+oglvOA89r56IAdfSeVIu3NiJG88vyS9cQTHe/TFE/w0CsfKgkRkRZb//mv9ntAwpqbaZg7F76sJCSv5fDFXkmI9De/xk9Of9A593Do/a3Az4B7gOT4lv2BS4AZwGNmdoBzrib4bHDwunkH7STfH9JBLBOAo7oTfCp9dIIWoMp39Y0d94IkbW1Q6V4RaZWoqel8JyBRV0fptGlpjkb6KyUh0m+Y2bfxE8nfBD4f/sw5twb4aZuvzDWz44En8VW2vgRc3s1mO3pOvQyItfP+nsOHD9959OjR7Xwk0qq8pJCtDc2d7ldRolO9iLSKDBhAorq68/0GDshANNJf6cok/YKZfQOfQCwCjnHObejK95xzTWZ2Ez4JOZLWJCTZ0zG43S923lOCc242vrxvezoZZCMCM6eO5b4XV9DUwZisooIIM/cfs8PPRaT/qTh9FjV3/qXjIVlFRVScfkbmgpJ+R9WxpM8zs+8CVwGvATOCClndsTZ4bXkkFAzL+gAYaGbt3eFNDF7f7mZbIl32ucMnUFTY8XjfosIInz18QmYCEpG8MPAr5xMpLu5wn0hxMQPP/1KGIpL+SEmI9Glm9kPgj8BCfAKypgc/c1jw2rYW6uPB68x2vvPxNvuIpNy4YRX88tMHUFZcQFHBtslIUUGEsuICfvnpAxg3rCJLEYpILiqaMIFhN1xPpLwcitoMiikqIlJezrAbrqdowoSsxCf9g5IQ6bPM7GL8RPQX8UOw1nWw76FmVtLO+0cD3ws272jzcXK9kR+b2dDQdyYA3wDqgT/1NH6Rrjh84k7c8fXpnHrgOAaUFhGJwIDSIk49cBx3fH26FioUkXaVHT2DkY8+woCzziJSORAiESKVAxlw1lmMfPQRyo6eke0QpY+LJBIaei59j5mdi59v0QxcSftzM5YF8zKSZXj3AeYAK4LP96d1LZCLnXM/b6ed3wMXBN/5O1ACfBq/zsi3nHNX9fAQ9H9MERERyRfdrgWsienSV+0WvBYC393BPjFaJ4bfDswCDsYPpSoGVgN/Ba5yzs1r7wecc983s1eAbwLnA3HgJeBS59z9vT8MERERkb5HPSEiuUn/xxQREZF80e2eEM0JERERERGRjFISIiIiIiIiGaUkREREREREMkpJiIiIiIiIZJSSEBERERERySglISIiIiIiklFKQkREREREJKO0WKFIP/TQQw+xatWqbIchIiIiaTZ69GhmzpyZ7TC2oyREJDd1e9Gf7njuuefeBPZOZxsiIiKSfcuXL39r5syZk7IdR1tKQkT6p4HB62ZgYZrbOgAYnKG2uioXY0qVvnxsIpIeffm8kWvHlsl4km0N7GzHbFASItI/vQvsDCx0zkXT2ZCZzQGOykRbXZWLMaVKXz42EUmPvnzeyLVjy2Q8obbeTWc7PaWJ6SIiIiIiklFKQkREREREJKOUhIiIiIiISEYpCRERERERkYzSxHSR/mk2MAdY1sfa6qrZ5F5MqTKbvntsIpIes+m7543Z5NaxzaZ/X39bRBKJRLZjEBERERGRfkTDsUREREREJKOUhIiIiIiISEYpCRERERERkYxSEiIiIiIiIhmlJERERERERDJKSYiIdJmZRdL8+0PT+fvdZWY7ZzuGdOnLxyYiIrlPJXpFpF1mNhkYA0SAd51zy4P3I865lJ84zOwW4APgGufch6n+/R7EcxtQCPzMOfdmtuNJpb58bCKSWma2B7DUORfPdiySPum6tndEPSEish0zuwp4EHgU+C/whJndYGYD0pSAXAGcB3wVONfMRqW6jW7GcylwNvAJ4Dtmtlc240mlvnxsIpJaZvY48HfgI+nuCc8GM/ukmY3OdhxJZnZMFtosAkhe2zP537nwkksuyVRbIpIHzOwe4FPAs8B1wCvAQcCRwIxYLLY4Fot9GI1Gm1PUXjHwSWBP4J2g7apYLPZONBqtSUUb3RWLxaYDBwAvAGcCpbFY7O1oNLo+G/GkUl8+NhFJHTP7EvAtYDSwL7AwFoutikajWY0rVczsUeAHQHUsFnstGo3WZjme/wIuFoutjEajL2WgvXNisdj/AF+MxWLTY7FYYywW2+ycqzWzgmg0mvZeEfWEiEgLM7sIOAX4JXCuc+4y59wPgaOBD4FpwBXADDMrTEWbzrlG/A1xHPgTsBi4CPifZI9IFp7AvQEMAG4BHga+CHw/2WtgZvl87uzLxyYiqdMUvP4TOBB/7v9oX+gRMbNDgaOArcDFwAVmNjyL8ZwMHAPUA9eZ2VfS3N7fgJuALwPH45PNe4HbzWyCcy6eiWuBLjYiAoCZlQNRYAVwrXNug5lFzKzQOfcG8AugAdgP+D2QypvW1UAj/qb4x8ByWhORcc65hJkNNrOxKWirKz4ANgNLgzhitN6sTwlO0MPNbM8MxZNKffnYRCR1ngZWAv8B/gwcDlzGDhKRPEtOlgIbgSeBp4ALge+GE5EMH88i/Hk5hv83v9bMzk9HQ2Z2K3447u/wIxD2AD4HvAt8HHjGzKZmIhFREiIiSSOBjwDrnXNrQ+8nu2TfA0rwJ8kpwB8BUjRZ8VmgFDjEOXcf8DNgGT4hmWVmBwJzgW+Y2cAUtNeZhUAzcIRzbgHggMfxN+tfNrOjgGcAZ2ZDMhBPKvXlYxOR1FkNDMGfL34I3AxMxycihwCY2TAzO87MCjI9qbmngl78Tfhe95eA/wNew19vvhs8hCkIHn4VZSCeAnwCshr4F/DdYPu6ZCKSjKO3SYGZfQI4HT/P5w/OuZXOuTX43q6f4h9SjQIeM7NJ6U5ElISISNIGYC0w3swOBz9RLZRkfAw/P+Rr+CE9x5vZSSlquxaoAvYPtv+G73l5G/g1foL8XsAbzrnqFLXZruDpVzOwBpgUvP0UPjF6CN9tfT8wFvivc25TOuNJpb58bCKSOsGNejXwMjDdObce+BWticivzOxE/Dy+bwG7ZCvW7nLONTvnGoAlwDHOuceAn+CP9cfABcHN91jgJ+nuFXbOxZ1z6/CjEGY65/6Bn6uyEZ+IfM051xSUVf+imQ3rRXN74Yfj3uWcW5dMMIJ/j6eAOvx/92HAP8xsbDqroikJEZHkBacO3+0+BF816YDQ55/FT2JeHZR0vSj4aL8UtF0QXOAWAgcEw7/izrm7gBuBIqASP1Trsd621xXOuVrgOXxFmEog4pybhx9D2whU4J+gzQ+OIeeGIZjZlPbe7wvHJiLpFdyoN+MfPB1pZkXOuSX4RORK/NDdvwPFwKPJEu75IPRkfxEwzsyKgx54hz/eC83scuB1/JyJnTIUz2KCYc7OuRtpTUSuNrMf4ntrLgZ6s8bTrsHryOA1EkpE1gM1wDX4h1GT8dUqI5am3hAlISKSvOA0AnfTWjXpbjO7z8wewScDxfgTMvguW+jF06/kzW3oKcu7+AoslcHnO+GfSjUAq4Bjgc+achlcEwAAG+VJREFU2biettkVoSEFi4HxwMDgqdho4Kognrfw46O/bmb75towBDO7F/h52/f7wrGJSGoFw123GeoTevjwDjACKAseEC0B7sRP6C7Dn5ufyWzEvRO65jyGTzAOC96/D/gmvqf/W/gHYFc65zJ1fI8CY81snyCem4Hz8UOzfoVfs+tSfDLSU68Er58J/ns2B9eAQjM7Dz8/5Hn8tXcdcFybEREppSREpB8yswPM7Bwz+5qZHZt83zk3H/gO/iJTiZ+8tjd+rZBpzrn3gl2X4ueK1HexvXFmdpSZTTW/8BXBeNvwE5aXgeFAY9DtvBAox49F/j7wJn4i3Zm9rcxlZoea2Vlm9plgDkT4s+Lgry8Ag4DyIJ4Xg3h+hE/GHsJfsL4Y+k7WBQnIycBpZvbxNp8lbyzy8thEJLXM7CHgeTPbNXyjGXr48BQwGPiYc67ZzMbjh8s24ieu7wn82sym5WKv6Q4Sq6R1+EQjvC7Vm8F2E37Y0kAzq0hhPNtdu0L/7svx/9YjQh8/gb/WJvDn7Ibg2tml+/d2jvlh/IOm44B7zexYM5uIv8ZejB8SNhffC/Qavhds13T9t1USItLPmNllwAPAbOBq4BHz9eABCJ76fAv/NPwkYAZwtnNuRehnvog/ST/ehfZ+hb+pfQJ/QbvHzE4P2kqeXME/TWsGvhTsVwZc7Jy7xjl3N7485DPAf4JhAj0SVAZ5GLgdn2w9YWZ3mNkpQUyNwa6v4sfGfqFNPNc6557CVwi7B7gh9J2sMrP/4MspPxi8dWLwhCvZ3Z78t867YxOR1DKzB/DlWQE+HbzX9r5wM758eiS4GX8af3P+Pfyip9fgrxE/xRcuyTUthUySD76g5Tjfw/fAHxW8twewINj9JnyvwQ+AX/RyHkbYNjfzyX/v4DVZsSvZM7UH/uFcHH+t2ghcZWbf7UbPRDihwTn3AXAqPuE5ET/s6mX83Mt6/JyUtcHvL8DnCWmbnB9JJNTTLtJfmF+I8Bh8UnA7fkjO5fhKIR8FlidP1OFhOOHtoLrGb/BzSE5yzq3qoL178b0prwV/xuDHEq8DzgjmIiT3nYAfo1uGfxrzS+D6Nqu4DnTOVfXi+O/GJ1Z3Bv8GOwPn4ifErwKuBX4d/BuMwlftGg+8j+8Ov77Nv0uZc66up/GkUpCAzMCXmnwOuBU/v+OQ4MKT3K8AGIrvDcmLYxOR1ArOF1F8r8YpwEvOuaPb2a8YX8Z2E74qYiX+HHND0DOyB/Bt/PljUYbC75SZ/Qg/zOoQ/Py2F4HfBBOww/s9jC+K8rVgnwHAhc65G8zsOHwyUgns3aZqZHfjORO/SOwh+Id385xzT7az3yvAHHxhlhfw5/AfOeduNLOz8NftzcBuHRUOMbOv4v/7noj/73efc+660Ofjga/gr30NwbHfGFTKSu7zMH4OyZR0DctVEiLST5jZTfjVyH8FXOec2xi8fym+K3aic25xm++Ek4+CYL8v4odNRZ1zr3fQ3rXAZ/EJy3XOuY3BROhL8E/RLnTO/aZNG9/AP3m6DLgs1O2c6O1J0Mw+h6/schXwi+QJ3Mz2xpcs/AF+SNJvgEuCts/Cj429Abg8GU86q4X0ROiG4sf4m4EaM/sz/t//0uD95jZJxmfwTy9z+thEJLVC54sf4h/G/Am/EO2XnHO3tLP/3fh5gkvx55Prk+Vrg6pNRc65prbfy5bgYduJ+LmLtfh5DsXAPHwv72POuZpg31/hS+JW45/4XwjclDweM5sJvB3MhelpPHcAn2Hb0UcLAXPO3RvsUxDMzfgzcCS+V6mknXjOBp53zr3VQXt/xvd2bMQ/8JuMn8PzJefcP5NzQTqJ+UzgOnyS+m2gMR2JiIZjifQDZvZF/DyBm/EXkI2hj4fgS/MmzOzjZhZNjlsNd1/jK4f8CP8U5shOEpBT8SfBu5PtBclGFX5V1kbgJGutxZ6cpH41vqfisvBNcYpOfnvju8Jvd85tsqDuenAyvwafGNUAFwR/xzmXPJnn7E26mT2BL5l5Ef5iVRN89Bv8f9dDgXhoDk7y3/ou/BPQnD02EUmtYAhWFP9g4jbn3NvAH/BDfg5vs2/y3P8DfI/A9bQmIAXJG+McS0AuB04ADDgYv/bVofhkaxp+fatzzGxQ8JWHg9cG/Dn0+iCxKgZwzj3UywTkb8As/LX3I8Bp+H/L/YBPhebcJa9x9wKj8cOdw/GUBPHc0UkC8g/8ef2a4PinA9/AzzXZL/iN5mDfotD3CkN//2TQdi1wqXOuIV09IUpCRPq4oPchil8b4jLn3IbQZ8fjV0gtAR7BzxV5HLjDgoopoZPP74D/AU5xfgX1HbVXgn/qsxN+aNOGNsO7FuAXIhxAcOINn+Ccc6+l8qY4NMZ5z+A4kxefcJubgb/ik6w48AUzmxZ8/G6u3qSbWRQ/nvnnwM3OuS2hG4eV+OFtRxJUNXO+ykk46cvZYxOR1DKzJ/FzxpJP1zcF58fX8HMEvmBmhyX3T56XnS+/+33n3G9z+XxhfrXzmfjhR1c6v/ZG3Dm3EF9l6lL8Q7cLgU+b2QDn3BzgDPyChdeFjq/Xc+HM7Mf4IbK/wvf8v+x8Ba4r8FXHPkmwXlPoGvgofpjUz9vE07BdA9u398ugvd/ir72rnHNb8T1A9fhEpEWQ3CSvBc1mVhwkqb/Dj3aY2XZ0RKopCRHp44Lehxvwk8uXhybmTccPjRqJP+F9FZ+Q3Is/OX41+RtB922Vc+5e59zqTtprwE90u8E5tzT4bvgpSjN+PkkJwTnI2kyGDJKWVF3kkm3PDV5PCOJsDt2wE5ys/4X/t9oH3wMSvhDn3EU3uIBOxj8t2xJO9oIL8B+CXY83s4rQBSfR5ndy7thEJHXMbDd8L/b/AbeEzhfx4Mn6Hfie4s+ZWVHbc3JwHUn1uTnVdgEm4he13WJmJc65xiDmFfhekD/iH0RdgO+ZAHjEORfu4UnFw69JwOfx1bZuDh7GJUcYvIbvmSmm9aEYwWcbgD87XySky/GY2dH4h00P46+9G0IfH4G/3ibM7G9m9h8zuzQYRtdSaStIvDbh5xQeHcSZVkpCRPoB59w859zLyZtUMxuCny9wIL5n4/fOuUedcw/jE5N38eVZt+m+7YbLCNapaPvd4Ga/Cj/+tjh8kjWzXYJ9Utb1G/qtF/DDwH4cjHdtO9wseeN+N34s7flmNsZysOwkbLPOylvOuc1tepuSng/+nARozQ+R/msZvgjH5eEHFqFk4y/BPscDFc7PT9ju3Jfj55A1wBb8BHqccw2h44wE5/frgVvww3N/FOzXMpwshQnWeGAsfjjTh0H7zaEhUMlqky0LD4bO6S2l77sRz9v46+pvww8KzexIfLXLAvxwrKH46/738YtNEvy3TiZIZwFfcM69283j7RElISL9SOgp+Sb80KtpzrmHzKwgmC9Q6Jx7GV+dA3ylqp60U+ec+7CDXQrwCUE8lIDMBOaY2Zc7+F6POedexI9tBrjIfOWTtmUbI865F/C9QUOAsly96LbTm7FdnM5XLvsP/inYd8xsQK4mVSKSPsFQzHXBQ6D2eniX4SdL74WfqJ3rCUd7qvFld49OXkdCCUjydS1+ONSr+BLmn05TLO/g19x6OhlH8H7yoVyyYmE9tExM3+bfu21v1I4E312Br2K1IJlQmNkh+NK7k4HPAZ90zh0LfAx4CTjFzC4M4msOJUFbe3C8PaIkRKSfCZ1o/uOceyncvR7qtZiIf1LzThraL8F3Qzcnx7kGc1N+BozD91ikus3kjfef8ZMCp/q3bSa0XKiKQxeBEfinajssgZjrQhewa/BzQw4Eytv2/ohI/xZcA+rw5+DNwOFmVpr8LKvBdVFwI74Fv+BeHXCumR0B7SYiy/DHmsCXoE055yez/821KevbTmJXG7yffBh3lJmdG36vC20l96sPtpPX8VpgAr6U/l3Bv0+yGMuF+Mnvu3QQW9opCRHpZ9p7gh5+CmN+4cJD8Kuk16ah/eQEu4ag9+UEfCWnvYGDnHMLdvztHrcZnidxGX7882HAFWZ2XvBZI4CZnYQfKzyfLq4In4tCF6YqfA34vfBd8Pn4hFNE0iT0YGIlfqXs4/FVnPLmXBE6380H7sJX+vq+mR0cfJ48xuR970r8HJi0JCFBm9Vt3wsldclEoSz02fH469NPzGxE2+92ob22a3u9Ckx2zj2WfCgVGg62GT8kOqsLTCoJEenn2szJOBlfnnY98PPw2NRUtoc/ARfhFzL8Nb6O+xHBSTOtnF9Q6xfAlfiKWbeY2V1m5szsiuD9MuB/M9ktnS7OuVp8tZNNwHHmF2EUEWkRDNdajS/MAb58bHlXhwTlimAY8LX4h2inAj8ND70N9RIciH/IlPKe904kk5BkSdzkcKwT8NfCPfEL+a7rTSOhhCTZ+xEPEpPk/JdPBW0/GLSflR4vLVYoIska4d/Grxo7FJiRrsoYZlaOX4l8OH4hpd3xCcgr6WivgziK8SdiB4zCr4q7AV/N5HyXQ6v/JvWkcktwE1ECPIZfsXd8by9wIpKb2jxUaq9YxY6+lxyutBPwD/yaGvs4v45I3gmqP16IL9n7Br4E+xX4B2Az8ef9EnwVqA929DtpjO8cYDa+ZHJzENsewPR0PIxr87+L0/AP25bi54ms6fDLaZRXGa6ItK83TzGCilQv4muZrwc+1lkC0sunJnH8wlBj8XNAep2A9CQe51yj84sRHosvYXg2/oJwaq4kIEHBgJHm13oJjxvu8vE6X4KzDt/Nf5ASEJE+rSL5l+7M/woNWV2Lr45YSOuQobwRmvP4FPAT/HlvN/zihQvwE9Jvxj8EOyMbCUgg+d9lJn4V97SOBghdOz6Pnw9TgX/YlrUEBNQTIpLXzOwA5xdi6tZTrza/MQC/OFIZMNs5tzKd7QXf/SPwReCw3tzw9yae3sSfCWb2f/hFJg8EVgH34eeyvOp86cmu1o/P6eMUkd4zsx/gVwY/GL/Ow/PA713r6tidngdCvSFDgCHBBO6c0ZNznpmV4UvTfg9fNjeBnzdylevFSujdiae97wRzL28AtgYxTe/sYVxP2gu+F8EXW7kUv7htAl+aP+3rgHRGSYhInjKze4GTgY87v75HbxODotB40bS2Z2YjAXrzFCbVx59LgmM7HliML505DT9MLrmo2GXOuZqeXpREpO8ws3uAE4EP8eP8d8ePdHkMvzjfE8652u4kIumOuTvM7Czg386vb9Ktc16bqlgpOa7exBP6jTPxa1JtBQ51zr2ervbMbCh+qPX/A54AfugytA5IZwovueSSbMcgIt1kZlfhhw8BnBiLxV6KRqNLotEoZhaJRqOdfX98LBbbNRqNtiQB0Wh0hye2VLcXjUZrotFoTWfHmal4comZ/QK/qJgDvuecuzEWi/0HX+VqGn5V+2GxWGyuc67ezAqi0Wi4KsqEWCx2UCwWWxWNRhuzchAikhFBMY1P4ReH/Qp+bsED+CFIUXzvSHUsFnsrVJmwvd8pjkaj8c7OnZkWJFg/AojFYvPbO+d1JLgmFCT/Hvxmp9eIdMWTFIvFIvjhbl92zr2Rzvai0WhdLBZbhp/rM9t1vIZXRmlOiEieMbPPAl8AngKuAoYBfzOzY6HzccBB6b9/Ai+b2bRcay/f4kklMxuIn5fyKnC1c26N+QUkX8WXMf42fpGrrwM/M7OK8FOx4InXDcAj+MpjItJHBT3KHwfmAlcE8zmanHPPAV/C94KMwk/QPtOCtT9C359kZhdBa4nyXGJmvwZOwa/78S3gR2Y2MBjO1On9azAUa7v1NnoxWiAl8QQxvA78wPk1OzLR3vvOuZecc5s7+14mKQkRySPmy6t+BigHvuac+zZ+QvlgungjHkxMTk5OXtvePtlqrzO5Fk8ajAY+Cqx1zlUHQ+SaAZxzG4F78InI+/g5NedZsDpuaJ9l+ONK+XorIpJTdsFPaH4tGKpTkkwmnHPL8ROeL8fPB7gAv/4RZlZovjrgb4Gfm9n1WYm+A+YrOJ2Pr1b4Vfy8uAvo4o24mU0E/mxmp0Dv1ztJdTxBTDssgZ+O9nKRkhCR/NKAX8X8S8lJZc65H+PXvWj3Rjx8M548aTnnTgDGdmFcaKbby7Xjz7QP8PNAxgZjf5vCF5pgOMV/8UO1moDP4eeKtCxC5Zw7H19aM+Wr3YtITlkL1ACTwJ8fwuc759f9uBa4DdiX1sVKm4Nk5efAcuCaDMfdoeAJ/qfxD5u+4Jy7Hf/w5UP8MXTlRvxEYBZwqZlVdNQ7nmvx5Nrxp5OSEJE8Ejzp/hm+5nlyfQ+ccxfTzo04EF4JPVmVI3mzuirX2su3eFLJWlfzfRt/w/ATaFlkKpyI1AEP4YdcHY7vGSKcsDiV4RXpD6rxDy4+bmbnwva9wMF57nL8eeUMMzsdWgqRzAf2ds69nPnQdyw4x/0WP1zpueDtR/E9Aitp50a8nZvsG/E9QWc457b2pick0/Hk2vGnk6pjieS5YM5Asgzjz4AfA5uBz7jWqlFfw09U/Glwgsub9vItnt4ys8OBGP4G41vOuTuC97epimJ+FeCHgWucc9/MSrAiklVm9ingduBp4ELn3LPB+9tUhTKzs4FbgQucc5eHvp9z1bCSzKw4PFcleOh0NL53Z2f8TfavnXPVoX1GujStfZHpeHLt+NNB1bFE8lw0Gk2YWWE0Gk1Eo9EnYrFYEXAc8IlYLPZ8LBY7APhd8N610Wi0Kp/ay7d4eiO4IXg/FovVAicBU2Kx2JpoNLooeZyxWKwgGo0mYrFYPb6L/p1oNPqv7EYuItkQi8Xexz9gORkYFIvFFkej0VXJSoFA8nwxFDgPeDMajT6c/H6uVcMKa1uxMTiO5cAi/HoXJwDFsVgsFo1Gk2tv/DEWi70cjUZTvghhpuPJteNPByUhIn1AOzfi4FdiPRU4PdjtUOfc4nxsL9/i6ankDUFwoSnEJyIHxGKx2mg0uiA4vkSwz5n4Cli3RKPR+VkKWUSyKBqN1sdisefxk85PAkYGDy6WRaNRQueL0/Ale6+LRqNpWZU7E0I34q/jb8SPA0pisdjewMXArsDl0Wh0fV+MJ9eOv7c0HEukDwmqozQEf/8X/iZ8I3Ck62AxpHxpL9/i6a7wkCszmwB8E7/SbwQ/rvsm/OTEk/CVUgYDUefce9mIV0RyQ3C+uAE4BngF+Au+hDn4Mr6Gf7BxrHMuL56Sd8TMSvBz4m7CVxUsB7YAH3NZWAk80/Hk2vH3lCami+SRNpWeBrT9PHQDfjZwILAJOKKnN+CZbi/f4kmlYChWPKjoVeGcW4afbH8+vgLOd4D5+OpZNwHDgVOUgIhIcL44D7gamAz8Gl+m+xXgZvz54sw+koAUBOf6GH7Npwpaz/XZSEAyGk+uHX9vqCdEJE+EJxCa2Rn4CWqXtS3FamYnA38DtuJ7AHp0Usp0e/kWTyq1c2zHAH9IlhA2synAacDBQBxYCNzm/FoAIiKAn8yMXyX9u8B4/Krc84HLc304aneZ2RfwZYYrgOnOuUX9KZ5cO/6eKMp2ACLSuTY3qScDv8RfYKyd3dfgLzrfSlECkvb28i2eVOrg2C4Jfb4IPxlRRGSHgmpKT5rZM6GqgTlbAaunzOwI/DlyGHBQtm/AMx1Prh1/T2k4lkgeCN2knorvZq8EJjnn1rSzWNELwMze1H7PdHv5Fk8qdXZs4XVOkt9ppya8iEhYvPNd8to7wIP4G/BcGG6b6Xhy7fh7RMOxRPKEmY0A3sBPUj7IObcsvEZGvreXb/GkUl8+NhGRdAgWXGzKdhxJmY4n146/J5SEiOQRM5sOrHLOLc7ETWqm28u3eFKpLx+biIhIW0pCRPJQf3/ikmvxpFJfPjYREZEkJSEiIiIiIpJRmpguIiIiIiIZpSREREREREQySkmIiIiIiIhklJIQERERERHJKCUhIiIiIiKSUUpCREREREQko5SEiIiIiIhIRikJERERERGRjFISIiIiIiIiGVWU7QBERESk58xsDnBUm7dnOOfmZD6a9pnZJmBw+D3nXCRL4YhIDlASIiIikiZmtgwYD5hz7pJU7bsDW4Da4O8NPfh+23hmAI8Hm4c65+Z34TtDgVVACfA159x1wUergTqgEBjR29hEJP8pCREREekbvuOcm53C35sDLMcnRucAnSYhwGfwCUg9cHfyTefc3gBmNgFYmsIYRSRPaU6IiIiIbMc5lwBuCzY/Y2bFXfjaOcHrfc65jemJTET6AiUhIiIisiPJJGQ4cGJHO5rZROCwYPPWdAYlIvlPw7FERET6CTMrAM7C91gcgJ8svg6YB/zBOfdceH/n3Ltm9hQwPfjOvR38fLIXZDXwcIpDF5E+Rj0hIiIi/YCZVeKTg9uAY/G9G7XAGOBTwNNm9s12vprs1fhEMPG8vd+OAGcHm392zjWlMnYR6XuUhIiIiPQPyeTjFeAkYIBzbjAwFLgIaAIuN7Ppbb73V3xlqxLg0zv47SOBCaF2REQ6pCRERESkjzOzY4HTgGX4NUQedM7VAjjnNjnnfgVcjL8vuDD8XefcZuCeYPMc2pd8f6Fz7uUUhy8ifZCSEBERkb7v3OB1tnNuww72uTN4nWFmhW0+Sw7JmmZme4Y/MLNy4JNt9hMR6ZAmpouIiPR9hwev3zOzr3WybwV+vsia0Hv/BVYCY4HPAy702WnAIPxwrjsREekC9YSIiIj0fWOC18HAqA7+JFWEv+ycawbuCDY/H0xET0oOxXrIORdOXEREdkg9ISIiIulTF7yWd2Hf5I1/bRriSD50PNU5d18Pf+NW4AfAbsARwDwzGw0cF/pcRKRL1BMiIiKSPuuD1zEd7WRmpcCwNt9JpdXB65Se/oBzbhHwQrD5+eD1LKAQ2Aj8u8fRiUi/oyREREQkfRYEr4d3uBccgr+ZD38nlZ4JXs/o5e8kezs+ZWZltA7Fuss5V9/L3xaRfkRJiIiISPr8I3jdw8xO7WC/C4LXpaQnCZkdvB5kZjsqswvAjhYkDPwFaMDPLfkJsH/wvoZiiUi3KAkRERFJE+fcE/jKUgB3mNlXzGxw8nMz29vM7sBXmAL4iXMunoY4HgL+GWzeYl7LEDEzG2pmp5rZvcAfOvid9cADwWZyPZG3nHPPpTpmEenbNDFdREQkvT4H3IsfknUdcK2ZbcKvQD4g2CcBXOycS2eJ23PwDx9PA34K/NTMNgMRfIndpNmd/M6twCxaH2SqF0REuk09ISIiImnknFsHHIWfzP0AfpL4wODjt4AbgY86536R5jhqnHOzgE/ge0U+wFftKgHexa/x8Ung65381IPA2uDvcVpL94qIdJl6QkRERNLMOdeEv1nP+g27c+4BWodU9eT7jcDI1EUkIv2RekJERERERCSj1BMiIiLSN/zJzP4U/H2Gc25ONoMJC+bADO50RxHpN5SEiIiI5LcNtC5GmNSQjUA6sJrW1eNFRIgkEolsxyAiIiIiIv2I5oSIiIiIiEhGKQkREREREZGMUhIiIiIiIiIZpSREREREREQySkmIiIiIiIhklJIQERERERHJqP8P9kl6t2rnBXgAAAAASUVORK5CYII=\n", "text/plain": [ - "
" + "
" ] }, "metadata": {}, @@ -1048,9 +943,9 @@ } ], "source": [ - "fig = plt.figure()\n", + "fig = plt.figure(figsize=(10,7))\n", "\n", - "ax_pd = fig.add_subplot(111)\n", + "ax_pd = plt.subplot(111)\n", "\n", "ax_pd.plot(U_spin_cs, Ts, \"o\", ls=\"-\")\n", "ax_pd.fill_between(U_spin_cs, Ts, [Ts[-1]]*len(Ts), alpha=0.25)\n", @@ -1058,7 +953,6 @@ "ax_pd.plot(U_charge_cs, Ts, \"o\", ls=\"-\")\n", "ax_pd.fill_between(U_charge_cs, Ts, [Ts[-1]]*len(Ts), alpha=0.25)\n", "\n", - "\n", "ax_pd.set_ylabel('Temperature\\n[Kelvin]', rotation=0, ha='right', multialignment='center')\n", "ax_pd.set_xlabel('U [eV]')\n", "\n", @@ -1069,7 +963,7 @@ "ax_pd.spines['left'].set_bounds(Ts[-1], Ts[0])\n", "ax_pd.spines['bottom'].set_bounds(min(ax_pd.get_xticks()), max(ax_pd.get_xticks()))\n", "\n", - "ax_pd.text(0.78, 0.15, \"AFM\", transform = ax_pd.transAxes, size=22, color='C0')\n", + "ax_pd.text(0.83, 0.15, \"AFM\", transform = ax_pd.transAxes, size=22, color='C0')\n", "ax_pd.text(0.07, 0.15, \"CDW\", transform = ax_pd.transAxes, size=22, color='C1')" ] }, @@ -1077,25 +971,27 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "As we can see the two phases are perfectly symmetric for $U=0$.\n", + "\n", "The SPHT also gives information about the superconducting phase of the attractive Hubbard model, this can be seen by transforming the ladder operators of the spin\n", "\n", "$$\n", - "S^+_j = S^x_j + iS^y_j = c_{j \\uparrow}^{\\dagger}c_{j \\downarrow} \\xrightarrow{\\mathrm{SPHT}} d_{j \\uparrow}^{\\dagger}d_{j \\downarrow}^{\\dagger} = \\tilde{\\Delta}^{\\dagger}\\,,\\\\\n", - "S^-_j = S^x_j - iS^y_j = c_{j \\downarrow}^{\\dagger}c_{j \\uparrow} \\xrightarrow{\\mathrm{SPHT}} d_{j \\downarrow}d_{j \\uparrow} = \\tilde{\\Delta}\\,.\n", + "S^+_j = S^x_j + iS^y_j = c_{j \\uparrow}^{\\dagger}c_{j \\downarrow} \\xrightarrow{\\mathrm{SPHT}} (-1)^j d_{j \\uparrow}^{\\dagger}d_{j \\downarrow}^{\\dagger} = \\tilde{\\Delta}^{\\dagger}\\,,\\\\\n", + "S^-_j = S^x_j - iS^y_j = c_{j \\downarrow}^{\\dagger}c_{j \\uparrow} \\xrightarrow{\\mathrm{SPHT}} (-1)^j d_{j \\downarrow}d_{j \\uparrow} = \\tilde{\\Delta}\\,.\n", "$$\n", "\n", - "The x- and y-components of the spin operator are transformed to the complex superconducting oder parameter.\n", + "The x- and y-components of the spin operator are transformed to the complex superconducting oder parameter with a phase factor.\n", "We wil focus on $S^x$, because even if we apply a Zeeman term the x- and y-components will be degenerate.\n", - "This means, that if we find a diverging $\\langle S^xS^x \\rangle$ in the repulsive model at some $U$ we will see a superconducting phase at $-U$.\n", + "This means, that if we find a diverging $\\langle S^xS^x \\rangle$ in the repulsive model at some $U$, giving us AFM inplane order, we will see a homogeneous superconducting phase at $-U$.\n", "\n", "To calculate $\\langle S^xS^x \\rangle$ we need the spin dependent general susceptibility tensor.\n", "We can obtain this from $\\chi^{(c)}$ and $\\chi^{(s)}$ if our system is $\\mathrm{SU(2)}$ symmetric.\n", - "This can be done via the `general_susceptibility_from_charge_and_spin` function from the module `triqs_tprf.rpa_tensor`." + "This can be done via the `general_susceptibility_from_charge_and_spin` function from `triqs_tprf.rpa_tensor`." ] }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 68, "metadata": {}, "outputs": [ { @@ -1109,11 +1005,11 @@ "Two-Particle Response Function tool-box \n", "\n", "beta = 11.6045250062\n", - "nk = 256\n", + "nk = 1024\n", "nw = 100\n", "norb = 1\n", "\n", - "Approx. Memory Utilization: 0.00 GB\n", + "Approx. Memory Utilization: 0.01 GB\n", "\n", "--> fourier_wk_to_wr\n", "--> fourier_wr_to_tr\n", @@ -1135,21 +1031,19 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We can then use the matrix representation of $S^x$ to do the contraction." + "We can then use the matrix representation of $S^x$ to do the contraction with `chi_rpa_general_wk` to obtain $\\langle S^xS^x \\rangle$.\n", + "This can be done via the function `chi_contraction` in `triqs_tprf.lattice_utils`." ] }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 69, "metadata": {}, "outputs": [], "source": [ - "S_x = 0.5 * np.array([[0,1], [1,0]])\n", + "from triqs_tprf.lattice_utils import chi_contraction\n", "\n", - "def chi_contraction(chi, op1, op2):\n", - " chi_op1op2 = chi[:1,:1,:1,:1].copy()\n", - " chi_op1op2.data[:,:,0,0,0,0] = np.einsum('wqabcd,ab,cd->wq', chi.data, op1, op2)\n", - " return chi_op1op2\n", + "S_x = 0.5 * np.array([[0,1], [1,0]])\n", "\n", "chi_sxsx = chi_contraction(chi_rpa_general_wk, S_x, S_x)" ] @@ -1166,8 +1060,15 @@ "\n", "and we therefore already know where the superconducting phase in the attractive model lies, it is degenerate with the CDW.\n", "\n", + "### Linearized Eliashberg equation\n", + "\n", "We will now use the implementation of the linearized Eliashberg equation to confirm this superconducting phase.\n", - "To do this we will construct the pairing vertex $\\Gamma$ in the singlet channel via the spin- and charge susceptibilites by using the `gamma_PP_singlet` function of the `triqs_tprf.lattice` module.\n", + "To do this we need to construct the particle-particle vertex $\\Gamma(\\omega, \\mathbf{k})$ which in the case of the attractive Hubbard model is just a constant \n", + "\n", + "$$\n", + "\\Gamma(\\omega, \\mathbf{k}) = -U\\,.\n", + "$$\n", + "\n", "We can then use the `solve_eliashberg` function of the `triqs_tprf.eliashberg` module to solve the linearized eliashberg equation for the specifc $\\Gamma$ to obtain the $\\lambda$ as an indicator for the strength of the superconducting phase.\n", "If\n", "\n", @@ -1185,80 +1086,60 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 70, "metadata": {}, "outputs": [], "source": [ - "from triqs_tprf.lattice import gamma_PP_singlet\n", + "from pytriqs.gf import Gf, MeshProduct\n", "from triqs_tprf.eliashberg import solve_eliashberg\n", "\n", - "def get_lambda_delta(p):\n", + "def get_lambda_delta(p, g0_wk=None):\n", " \"\"\"Solve the linearized eliashberg equation for model parameters in a ParameterCollection\n", " \"\"\"\n", + " if not g0_wk:\n", + " H = SquareLattice(**p)\n", + " e_k = H.on_mesh_brillouin_zone(n_k=(p.nk, p.nk, 1))\n", "\n", - " e_k = get_disperion_relation(p)\n", - "\n", - " wmesh = MeshImFreq(beta=temperature_to_beta(p.T), S='Fermion', n_max=p.nw)\n", - " g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh)\n", + " wmesh = MeshImFreq(beta=temperature_to_beta(p.T), S='Fermion', n_max=p.nw)\n", + " g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh)\n", " \n", - " chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw)\n", - "\n", - " U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norb, p.U, 0.0, 0.0, 0.0)\n", - "\n", - " chi_c_wk = solve_rpa_PH(chi0_wk, -U_c)\n", - " chi_s_wk = solve_rpa_PH(chi0_wk, U_s)\n", - "\n", - " gamma_singlet_wk = gamma_PP_singlet(chi_c_wk, chi_s_wk, U_c, U_s)\n", - "\n", - " Es, eigen_modes = solve_eliashberg(gamma_singlet_wk, g0_wk,\n", - " solver='IRAM', tol=1e-5)\n", + " # -- Make particle-particle vertex that is constant is frequency and momentum space\n", + " wmesh_boson = MeshImFreq(beta=temperature_to_beta(p.T), S='Boson', n_max=p.nw)\n", + " gamma_pp = Gf(mesh=MeshProduct(wmesh_boson, g0_wk.mesh[1]),\n", + " target_shape=g0_wk.target_shape*2)\n", + " gamma_pp.data[:] = p.U\n", + " \n", + " Es, eigen_modes = solve_eliashberg(gamma_pp, g0_wk, solver='IRAM', tol=1e-5)\n", "\n", " return Es[0], eigen_modes[0]\n", "\n", "def get_sc_phase_transistion(p, guess=None):\n", " \"\"\"Return U at which model p transitions to superconducting order via root search\n", " \"\"\"\n", - " \n", - " e_k = get_disperion_relation(p)\n", + " H = SquareLattice(**p)\n", + " e_k = H.on_mesh_brillouin_zone(n_k=(p.nk, p.nk, 1))\n", "\n", " wmesh = MeshImFreq(beta=temperature_to_beta(p.T), S='Fermion', n_max=p.nw)\n", " g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh)\n", - " \n", - " chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw)\n", - " \n", - " def lambda_minus_1(U):\n", - "\n", - " U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norb, U, 0.0, 0.0, 0.0)\n", - " \n", - " chi_c_wk = solve_rpa_PH(chi0_wk, -U_c)\n", - " chi_s_wk = solve_rpa_PH(chi0_wk, U_s)\n", - "\n", - " gamma_singlet_wk = gamma_PP_singlet(chi_c_wk, chi_s_wk, U_c, U_s)\n", - "\n", - " Es, eigen_modes = solve_eliashberg(gamma_singlet_wk, g0_wk,\n", - " solver='IRAM', tol=1e-5)\n", - " lamb = max(Es)\n", - " \n", - " print(lamb, U)\n", " \n", + " def lambda_minus_1(U):\n", + " lamb, _ = get_lambda_delta(p.copy(U=U), g0_wk) \n", " return lamb - 1.0\n", " \n", - " upper = guess\n", - " lower = 0.5*guess\n", + " upper = 1.1*guess\n", + " lower = 0.9*guess\n", " \n", - " U_c = brentq(lambda_minus_1, lower, upper, xtol=1e-4)\n", + " U_c = brentq(lambda_minus_1, lower, upper)\n", "\n", " return U_c" ] }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 71, "metadata": {}, "outputs": [], "source": [ - "%%capture\n", - "\n", "Ts = [1000, 750, 500, 250]\n", "hubbard_models = parameter_scan(hubbard, T=Ts)\n", "guesses = [-ele for ele in U_spin_cs]\n", @@ -1269,12 +1150,12 @@ " \n", " U_sc_c = get_sc_phase_transistion(hubbard_model, guess)\n", "\n", - " U_sc_cs.append(U_sc_c)\n" + " U_sc_cs.append(U_sc_c)" ] }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 78, "metadata": {}, "outputs": [ { @@ -1283,15 +1164,15 @@ "Text(0.07,0.15,'SC')" ] }, - "execution_count": 27, + "execution_count": 78, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ - "
" + "
" ] }, "metadata": {}, @@ -1299,17 +1180,16 @@ } ], "source": [ - "fig = plt.figure()\n", + "fig = plt.figure(figsize=(10,7))\n", "\n", - "ax_pd = fig.add_subplot(111)\n", + "ax_pd = plt.subplot(111)\n", "\n", - "ax_pd.plot(U_spin_cs, Ts, \"o\", ls=\"-\")\n", - "ax_pd.fill_between(U_spin_cs, Ts, [Ts[-1]]*len(Ts), alpha=0.25)\n", + "ax_pd.plot(U_spin_cs, Ts, \"o\", ls=\"-\", color='C2')\n", + "ax_pd.fill_between(U_spin_cs, Ts, [Ts[-1]]*len(Ts), alpha=0.25, color='C2')\n", "\n", "ax_pd.plot(U_sc_cs, Ts, \"o\", ls=\"-\", color='grey')\n", "ax_pd.fill_between(U_sc_cs, Ts, [Ts[-1]]*len(Ts), alpha=0.25, color='grey')\n", "\n", - "\n", "ax_pd.set_ylabel('Temperature\\n[Kelvin]', rotation=0, ha='right', multialignment='center')\n", "ax_pd.set_xlabel('U [eV]')\n", "\n", @@ -1320,17 +1200,10 @@ "ax_pd.spines['left'].set_bounds(Ts[-1], Ts[0])\n", "ax_pd.spines['bottom'].set_bounds(min(ax_pd.get_xticks()), max(ax_pd.get_xticks()))\n", "\n", - "ax_pd.text(0.78, 0.15, \"AFM\", transform = ax_pd.transAxes, size=22, color='C0')\n", + "ax_pd.text(0.9, 0.5, \"in-plane AFM\", transform = ax_pd.transAxes, size=22, color='C2', rotation=90)\n", "ax_pd.text(0.07, 0.15, \"SC\", transform = ax_pd.transAxes, size=22, color='grey')" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The superconducting phase gets correctly predicted by the linearized Eliashberg equation." - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -1347,80 +1220,40 @@ "\n", "and the CDW will therefore no longer be degenerate with the superconducting phase.\n", "\n", - "To add the Zeeman term in the repulsive model we will introduce a new function for the disperison relation and use a Hubbard model with explicitly carries spin as an index, i.e. two orbitals instead of one." + "The Zeeman term is already included in the `SquareLattice` class, but to use it we have to input a Hubbard model that carries spin explicitly.\n", + "We therefore create the `hubbard_spin_dependent` variable which is a copy of `hubbard` but with `spin=True`." ] }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 95, "metadata": {}, "outputs": [], "source": [ - "def get_disperion_relation_spin_dependent(p):\n", - " \"\"\"Return the disperion relation for model parameters in a ParameterCollection\n", - " \"\"\"\n", - " \n", - " try:\n", - " zeeman = p.zeeman * np.array([[1,0], [0,-1]])\n", - " except AttributeError:\n", - " zeeman = 0.0 * np.array([[1,0], [0,-1]])\n", - " \n", - " t = -p.t * np.eye(p.norb)\n", - " \n", - " # next-nearest neighbour hopping only if p has `tp` attribute\n", - " try:\n", - " tp = -p.tp * np.eye(p.norb)\n", - " except AttributeError:\n", - " tp = 0 * np.eye(p.norb)\n", - " \n", - " H = TBLattice(\n", - " units = [(1, 0, 0), (0, 1, 0)],\n", - " hopping = {\n", - " # Zeeman term\n", - " ( 0, 0): zeeman,\n", - " \n", - " # nearest neighbour hopping\n", - " ( 0,+1): t,\n", - " ( 0,-1): t,\n", - " (+1, 0): t,\n", - " (-1, 0): t,\n", - " \n", - " # next-nearest neighbour hopping\n", - " ( +1,+1): tp,\n", - " ( -1,-1): tp,\n", - " (+1, -1): tp,\n", - " (-1, +1): tp,\n", - " },\n", - " orbital_positions = [(0,0,0)]*p.norb,\n", - " )\n", - " \n", - " e_k = H.on_mesh_brillouin_zone(n_k = (p.nk, p.nk, 1))\n", + "hubbard_spin_dependent = hubbard.copy(spin=True)\n", "\n", - " return e_k\n", - "\n", - "hubbard_spin_dependent = hubbard.copy(norb=2)\n", - "\n", - "e_k = get_disperion_relation_spin_dependent(hubbard_spin_dependent.copy(zeeman=1.0))" + "H = SquareLattice(**hubbard_spin_dependent.copy(zeeman=1.0))\n", + "e_k = H.on_mesh_brillouin_zone(n_k=(hubbard_spin_dependent.nk, hubbard_spin_dependent.nk, 1))" ] }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 96, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "Text(0.54,0.65,'$\\\\downarrow$')" + "Text(0.52,0.6,'$|\\\\downarrow \\\\rangle$')" ] }, - "execution_count": 29, + "execution_count": 96, "metadata": {}, "output_type": "execute_result" }, { 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\n", 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\n", "text/plain": [ "
" ] @@ -1430,89 +1263,62 @@ } ], "source": [ - "fig = plt.figure()\n", - "\n", "# -- Bandstructure\n", - "ax_bs = fig.add_subplot(111)\n", + "ax_bs = plt.subplot(111)\n", "\n", "lower_limit = np.min(e_k.data.real)\n", "upper_limit = np.max(e_k.data.real)\n", "\n", "path = 'G-X-M-G'\n", "\n", - "ax_bs.bsplot(e_k[:1,:1], path)\n", - "ax_bs.bsplot(e_k[1:2,1:2], path)\n", + "ax_bs.bsplot(e_k[0,0], path)\n", + "ax_bs.bsplot(e_k[1,1], path)\n", "\n", "ax_bs.spines['left'].set_bounds(lower_limit, upper_limit)\n", "ax_bs.spines['bottom'].set_bounds(ax_bs.get_xticks()[0], ax_bs.get_xticks()[-1])\n", "\n", "ax_bs.set_ylabel('$\\epsilon(\\mathbf{k})$')\n", "\n", - "ax_bs.text(0.54, 1., \"$\\uparrow$\", transform = ax_bs.transAxes, size=22, color='C0')\n", - "ax_bs.text(0.54, 0.65, \"$\\downarrow$\", transform = ax_bs.transAxes, size=22, color='C1')" + "ax_bs.text(0.52, 1., r\"$|\\uparrow \\rangle$\", transform = ax_bs.transAxes, size=22, color='C0')\n", + "ax_bs.text(0.52, 0.6, r\"$|\\downarrow \\rangle$\", transform = ax_bs.transAxes, size=22, color='C1')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We will introduce versions of the functions we defined before, i.e. `get_chi0`, `get_chiRPA`, as a spin dependent version.\n", - "Also we introduce the function `get_sus` to get the interacting susceptibility for any two operators and `get_phase_transition` to find the phase transition for any order defined by any two operators." + "We also define `get_chiRPA_spin_dependent` that outputs the spin-dependent general RPA-susceptibility from which we can build any kind of particle-hole susceptibility for two operators.\n", + "The function `get_phase_transition` can then find ...." ] }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 82, "metadata": {}, "outputs": [], "source": [ - "def get_chi0_spin_dependent(p, e_k=None):\n", - " \"\"\"Return the non-interaction susceptibility for model parameters in a ParameterCollection\n", - " \"\"\"\n", - " \n", - " if not e_k:\n", - " e_k = get_disperion_relation_spin_dependent(p)\n", - "\n", - " wmesh = MeshImFreq(beta=temperature_to_beta(p.T), S='Fermion', n_max=p.nw)\n", - " g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh)\n", - " \n", - " chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw)\n", - " \n", - " return chi0_wk\n", - "\n", - "from triqs_tprf.rpa_tensor import quartic_tensor_from_charge_and_spin\n", + "from triqs_tprf.rpa_tensor import kanamori_quartic_tensor\n", "\n", "def get_chiRPA_spin_dependent(p, chi0_wk=None):\n", " \n", " if not chi0_wk:\n", - " chi0_wk = get_chi0_spin_dependent(p)\n", + " chi0_wk = get_chi0(p)\n", " \n", - " U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(1, p.U, 0.0, 0.0, 0.0)\n", - " U_abcd = quartic_tensor_from_charge_and_spin(U_c, U_s)\n", + " U_abcd = kanamori_quartic_tensor(2*p.norb, p.U, 0, 0, 0) # Two time norb to take spin int account\n", " \n", " chi_rpa_wk = solve_rpa_PH(chi0_wk, U_abcd)\n", " \n", " return chi_rpa_wk\n", "\n", - "def get_sus(p, op1, op2, chi0_wk=None):\n", - " \n", - " chi_rpa_wk = get_chiRPA_spin_dependent(p, chi0_wk)\n", - " chi_op1op2 = chi_contraction(chi_rpa_wk, op1, op2)\n", - " \n", - " return chi_op1op2\n", - "\n", "def get_phase_transition(p, op1, op2, lower=0.0, upper=10):\n", " \"\"\"Return U at which model p transitions to any order of op1 and op2 via root search\n", " \"\"\"\n", - " # Make copy\n", - " p = p.copy()\n", - " \n", - " chi0_wk = get_chi0_spin_dependent(p)\n", + " chi0_wk = get_chi0(p)\n", " \n", " def one_over_chi(U):\n", " \n", - " p.U = U\n", - " chi = get_sus(p, op1, op2, chi0_wk)\n", + " chi_rpa_wk = get_chiRPA_spin_dependent(p.copy(U=U), chi0_wk=chi0_wk)\n", + " chi = chi_contraction(chi_rpa_wk, op1, op2)\n", " \n", " # -- If any value is below zero we are already in an ordered phase\n", " if np.any(chi.data[np.abs(chi.data) > 1e-3] < 0.0 ):\n", @@ -1532,12 +1338,15 @@ "metadata": {}, "source": [ "We can then scan the phase space of the repulsive Hubbard model with a Zeeman term of strength $\\xi$ and an attractive model which is doped by $\\mu=\\xi$.\n", - "And as we know the AFM and CDW phases should be symmetric for $U=0.$" + "And as we know the in-plane AFM, defined by $\\langle S_z S_z \\rangle$, is symmetric to the CDW, defined by $\\langle nn \\rangle$, for $U=0$.\n", + "The same is true for the out-of-plane AFM, defined by $\\langle S_x S_x \\rangle$, and the superconducting phase, defined by $\\langle \\Delta \\Delta^\\dagger \\rangle$.\n", + "\n", + "The calculated phase doagram confirms this." ] }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 83, "metadata": {}, "outputs": [], "source": [ @@ -1548,7 +1357,6 @@ "# Spin operator\n", "S_z = 0.5 * np.array([[1,0], [0,-1]])\n", "\n", - "\n", "xi = 0.1\n", "\n", "Ts = [1000, 750, 500]\n", @@ -1557,36 +1365,42 @@ "\n", "U_spin_cs = []\n", "U_charge_cs = []\n", + "U_sx_cs = []\n", + "U_sc_cs = []\n", "\n", "for hubbard_model_doped, hubbard_model_zeeman in zip(hubbard_models_doped, hubbard_models_zeeman):\n", " \n", " U_spin_c = get_phase_transition(hubbard_model_zeeman, S_z, S_z, 0, 10)\n", - " U_charge_c = get_phase_transition(hubbard_model_doped, n, n, -10, 0) \n", + " U_charge_c = get_phase_transition(hubbard_model_doped, n, n, -10, 0)\n", + " U_sx_c = get_phase_transition(hubbard_model_zeeman, S_x, S_x)\n", + " U_sc_c = get_sc_phase_transistion(hubbard_model_doped.copy(spin=False), guess=-U_sx_c) \n", "\n", " U_spin_cs.append(U_spin_c)\n", - " U_charge_cs.append(U_charge_c)" + " U_charge_cs.append(U_charge_c)\n", + " U_sx_cs.append(U_sx_c)\n", + " U_sc_cs.append(U_sc_c)" ] }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 99, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "Text(0.4,0.5,'AFM')" + "Text(0.5,1,'Hubbard with $\\\\mathrm{Zeeman}=\\\\xi$')" ] }, - "execution_count": 32, + "execution_count": 99, "metadata": {}, "output_type": "execute_result" }, { "data": { - 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\n", + "image/png": 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\n", 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" ] }, "metadata": {}, @@ -1594,301 +1408,90 @@ } ], "source": [ - "fig = plt.figure()\n", - "\n", - "ax_pd_spin = fig.add_subplot(122)\n", - "\n", - "ax_pd_spin.plot(U_spin_cs, Ts, \"o\", ls=\"-\")\n", - "ax_pd_spin.fill_betweenx(Ts, U_spin_cs, [max(U_spin_cs)]*len(U_spin_cs) , alpha=0.25)\n", - "\n", - "ax_pd_charge = fig.add_subplot(121)\n", - "\n", - "\n", - "ax_pd_charge.plot(U_charge_cs, Ts, \"o\", ls=\"-\", color='C1')\n", - "ax_pd_charge.fill_betweenx(Ts, U_charge_cs, [min(U_charge_cs)]*len(U_charge_cs), alpha=0.25, color='C1')\n", - "\n", - "\n", - "ax_pd_charge.set_ylabel('Temperature\\n[Kelvin]', rotation=0, ha='right', multialignment='center')\n", - "ax_pd_charge.set_xlabel('U [eV]')\n", - "ax_pd_spin.set_xlabel('U [eV]')\n", - "\n", - "ax_pd_charge.set_yticks(Ts)\n", - "ax_pd_spin.set_yticks([])\n", - "\n", - "ax_pd_charge.set_xticks([np.round(ele,3) for ele in U_charge_cs])\n", - "ax_pd_charge.set_xticklabels([np.round(ele,3) for ele in U_charge_cs], rotation=45)\n", - "ax_pd_spin.set_xticks([np.round(ele,3) for ele in U_spin_cs])\n", - "ax_pd_spin.set_xticklabels([np.round(ele,3) for ele in U_spin_cs], rotation=45)\n", - "\n", - "ax_pd_charge.spines['left'].set_bounds(Ts[-1], Ts[0])\n", - "ax_pd_spin.spines['left'].set_visible(False)\n", - "\n", - "ax_pd_charge.text(0.2, 0.5, \"CDW\", transform = ax_pd_charge.transAxes, size=22, color='C1')\n", - "ax_pd_spin.text(0.4, 0.5, \"AFM\", transform = ax_pd_spin.transAxes, size=22, color='C0')" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": {}, - "outputs": [], - "source": [ - "%%capture\n", + "fig = plt.figure(figsize=(11,7))\n", "\n", - "xi = 0.1\n", + "ax_pd_right = plt.subplot(122)\n", "\n", - "Ts = [1000, 750, 500]\n", - "hubbard_models_doped = parameter_scan(hubbard.copy(mu=xi), T=Ts)\n", - "hubbard_models_zeeman = parameter_scan(hubbard_spin_dependent.copy(zeeman=xi), T=Ts)\n", + "ax_pd_right.plot(U_sx_cs, Ts, \"o\", ls=\"-\", color='C2')\n", + "ax_pd_right.fill_betweenx(Ts, U_sx_cs, U_spin_cs , alpha=0.25, color='C2')\n", "\n", - "U_sx_cs = []\n", - "U_sc_cs = []\n", + "ax_pd_right.plot(U_spin_cs, Ts, \"o\", ls=\"-\", color='C0')\n", + "ax_pd_right.fill_betweenx(Ts, U_spin_cs, [max(U_spin_cs)]*len(U_spin_cs) , alpha=0.25, color='C0')\n", "\n", - "for hubbard_model_doped, hubbard_model_zeeman in zip(hubbard_models_doped, hubbard_models_zeeman):\n", - " \n", - " U_sx_c = get_phase_transition(hubbard_model_zeeman, S_x, S_x)\n", - " U_sc_c = get_sc_phase_transistion(hubbard_model_doped, guess=-1.2*U_sx_c) \n", + "ax_pd_left = plt.subplot(121)\n", "\n", - " U_sx_cs.append(U_sx_c)\n", - " U_sc_cs.append(U_sc_c)" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.6,0.35,'prediction')" - ] - }, - "execution_count": 34, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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c5o9c/3ffUXDxFEIVFTZHJoRoiiRKQogW4TAMRg0cRFpK7Uq40jhNDpJPPYX0O++Mtv3LllF06eWEq6ttjEoI0RRJlIQQLcbldJp7wlmPncqrqnhv7hx8Ab/Nkdkj5ZyzSbv55mjbu3AhRddcS9gfn9+HEG2BJEpCiBaVlpLCqIGDMAyzFi6vqIhP4rQSDsD9u9+SetWV0Xb1jJnsvfkWwsGgjVEJIRoiiZIQosV19Hg4sm/faHvdtm3MWxW/q1WnTp6Me9KkaLvq/z6i+K4/xm3yKEQsk0RJCNEq+nTpSt8alXALV69mbRwvwJh61ZWkXHBBtF355luU6AckWRIixkiiJIRoNUNz+9KpRiXcJ4sXsbMg38aI7GMYBmk330TyWWdF+ype+gdlTz9jY1RCiLokURJCtBqHYXBsjUq4YCjEe3PitxLOcDhIv/MPJJ18crSv7KlplL3woo1RCSFqkkRJCNGq6lbCVVRXM31O/FbCGU4nGffdS+Jxx0X7Sh94kIp/v2FjVEKICEmUhBCtrm4l3J69RXy8MH4r4YzERDIfehDXkUdG+4rv+iOV//mPjVEJIUASJSGETcxKuH17wv2wfRtzV66wMSJ7GcnJZD72KM5BA82OcJi9N91C1Rdf2BuYEHFOEiUhhG36dOlC367dou1Fa9bEdSWcIzUVzxNPkJCba3YEgxRdcx3V8xfYG5gQcUwSJSGErYbm5tLJkxVtx3MlHIAjMxPPU0+R0L272eH1UnTZ5Xi/+dbewISIU5IoCSFsZVbCDZRKuBoSOuTgmfYUjo4dAQhXVlJ48SX41qy1OTIh4o8kSkII27mcTkbXqYR7d85sfHG8B1pC1654pj2FYa07FS4tpXDiJPwbN9ocmRDxRRIlIURMSE1J4bhBg6OVcD/t3ctHixbGbSUcgLN3bzNZSksDIFRYSMG4CQS2b7c5MiHihyRKQoiY0SEzkxE1KuHWb98e15VwAK5+/fA8/hiG9WgylJdHwbjxBPPybI5MiPggiZIQIqb07tKFI7rVroRb8+OPNkZkP9ewYWQ+8jAkJgIQ3LqNggmTCBYV2RyZEO2fJEpCiJgztE8unbL2VcJ9umQxO/LjtxIOIPGYY8jU90NCAgCB9espnDSZUGmpvYEJ0c5JoiSEiDmGYXDsgIGkp7gBqxJu7hxKysttjsxeST/7GRl/ugeseVz+VaspnDKVUFWVzZEJ0X5JoiSEiEkup5Pjhwwh0aqEq4zsCRfHlXAAyaefTvrv74i2fV8vpejyKwh7vTZGJUT7JYmSECJmpSYnM6pmJVzxXj5auCCuK+EAUs49l7Qbro+2vXPnUXT9DYQDARujEqJ9kkRJCBHTOmRmMuKIGpVwO3YwZ8VyGyOKDe6xY0m99NJou/q//2PvbXcQDoVsjEqI9kcSJSFEzOvduXYl3OK1a1kd55VwAO6pU0gZOzbarnr/fUr+dG/cj7gJcThJoiSEaBOG9smlc41KuM+WLGZH/k82RmQ/wzBIu/46ks87N9pX8fo/KX30MRujEqJ9kURJCNEmGIbBMQMGku6uUQk3RyrhDMMg/bbbSPrF6dG+8uf+Rtlfn7MxKiHaD0mUhBBthsvp5PjBNSrhvF7enTMbb5xXwhkJCWTcfTeJJ54Y7St99DHKX3nVxqiEaB8kURJCtCmpycm19oTLLy6WSjjAcDrJ1PfjOuaYaF/JvfdR8c67NkYlRNsniZIQos3JycxkxBH9ou0NUgkHgJGURObDD+EcOjTaV3zH76n65FMboxKibXM29qbW+mD/ijZXKXXqQZ4rDoHWejRwNrBOKfW23fEI0VJ6d+5MeWUlG3ftBMxKuJyMTI6ssZRAPHK43Xgef4ziW24hsGEjhEIU3XAjOW43yWNOszs8IdqcpkaU9jTwJzIhoLqB92WnRvuMBhQw3u5AhGhpQ/r0qVUJ99+vlrD9p/iuhANwpKfjefJJEnr1Mjv8fgqvvBLv4sX2BiZEG9ToiJJSqkt9/VrrOcApwDtKqamHPywhhGhapBJu/upVlFVWEgyFeH/uHKae80s8aWl2h2crR1YWnmlPsfeGGwnl5UG1l8Kpl9HhnbdIHDnS7vCEaDNkjpIQok1zOZ2MHjyERJcLMCvhpkslHAAJnTrheXoajpwcAMLl5RRMmoz/++9tjkyItqPREaXDSWt9IXAZcCzgwXw8twh4Vik1t57jbwGeBv5PKfUbrfVlwLXAIKASmA3crZT60Tq+N3AP5vycTsAW4P8Bf1FKhetceySwHChRSnm01r8A/gAcAyQD31vnvlL33DrXORa4GXN0rbMV10rgdeB1pVSozvF1P/dU4DbgOKAj8KBS6n7r2KOB3wC/AHpZ91QKrABeA96oGZvW2gPsrfFx59czx+wopdSKunE0cG+/AT4EViqlRtZ5rxjIBI6yYvojcCbQFVhUd36a9f1eC5wAdLDO+QZ4Xin1n/o+X4gD4U5O5rhBg1i4Zg3hcJj84mL+b8F8LjzlVByO+P77oLN7d3Nk6aabCZeUEC4uoWDCJDp+8D7Ovrl2hydEzGvxnyBa6xSt9X+A6cA5mAlBFWZicQEwR2t9dxPXeB54GRhhdXUCxgELtNY9tdZHAl8DV2L+AncBA4FngIeauPalwOfAGZjfRxJmwvQP4HWttdHAefdYnzkZ6An4gAzMpOkV4COttauRz70CmAWcZ31m3Q2avgbuxUwuOmN+ZznA6cC/gDfrxBbCnB9WZrW9NDy37HA5ClgGXGHFVmtHTq21Q2v9d2AG8FvMRKoKyAbOAj7UWr9wmGMScSonI5ORNSrhNu7cKZVwFmduLp4nn8CwFusM5edTMH4CgZ27bI5MiNjXGn/V+jtwPvAD5i/LVKVUJmZCcyvmKMzDWutzGjj/VGAKcBVmIpKBOQKzFfMX78PAW8AaYHCNaz9unf8Ha7SpPm7gb5gjJz2UUlmYv8S19f7FmCMhtWitp2AmYKWYI0IdlFLp1vXOwxzN+hUNJ2lu4Dng3zU+NxWouTrcDOu+ewLJ1n1lYCaDRZiTta+IHKyUKrXmlN1ndf1PKdWlzp+1DcRzsP6C+e/1WKVUmlLKXTMmzETvWmAX5mhipnUfacAlQAFwldZ6v+9YiIPRq3Nn+nXvHm0v+e47Vm3aZGNEscM1cCCZjz0KSUkABHfupHD8BIL5+TZHJkRsa9FHb1rrY4CpQB5wmlJqd+Q9pVQp8IzWuhJ4AfOx2X/ruUwmcItS6qUafUu11jcCH2EmM7swf1lXWdcuB+60HvkcjZmo/aWea7swR0TGKaWCNeK633qUdTNwr9b6RaVUwLqnZOAJ6/zfKqW+rHFPXuATrfUW67o3aq0ftq5Z93P/q5SaUuNcH2byF2nvlzgqpcqAf2it91j3fh3wUt3jWlEZcJZSqjjSoZTaCKC17grcjZkIn1kzSVNKVQL/su7jc+BurfXzjT3mFKK5hvTuQ3llFXl7zeLbz75aQlZ6Oj07dbI5MvsljhhB5sMPUfLHu8HvJ/DjjxRMmEjH6e/iqFE9KITYp6VHlKZar2/XTJLqeAsIA6O11vWVqRRjzheqa5Z1HsAzkSSpnmMAhjUS42ORJKmORzEfZ3UBfl6j/1eYjw9X1EySalJKrQFWASnAzxr43Cca6G+OzzEfox3ZwHfWWl6qmSTVMRFIBL5oaCRLKfUFUAj0wJx7JsQhMwyDowcMICPymCkU4r25cyguL2vizPiQdNxxZKr7ICEBgMD36yi4eAqhON8zT4iGtPRk7sjGQ5dprSc0cWwC0A1YX6d/vTXaUotSqlJrXYH5GGdNA9fcY7029lelOfV1KqXytNY/AIMxR6Uix0XuaZDWOq+R60YmSfes570wsKSRc9FaOzCTjQmYc7M6YM5lqqsLsLGxa7WgxhZliXxPZzTxPWVarz0xJ9ELccgie8LNXbUSn99PldfLu7NnM+Wss0lKTLQ7PNslnXwy6XfdSdnDjwDgX76cwksvp8M/X8NISbE5OiFiS0uPKHW1XjMwJyQ39CcyKdldzzUaGokCCDZxTOT9hiZVVyml9jbwHsBO67Vjjb7IPSXT+D1Fkpr67qmigREwIPp473+Yk7Z/CXTHTK4K2DcxOzKaltpI/C2tsckNke8plca/p0iyXt/3JMRBc1t7wjmsPeEKSkr4v4ULCIXq1k3Ep5SzziLt1luibd+iRRRefS1hWVZBiFpaekQpkohNUUr9s4U/qyXUV/EWuadXlVKXHeR163vUV9OtmFV4JZjLFnxc99Gl1roMczSt3qq8VtLYfUS+J6WUeqA1ghGirpyMDEb068fyDRsAsxJu9vLlnF5j49h45r7gAsKVVVS8YBafemfNYu9NN5P13F8xrEdzQsS7lh5Rijz6GtLCn3OwUqxJ2w2JjIrUHDlpjXu6yHq9Syn1Yj1JUipmknSwImX8yY0ck9nIe80R6//uRZzo1akz/br3iLa/+v47Vm6062l17EmdNBH3xZOj7aqPPqb4D3cSlpE3IYCWT5Qic1guaGg9ohhwSn2dWuvOmGsxgVnBFhG5p2O11r1aKKbIT/WGFoE5vZFzIz/dGvu+IxOwk7TWHRo4ZlQj5zdH5Hs6y0rshLDNkN696ZKdHW3/9+uv2LZnTyNnxJfUK64g5Xe/jbYr336HkvsfIByWQlQhWjpRiqwLNAC4sbEDtdZ21abeqbWub4z5D5gTzPOABTX6P8as1EoAnm4sATyEeyqxXofXc80k4P5Gzo0sRdDgSJlSagf7VvE+v57P6I65kOaheAOzMs8DPNjYgTb+uxdxIrInXM1KuPfnzWVvmVTCgfn9pN14I8nnnB3tq3j5ZcqemmZjVELEhhado6SU+kpr/QrmYoPPaK17Ym4psh1Aa52BWXo/FTPx+F1LxlMPPzASeEtrfatSaqfWOh1zjtBt1jEPRtZQAlBKVWitbwX+ibmA5sda63uVUssBtNaJmCtWjwcupP6qt6bMAPoBj2ittwMzlFIhawXyvwD9MVcCr698J1KKf6zWerhSanUDnzEdcxHPR7TWWzG3hAkBJ2Oua3VI4+5Kqe1a6weBB4BbrWToz0qp9QBaazdwPDAJMyE8/lA+T4imOBMSOH7wEOatWonXqoSbPkcq4SIMh4P03/+ecFUV3jnmrlJlTz+DkZZK+jXX2BydEPZpjb3ersP8hT4ZuAO4Q2tdilm1lcG+R0R27PlViZkU/QO40NrDLAMzaQOz6my/NZyUUv+yfvFPw1xX6Vda6yrM7Tkya5zf0BpDTXkQ+DVmtdv/AK/W2gekYyZ3EzC3dKnvp/s3mPvNjQBWaa0LgArrvV8qpb6z/vl+4FzMJRlmANWYyZEbc7XtP3Doi1k+hDmX6g+YyfBUa0kHH+b3FBnRXHGInyNEs0Qq4RauWU0oHKagpIT/LFjARafKnnAAhtNJxr33UlJVhe+rrwEoffBhHKlppF58qIPMQrRNLf6TQSnlVUpdjFnF9TawHXMScTLmVh/TMX/xX9zSsTQQ36uY+47NtLp8wLeYW4VMaWi1aKXUXzAnKv8NWIeZZKRjTvyeAdwEDD3ImHZjbtPyMubSBw6gHHgXOEEp9X4j54YxNwZ+GdiGmZD0tv4k1jhuNzAac4PdPdZn7AGetD674GBirxuLUupOzPlOrwI/Wp+Tirma+seYW5784lA/S4jmys7IYGS//tH2pl07+XL5skbOiC+Gy0Xmgw/iGjEi2lf8x7up/OBDG6MSwj5GPE7W01qPxJwoXaKUaqzqTYhWp7WeA5zSu3dvpk6dekDnVpeVsXT2bNLdMn++Kd9t3cKGHTui7V8eP5qR/fs3ckZ8CVVUUHzrbQTWrTM7EhLIfukFUs46y97AhGhYixSNyVizECIuDe5VuxLuf19/xVaphItypKbieeJxEnJzzY5gkKJrrqN63nx7AxOilUmiJISIS9FKuFRz9C0UDvOBVMLV4sjMxPPUUyR07252+HwUXXY53qVL7Q1MiFYkiZIQIm6ZlXCDSXKZuxxF9oSr9u23vWTcSuiQg+fpaTg6dQIgXFVF4cVT8K1uqKBWiPZFEiUhRFxzJyVz3OB9e8IVlpbwnwXzZU+4GhK6dMHz9DSMLHPJs3BZGYUTJ+O3toYRoj0CsPX7AAAgAElEQVRrjeUBYo5SagX27pEmhIgh2elmJdyyDesB+HHXLmYt+5Yzjj3UBerbD2fPnmRNe4q9N95EuLycUFERBeMn0PHDD3D2aqlNCoSwn4woCSEE0LNTJ/r32Lcn3NJ166Kb6QqT84gj8Dz5BEZKCgChvD0UjJtAcPfuJs4Uou2SREkIISyDe/Wma3ZOtP3511+xNS/Pxohij2vIEDL//AhYq5kHt22jYMIkgoWFNkcmRMuQREkIISyGYXD0gAFk1qiEe3/eXIrKSps4M74kHn00mQ8+AAnmJgSBDRsonDiZUKl8T6L9kURJCCFqiOwJF6mEq/b5mC6VcPtJOuEEMu79E1hbv/jXrKHwkqmEKittjkyIw6vNTObWWu+3hLhSKmYmZGutd2DuzXaSUmrBYbieE3NfN4CeSqkdjR1/ANc9Fqi7CMospZRsIyKEJSUpieMGD2Hh6lWEwmEKS0v5z/z5jD3tNNkTrobkMWMIV1VR9tjjAPiWLqXo8ivIee1VjKQkm6MT4vBoM4lSDQVAsL43tNanArOtZq5SaksDxz0K3Gk1H1JK3XuYY4xlfsw93QBSMDcBFkLUkZ2ezlH9+/PteqsSbvcuZn77LWeOkkq4mlJ+9SvCFZWUP/ccAN558ym67nqyX3gew9kWf8UIUVtb/K94VEMJUHNorZ8GbrGa9yilHjksUR1+YeAH65/9jR14IJRSK4EuAFrrK4CXDte1hWhvenTsRFllFet3bAfgmx/W0SEzk6MHDLA5stjiHnsR4apKKl5+BYDq/33O3ltvJ+vZpzFkBE60cW0xUTooWmsD+DtwjdV1m1LqaRtDapRSKggMsjsOIeLdoF69KKuqZLdV1fXF0q/JzsigT5cuNkcWW9yXXEK4spLKt94GoOqDD3Ckusn88yMYRszMkhDigMVFqq+1dgAvYyZJYeC6WE6ShBCxwzAMju5fuxLug3lzKZIKr1oMwyD1mmtIOf/X0b6Kf/2b0ocfIRzeb4qpEG1Gux9RsiZFvw5MBELAFUqpV5s4Jxe4HTgT6AEEgPXAu8BzSqlmlXVorV8DpgDvKKXGN3LcvcADwFKl1HE14q53MrfW+iHgHuBlpdQVWutLgWuBIZjzt74BHlFKzWpOnEKIxkUq4eauXIHX76fa5+PdObOZevY5JFvrCQkzWUq79VZClVV4Z8wAoPz/PY8jPZ30m2+yOTohDk67HlHSWruAtzGTpABwcTOSpIuA74Hrgf5WdxJwDPAYsEhr3bGZIbxpvZ6ntU5r5LgJdY5vNq31q8ArwFGYiWAGMAb4Qmt9/oFeTwhRv5SkJI4fPCRa9VZUWsqH8+fJnnB1GA4HGX+8i8Sf/zzaV/r4E5T/42UboxLi4LXnRCkJ+AD4HebIzDilVKOJiNZ6NGaykgD8GeillHIDbuBEzJGaEcBrzYxhFmaFmRuoN2nRWo8ABmMmOe8087oRvwPGAVcDmUqpDOAIYAHmv9vntNYJB3hNIUQDstLTOapf/2h78+7dzPz2Gxsjik2G00mmug/XscdE+0rU/VS8/baNUQlxcNpzovQWcC7gBS5QSn3QjHOexnwceZtS6m6l1HYwJ1YrpRYDZwN5wC+11iObupg1IftdqzmxgcMio0mzlVIHumGSB7hUKfVi5HGgUupH65p+zMeGxx/gNYUQjejRsSMDe/aMtr/54QeWWUsIiH2MpCQ8Dz+Ma9iwaF/x7++k8qOPbYxKiAPXnhOlo6zX15VSnzZ1sNZ6IDAaqABerO8YpVQh8LnVPKOZcURGsc7QWufUfMOqxBtf57gD8aNSar9RKGs+07dWc1jd94UQh2Zgz150y6mxJ9zSr9mSJxvD1mWkpJD52KM4+1ujcKEQe2+8iepZX9obmBAHoD1P5v4KczTlKq31SqXU35s4/kTrNQnYqrVu6LjIXKOeDR1Qk1JqidZ6E+YjsYuA5+t8Zm/MUa/3m3O9Ohob899pvWYdxHWFEI0wDIOj+g+gono1JRXlhMNhPpg3jylnn0NOhqzhWpMjPR3PU0+y94YbCW7bBoEAhVddRYd//YukE0+wOzwhmtSeR5QuAf5n/fNzWuvLmzi+q/XqBDo38ifVOs59ALFEHsxPqNMfaX+mlCo5gOtFlDXyXrX16jqI6wohmmBWwg0myWVWvZl7wn1Jlddrc2Sxx+Hx4Hl6Go6u1o/Zai+FUy/Ft2y5vYEJ0QzteUTJB1wAfAKcDryota5WSr3RwPGRpDFaon8YvYFZzn+S1rqHUmqHNcn6Iuv9g3nsJoSwmVkJN5gFa1YTCoUoKivjw/nzGDfmdBJkRepaEjp2JOvpaey94UZCBQWEKyoouPhiOk6fjmvIYLvDE6JB7fr/ZKVUNfBrYD7mvb6utb6wgcMj+58NPNyVYkqp74GVQM05SacDnYBSzGROCNEGZaWnc3T/fZVwW/LymPmNVMLVJ6FbNzzTnsLIzAQgXFxCwcRJ+Df9aHNkQjSsXSdKAFY12K+AJZhl/29qrX9dz6GLrdcMzCTmcIuMGkWq3yKP3T60EjohRBvVvUPtSrhv1//Atz/80MgZ8cvZpw+eJ5/EiKx0np9P4fgJBHbubOJMIezR7hMlAKVUGWZp/zLMOTvvaq3PqnPMGvZNjn5ca93gHCSttVtrfaDL8b6FuX3KUdbaSRdY/fLYTYh2wKyE6xBtf/HNUjbvlkq4+rgGDiDz8ccgORmA4K5dFIwdT/Cnn2yOTIj9xUWiBGBNlj4DWIVZ2fah1vq0OofdgDm3aQQwT2s9JvIYTmvt0FoP01rfB2zCfGx2IJ+/HXMhSDBX0s7EfNwn24wI0Q6YlXD98aSZhbGRSrhC2ROuXonDh+N5+CFwmfUmwS1bKJg4idDevTZHJkRt7Xky936UUkVa6zOAOZirYX+stT5LKbXQev8rrfXvMEd5jsFMYnxa6zLMR3I1K8gOZpfHN4GTgKOt9rvWopTiMNNaTwUa3a4GCCmlIolwH2BzI8c2uF+f1noK5pY3kb32lgNPKqVk7lmccSYkcNygwcxbtZJqnw+v38dbs2bSp0sX1m3bhs/vJ9HlYlifXI4fMoSs9HS7Q7ZV4qhRZN6vKLlPQTBI4Pt15F80lsSRI6n6+BPCFRUYqam4f3sBaVdfhbNPH7tDFnEobkaUIpRSP2HOQdqAWer/mdb6uBrvf4K5x9sjmL/wqjFXwC4FFgL3AoOUUgfzQH06+za6BXns1pJWALqBP5HV7v5bz3krGzjnvfo+RGv9JOaWNl2Bl4B/A8Mxk/AbDs+tiLYkJSmJ4wYNjla9lVZUsGrTJnx+8399n9/Pio0b+McnH7NJ5uWQdNJJZPzxLjAMAALfr6PyrbcJl5dDOEy4vJyKN9/ip1+cSfWXs22OVsQjIxw+mIGR1qe1jgSaq5TaYmcs7YXW+grMX+6zlFK/sDue1qK1Xoy5Cvv5SqmPrL4+mCNKryulpjbzOidiJs+bgFFKqb01rvUtZiI+6ED/e9VazwFO6d27N1OnNiuUqOqyMpbOnk26O7Xpg0WL2rRrF2s2N17N5UpI4Ipzz4v7kSWAitdfp+LlVxo9xkhJodPML2RkSTTEaImLxt2IkohvWuthmEnSTqDJrW2acI31+nAkSQKwEqO/Yc6Fu/QQP0O0UeVVlU0eEwyF+Pr771ohmtgXLCyMjio1JOz3U/7iP1opIiFMbXGO0ubI9iJKqRbJHtszrfWxwFK747DR1dbryw3MD+umtb4ayAEKgcVKqVUNXGuM9fq/et77L+Zj2jGAqu9kax7V1HreanLDZRH7duTnN3lMKBxmzebNnHWc7F3t/WIGNPWEIxCg8oP38TzyUOsEJQRtK1Ha0/Qhohn87P9dFtkRSGvTWqcAk4EQ0NBfS8+gzobH1qOwKUqpbTX6UoHuQLlSqr4a8A3W64BGQuoDnNKc2EXbEwg2r07D6/c3fVAcCFdVNe+48ooWjkSI2tpMoqSU6mJ3DO2BUmolEK/f5VjMifmfWss11FQJPAj8B4hMLDkSuB84DZiltR6plIr8lM60Xhvaoy/S72kkni3A3Hr6R9a4vmijnAkJzUqWklyyHSOY84/ClU0/rjTSZP6daF1tJlES4jC4ynp9oe4bVjXkfXW652mtz8Rc/+p44Arg2QP8zAafJSilXsOsmKslMpn7AD9HxJgeHTuyNS+v0XVEDMNgWG5uq8UUy5LOPIPqTz6FQKDhgwyDlAsuaPh9IVqATOYWcUFrPQQ4EdgBfNbc85RSAfY9pju5xluREaOGRn6aGnES7Vy/bt1xNLExbjgcpmenzq0UUWxzjxsHzib+7h4OE9i2nbA8rhStSBIlES+amsTdmMis3OiYv/UIbieQprXuWs85kV1S1x/gZ4l2IjUlhVGDBpHgcDRas/zZksXsKihotbhilbN7dzIf0Oa2JnUTphrVcL45cyi67nrCPl8rRyjilSRKot3TWicDF2NO4n75IC4x2nqtuyhOZOHKs+s555w6x4g41Dkrm9NGHkXvLl1wJiQA5tyl7h064LKSAV8gwNtfziKvsNDOUGNC0ujRZL/6CsnnnWtummsYGKmpJJ9/PknnnBM9rvqz/1J0zbWSLIlWIXOURDy4CMgCPqlnEjcAWuvjgeVKKV+d/jHArVbz33VOex4zAbtHa/2fOgtOXg94aXobFdHOpaakMOKIfow4ol+t/tKKChauWY0vEKDa5+PNWTOZfMaZdMrKsinS2ODs3p2MW2+FW2+t1R8OhynPyKDqnXcAqP78C4quuprsF57HSEqyI1QRJyRREvEgMon7xUaOeQwYak2k3mH1Hcm+tZLuVUotqnmCUmqR1noacBuwSmv9HpAIjAOygRtlFXnRkIzUVE4YOoxFa1bjDwbNZGnmDCadcSYdPY0VS8YnwzBIu+5aDIeDyrfeAqB6xkwKr7yanBefx0hOtjlC0V7JozfRrmmtBwM/p+lJ3P8CvgJGAVcC12HOM3oXOFkpVe8Kd0qp2zEXjczDTMguAdYC5ymlnjs8dyHaK09aGicMHRZ9LFfp9fLmzBkUlpbaHFlsMgyD1Guuxj15UrTPO2sWhVdcSbi62sbIRHvWZvZ6EyJeyF5v8aeotJRFa9cQDIUASE9xM/nMM2UPuAaEw2EqXn6Fyn/+M9qXdMrJ5Lz8D4yUFBsjEzaTvd6EEKI9ys7IYPSQoSRYywmUVVXy5swZlJSX2xxZbDIMg9TLL8M9dUq0zzt3HoWXXk6omSt8C9FckigJIUQM6JCZyfGDh0TXXiqpqOCNmTMoa8Zq1fHIMAzSLruM1Ev37TvtnT+foimXSrIkDitJlIQQIkZ09Hg4btBgHNa6QcXl5bwxYwbl8ou/QamXTiX18sujbe/ChRRePIWQJJjiMJFESQghYkjnrCxGDRqEYSVLRWWlvDlzBhUyWblBqVMuIfWqK6Nt3+LFFF58CaEK2UBXHDpJlIQQIsZ0yc7h2AEDozNTC0pKeGvWTKq8XlvjimWpkyeTes3V0bZvyVcUTr6YkMzzEodIEiUhhIhB3Tp04OgBA6Ptn/bu5a1ZM6mW1agblDpxImnXXRdt+75eSuGkiwmVldkYlWjrJFESQogY1aNjR47q3z/azisq4u0vZ+GVZKlB7vHjSLvh+mjb9803FEycTEjWphIHSRIlIYSIYb06dWZkje1PdhUU8M7s2fj8fhujim3usWNJu+nGaNu/bBkFEycRKimxMSrRVkmiJIQQMa53ly4M79s32t6R/xPT58zGHwjYGFVsc194IWm33BJt+5evoGDCRELFxTZGJdoiSZSEEKIN6Nu1G8P65EbbW/fs4b25cwgEgzZGFdvcv72AtNv2ba7rX7mKgvETCe3da2NUoq2RREkIIdqII7p3Z3Dv3tH25t27+WDeXIKSLDXI/ZvfkH7H7dG2f/VqCsZPJFgkyZJoHkmUhBCiDRnQoycDe/aKtjfu3MmHC+ZH94kT+0v59a9J/8PvwVqbyr9mDYXjxhMsKrI5MtEWSKIkhBBtzMCePenfo0e0vX77dj5auICQJEsNSjn3XNLv/MO+ZOm77ygYO45gYaHNkYlYJ4mSEEK0MYZhMLhXb47o1j3a9/3WrXyyeJEkS41I+eUvSb/rrmiyFPh+nZksFRTYHJmIZZIoCSFEG2QYBkP79CG3a9do35rNm/nvV0sIh8M2RhbbUs45m4x77gZr8+HAuh8ouGgcwfx8myMTsUoSJSGEaKMMw2B4bl96d+4S7Vu5aROfL/1akqVGJJ95Zu1kaf16Ci4cS3DPHpsjE7FIEiUhhGjDDMNgxBFH0LNTp2jfsvXrmfntN5IsNSL5jDPIuPdeSEgAILBxo5ks5eXZHJmINZIoCSFEG2cYBkf160+PDh2jfUvXrWP28uWSLNUj8p0knz6GjPtqJEs//kj+hWMJ7t5tZ3gixkiiJIQQ7YBhGBw1YADdcnKifUu+W8u8VSttjCo2GYZB2Fp7Kvm008hQKposBTdvNpOlXZIsCZMkSkII0U44DINjBgykS3Z2tG/h6tUsWL3Kxqhih+/bbyl97HEADCsxAkg+9RQy9f37kqUtW8i/8EICO3faEaaIMZIoCSFEO+JwODh24CA6ZWVF++atXMmStWttjMp+vhUrKL7tdqo/+4zgrt3Rx29hazmFpJNPJvPBB8HpBCC4dRsFF44lsGOHbTGL2CCJkhBCtDMJDgfHDRpMx0xPtO/L5cv4et33NkZlH9+KFRTfbG6Qm3z2WZCQQNBKgAyHI/oYLunnPyPzoQfB5QIguG0bBb+7iMC2bfYELmKCJEpCCNEOJTgcHDd4MDkZGdG+md98w7L1622MqvX5VqyMJkkkJBDYuInCsWMp/v0fKH/lVcB8DBcdWTrxRDIfeggSEwEI7thhjixt3WpL/MJ+kigJIUQ75UxIYPSQoWSnp0f7/vf1V6zcuNHGqFqPb+VKim++GQD35MlkPvQgWX97jswnnsDZty+Vr7++L1ly7Pt1mHTCaDIfeXhfsrRzpzmytHlz69+EsJ0kSkII0Y5FkiVPWlq079Mli1nz4482RtXyfCtWUnyTmSSl33UXaVdeQdKJJ2IkJ5N03CjSrrqShB49qHrnHfyr1+x3ftJxx+H58yP7kqXdu8m/cCyBHyVZijeSKAkhRDvncjo5YegwMlNTo30fL17Ed1u32BdUC/ItXx4dSUq75WZSzjk7+l44FCIcDuPs04ek08cQrq4muKf+RSYTR43C89ijkJQEQCgvj/wLL8S/cVPL34SIGZIoCSFEHEi0kqUMtxswF138vwUL+KGdTVT2rVhJ8S23AuAaOZKkk06u9b7hcIA1H8lIMCvcQmVlDV4v8Zhj8DxaI1na8xMFF43FHyePL4UkSkIIETeSXC5OHDqMtJQUwEyWPlwwnw3tpAS+5pwkIzMTR042CR1y9jvOSEggWFhI9Zdfmm0reQRqrWQe+efEY47G88TjkJwMQOinnyi4cCz+OJsYH68kURJCiDiSlJjIz4YNJzXySz8U4oN5c/lx1y6bIzs0vpX75iRlaE3ymNMwaiSEkao2gFBlJd758wnl5eEcPJikE080jwsEMAwjelzNFbwTR47E88Tj0WuG8vMpuGgc/nXrWuX+hH2cdgcghBDNVVZZyY+7dpFfUkK1z0sYSHK6SE5KJDs9nU5ZWXTyZNV77p6iInYU5LO3rIxqn49wOEyiy0Vmaiqds7Lp0bEjLmd8/EhMtpKlBatXUen1EgyFeG/uHMaeNoY+XbrYHd4B8327jOLbbgMg4777SD71FPxr1uCbOw/f6tUkDh8OVgIUKinBu2gxVe+8SzgQIOmEEzCSkswkyfr3X3znXRjpaWT+6U+1VvBOHDGCzCefoOSO3xOuqiJUUEDBRePo8O7buAYPbv0bF61CRpSEEG3Czvx85qxYzpY9eQRDQXIyM+mWnUOaO4WKqio27drFd1v2X+vG6/OxYPUqlnz/HTvy8zEMg06eLLrm5OBOSia/uJhVP25i5rffUFldbcOd2SMlKYmfDRtOijX3JhAMMn32l2z/6SebIzsw4erqfUmS1iSfPgaAxKNGEiovp+L5F/AuXkywsBD/999T/uKLVLz8MsFdu0gecxop5/8aIzExmiSVPPAAviVL8M6YSbiqat/nWCNSicOH43nyyejjulBRkTmytPa71rxt0Yri469PQog2rdrnY/nGDYTCYYb1yaVvt261HpGEw2EKS0spKi2tdZ4/EGD+6lVUVFeTlZ7OiCP61ar8ihyzJS+P9Tu24w8EWuV+YoU7OZmfDR3GgjWrqfb58AeDvPPlLCb84hd079DR7vCaxUhOJvvVVwju3EXSST8nHA5jGAZJP/sZaVdfRflfn6Pkj3djZGaaiY/Xi6NDB1LOP5/US6fi8OxbvbzkgQfwzvoSXC5Szv0Vge3bwTBw9e8fXcHbSEjANXwYnqeepPiO3xOuqCC0dy/5Y8fR4Z23SBw2zMZvQ7SEhPvvv9/uGIQQNcydO3cq0Mfj8TBy5MgDOjfg87FryxaSXIktEptddubns7uokKz0dI7q379WkgTmXBJ3cjI5mZm1+lds3EBhaSmetDR+PvzI6OhJTQkOBzkZGXTL6UCiy4WzxqOWeJDoctE5K4tdhQUEQyGCoRDrtm4lt2tX0mtMco5ljqwsnL177euwkiXXkCEk9OkNCQmEiopIyMkhcdQo3BdPJvmX5+CosWp5yYMP4Z01C1wucx6Sw0HFiy/h++prwpVVJI4cUWtRyoROnUg8+mi8c+aAzwfV1VR98glJJ/2chM6dW/HuRQ26JS4qI0pCiJjn9fsBs2qruSqqqtiRnw/AiCP6keBofKZBpBIsHqW73Zw4bBgLV6/GFwjg9ft5a9ZMJp1xBp2zsu0O74AYhgGGQTgUwnA4SD7tNJJPO41QZSVGQgJGPclyyYMP4Z05EyMlhbRbb8HVvz/Ovn3xrVhJ1YcfUPHKK4QrK0m79ppa57mGDMYz7SmKb7udcHk54eISCsZPpMOb/ybxAP+SI2KXzFESQsS8yEhQfnEJpRUVzTonb28RABlud61VqUX9MtypnDhsWHRCe7XPx5szZ5JfXGxzZAfHqJMYO9zuaJIU9vmi/dEkye3G8/Q0Us46C2ffvgAkjhyBe9IkEvr0wTloYL2f4xo0CM/TT2NY28SES0oomDAJ3/LlLXFbwgaSKAkhYl6X7GySExMJhoLMWbmCJd+tZcOOHeQXFzc4r6i4vBwAT1p6ve+L/WWmpnHi0GHRx49VXi9vzpxBYUmJzZEdPuFAAMPalqRWkvTXv+AaPDg6aTscDhMOh3ENGEDWs8+QfNppZn8wWGutJQDXwAF4np6GYT3KC5eWmsnSt8ta8c5ES5FESQgR81xOJycOHYYnLY1wOMyevXv5busWFq1dw2dfLWH+qpXstB6zRfj8ZgJ1II/rBHjS0jhh6NDoo8qK6mremDmDvY2sXt2WRKvb7te1k6R+/czJ2tZ9G4YRnQvn8Hii6ynh99cuJLASK9eAAXieeRrDmicXLiujYOIkvEu/aa1bEy1EEiUhRJuQ7nZzyoiRnDT8SPr36EGHzMzoY6KisjK+Wf8DyzbISsmHQ3Z6Rq1kqbyqijdmzKDEGqVr67xfL8U7eza4XGQ999d9SVI9E/mDhYX4li6l5O57KLr2OoquuJKy557Du2AhQLQaDsDVrx9ZzzyNYVXShcvLKZw0Ge/XX7fezYnDTqrehIgxUvXWuJSkJDp6PPTq1Jl+3bvTyZNFlc9LZXU1pRUVpLvdZLjd/FS8l9LKStJSUuias/82FqJx7qRkstLT2VlYQDgcxuv3s2HHDgb27EVSYtv+78vZvTuO7CxSp0zB1b+/OfG7niTJ/8MPVL7xJhWvvEJwyxYIhyEQwP/NN3jnzyfs85N49NFmshQKYRgGjuxskkaPpnruXKiuBr+fqo8/IfG4UTh79Gj9m40vLVL1JiNKQog2yzAMsjMyOGHI0Oj6SHmFhQDRCdzF5e3jkZEdOno8HD9oMA7rUVNxeTlvzpxBeWWlzZEdvMjoT8r55+MaOKDW47aaAj/+SOW/3zD3g0tMJP2uO8l5522yX38Nz7PP4Bo8mMp//YvyV14Fak8ed+bmkvXsMziyzYrBcGUlhZMvwbtocSvcoTjcJFESQrR5hmHQMdN83OENmEsJRMraSysroxO7xYHrlJXFqEGDo/NyisrKeGPWTCqqq5o4MzbVHTmq247MOfLOn4938WKMhATCpaUEd+7CcDoxUlNJHDmS9FtuxjloEFXvvovvm/3nITn79MHz7DM4rNHMcFUVhRdfEn1kJ9oOSZSEEDGvbpVRfSq9XgBSrMdCaSkp0dWlV23aRLDGpqj1qaiqorpG2bjYp0t2NscOHEhkCnNhSQlvzpwZ/c7bE8PhIFhQSNVHH+NITyd1yhQSR4+2Ro9eiSaMziOOwD32IsLV1QS2ba/3Ws7evfH85VkcHToA5nYrBVOmUD1vfqvdjzh0kigJIWLe5rzdLNuwvt7Kq1A4zJa8PHYVFgDU2nrjyL59cScns7e8jEVrVte7BlMgGGTjzp3MWbkCryRKDeqW04FjBu5bSyi/uJi3Zs6kqh0mS4ENGwgVFOA6aiTu8eNIu+ZqM1l6/Z9UvPpa9DhHdjaEwwTWN1xE4OzZE8+zz+LoaP13We2l8NJLzTlMok2QlbmFEDEvHA6z/aef2P7TTyS5XGSmppHodOILBCitrIiOBPXr3p1OWVnR8xJdLk4afiRLf1hHUWkps1csJz3FTZo7BYdhUO3zsbesjFA4TJLLhcslPxIb071DR0KhcLS6cM/eInNvuNN/0eYneNcUth4rJliTr525uaReeQUYUPHaa+AwSJ0yhcAP5vfg6Nih0es5e/bA8+wzFN98C6H8fCtZupycl1+Krs8kYpf8VBBCxLxenTrjTkomv7iYveVllFZW4PX7cSnwXmYAACAASURBVBgGyYlJ9OzUid6dO5OTkbnfucmJiZw0/EjyiorYmZ9PUVkpP+3dSzgcJtHloqPHQ5fsHHp07Bh3+7wdjJ6dOhEKh1ixcSMAuwoLeWf2l4wfczqJ7WTNKmduLkZqKqHdedE+V79+pF5xBQAVr7xKYOs2glu3gsNB0nHH1zo/sn1KrWv26EHWX//C3ptvIbRnD3i9FF52BTn/eInk08e0/E2JgyaJkhAi5rmcTrrm5BxSmX+X7Gy6ZLetfctiVe/OXQiFwqz6cRMAO/LzeXfObMadNia6tlVbFQ6HcXg8uAYPpnr2bJJOH0PS6NGAmSylXXkl5Y4EcwNdIGXsWJwDB9S6Rt0kKZI4JXTrRtZfnjWTpbw88PkovOJKsl98gZQzftE6NygOmMxREkIIccByu3ZlWG5utL1tzx7emzuHQGQF6zbKMAwcHg/J550Hfj+V//wXvpUro+87jziC1Isnk3TSSSSffRbJY06Lboni/+EHqmd9Sfn/e56qTz/Ft2KFec0ai1ImdO1K1l+exdG1q3lBn4+iK6+i6vPPW/dGRbPJgpNCxBhZcFK0FdnpGSQ4HOSXmBvnFpeXk1dUxKBevXDUszZRWxAOhzEMA2efPhipqVR/+in+dT/gyMrG2ac3AAkdO+IaNAjXkCG4+vcHoPzFFyn/29/xfvEF/jVr8C1cRPXMmYT9+y9KSThM4tFH41u2jHBZGYRCVH36Ga5BA6PXEwelRRaclERJiBgjiZJoS3IyMjAMKLA2zt1bVkZ+8V4G9uodXaiyLTEMI5rQuIYOxdGxI75FZtIT2LwZR1oaCd264UhPN/eACwQoe+JJqj74ALxekk49heQxY0g66SRCe37CO3cuOAwSR47EMAxCZWVUf/455U8/Q9oNN/z/9u47PKoye+D4985MekJoIqLSm7Rl7YBCxIYrLqIg9sVe1nVdddW1vRyxrN1d/a2uFRu2VaxYQCQiomJBERAsYEXppLeZ+f3x3pkMIQMBkpk7yfk8T57J3Ln35sxNMnPmLeelZtmy2mRp+uuk9e5NWm9NlraTVuZWSinlPX1270zv3XaP3l/200+89N4cQlupXeVVkdYfgKzRR9Lq2mvIPPRQqj6aj+NWgI8oueceKqZPByD/+utpdeWV5PzpT2Qfeyytrr2G9H33peLNtwht2ECouJjKWbMoe/oZQuvXE1y+nPx/3YV/d/fa1dSw7rzzKXv5lYQ+X7VlmigppZTaYX07d6bnrrtG73/1ww+88v7c1E6W3EKn6XvuSd5Ff6Xd1CdJ22OP6Pby116jfNqLAOTfeisZBx4A7nilcChEoFs3so8/nuAvv1C9dCmVhYWUPjKFcFkZOaefTvbxEwh06EDrf92Fv3Nn+4ODQdZf8BfKXnop8U9a1UsTJaWUUjvMcRz6delK9106RbctWrGC6R980KDK6l7kxHQdOhkZ+PLd8hPhMOFwmOqFCwHIPe88MvbdJzq+KSIcCuHvvDu+jh2p+uBDSh9+hHBVFdnjx5M94TicrCwA/O3bk3/bbXWSpQspmzYtMU9UbZEmSkoppRqF4zgM6NaNrh07Rrd98d23vPHRhymbLNXH8fkIb9xI1YLPwXGi5QE2Sax8Prscyg8/EFq5kvJp0whXVtok6YTjcTIzo917wd9WUf7UU+ScdRb+rl3tCUIh1l94EWXPv5Dop6fq0ERJKaVUo3Ech0Hde9C5w87RbZ99/TUzPp7frJIl0tNx0tPx7bQTaQMHArUL6kYEV62i/JVXAfB17EjWscfUJknhcLTeUtX8+ZS/+CKl991H/vWT8UfKLoRCrP/rRZQ++1zinpfajCZKSimlGpXjOAzu2ZPddqpdd+/jpUuZ9emnzSJZipYQ6NyZ0KpVVM2fD2xaLym0fj0Vb79N1fz5+Nq0IfOwQ8k54QSczEy7r+MQKisDIGPEcLKOPpqcM88g0Lkzbf51F4EePSI/jA0XX0Lp008n/okqQBMlpZRSTcBxHH7fqzed2tWug/bhksUUfr4giVE1DsdxcLKyyHCXHil7+mmq3PFKjt9PzQ8/UPb8C5RNfQqArDFjyDnxxOiYJIDgmrWU3Hknxffcgy8vj9y/XEDmwQfbc+Tn0/rOOwj06ml3DofZcMnfKXXPpxIrtWvNK6WU8iyf47BX796El4ZZuW4tAO9/+SUBn58DBg1KcnTbL9KilHnQQYTWrKXkgQcouuZaAn374stvReX78wiXluLk5JA9bly0uy0iuGYtZU8+ScVbM3CyssgaPZpAZGwSbiLWujWt77yTDX+7mJqvvwZgw98vg2CQnFNOTvRTbtG0RUkppVST8fl87N2nDzu3aRPd9u4XnzNv0ZdJjGrHRIpSAmSPH0f+dUL2hAmEKyqoXryEcFERvvbtyRo7tv4k6fHHKX/hBfy77Uarq6/eJEmK5WvVitZ33UmgT5/otg1X/IOSKY826fNTm9JESSmlVJPy+Xzs03cPdmrdOrrtnc8+46Mli5MY1Y6JLUqZsf/+ZJ9wPBlDhxJavx5fhw5kjjqcnHhJ0osv4u/UidzzzyPjgGHA5gPBI3x5ebS+43YCfftGt2286mpKHpnSdE9ObUITJaWUUk3O7/Oxb989aB+pRQTM/OQTPlm6NIlR7Rinznp2TnYW4eJiMg8/3A7crjMmaZMk6YI/kzHMTZJqajY5V2TAe+TWl5dH69tvI9CvX3SfjVdfQ8mDDzXZc1O1NFFSSimVEAG/n/326EfbvFbRbW/O/4gF7hicVJc1ejRt7r2XnJM2H7gdL0kCcAIBwtXVhIqLCW3YEK3HFNvF58vLo/VttxLoH5MsmUmU3P9Agp5dy6WDuZVSSiVMwO9n/379mLdoEetLigGY/uEH+P0+BnbvkeTotl84FMLx+Ujrt8cm27eWJFUvW0ble+9R+c5sQhs2QDBIxgEHkL7ffmQePDJacsDx+/Hl5tL6ttvY+PfLqP7SjvHaKNcRDgXJO/fchD7flkRblJRSSiVUWiDAkP79yY9ZYPbVefNYvGJF8oLaQXW74QCCq1dTOmVK3CSp6pNPKbpuMmWPPkbwxx/x5efja9OGihkzKLr+ekoesK1Fjt9f27KUk0P+bbeSNmhg9DxFk2+g+P/+08TPsOXSFiWllFIJlxYIMLT/AOZ+uZCisjLC4TAvzX0Pn89H38iaZyku+PPPVLzyCr6ddiL3LxeQMXRo9LGqL76g6MYbCa1ZQ8aBB5Jx8MhoElW9dCllUx6l7Iknwe8n9/TTN0nEfNnZ5N9yCxsvv4Lqzz8HoOjGmyAYJO/CvyT2SbYA2qKklFIqKdLT0hg6YCB5WdmAHbz84px3+fqnH5McWeNIHzyYvCuuIPeC2iQpHAoRXLuWsqlP2STpkENsEjV8OE56Ovh8pA8cSO4FfyZtr70of/Y5KufM2eS84VAIX3Y2rW+5mcDgwdHtRTffQtGddyX0ObYEmigppZRKmoy0NIYOGEBOph38HAqHeeHdd/n2l5+THNmOiXSVZR0xisyCEdFtjs9HeMMGqpcswd+tG9knHI9/551x/H7ADuwGCHTrRs6ppxCurKTq008JV1Vteo7KSpysLNrccjOBPfeM/tzi226n6I47E/lUmz1NlJRSSiVVZno6wwYMINutORQMhXi+sJDlK1cmObLtV9+YpegiuB9/THjDBtJ69yatZ8+450gfPJjcs8/Gv9tuOOnpBH9bZZOkmhrWX3QR6844AyczkzY3/5O0vfeOHld8+x0U3Xpbs1hXzws0UVJKKZV0WRkZDOs/gKyMDABqgkH+N/sdflj1W5IjawIhm8AEenQHbB2leDIPP4zsY48luHYtJXffTdGtt1E0eTI1i5cQ/PU3gr+sxMnIoPVNN5K+777R44rv+hdFN9+iyVIj0ERJKaWUJ2RnZjJswEAy09MBqA4GeXbWLH5avTrJkTWuQJ/eEAgQdJ+XEwjETWh8bdvafbKyCNfUUPHqq1TOLsTfrRtt7v0P/k672MczMsi/4XrS99svemzJ3fdQ9M+bNVnaQZooKaWU8owcN1nKSEsDoKqmhmdmvc3KtWuTHFnj8e20E/5dd6Vi+utULbCz1hzHqTehibQ2+bKzCZeVRbcHevYg4M4ODAeD9hyRZGnIkOh+Jff8H0U33KjJ0g7QREkppZSn5GZlMXTAQNIDNlmqrK7mqbdn8tu6dUmOrHEEdt+d7BNPIFxaSukjD1O1YAFAtCJ3RDgYxAkECJWWssEtBeDv1In0ffahcsZMiu+5xx4XU2fJSU+n1SRDekwpgpJ776PousmaLG0n/6RJk5Idg1IqRmFh4USga+vWrRkcM/W3IWqqqvhlxQoy0tKbJDalEiUjLY0Obdrw85o1hEIhaoJBvvrhB3rs2ik6Qy4VhcNhHMchrWdPnNxc26r00UeEQ0ECnTtHF9GNVOMOlZVRNHkyVR98gL9zZ1rfdisZQ4YQWr+OitemE1y9ioxhw6JJVqi4mPIXXyJjxAjCZaUEf/gBsMUtQxuLyCgYsVlC1oxIU5xUW5SUUkp5Un5ODkP7DyDNnTpfXlnJ1JkzWbNxY5Ij236x67dljx9HqyuvxNehAxWvvErVJ58AdZKk666jap5NkvInGfy77IK/0y7knHYa6fvuQ7iicpPB4NULFlB6//0UXXstuRdeSMbw4dHHSh96iI3XGm1Z2kZamVsppZRntc7NZUj/Aby/6EtqgkHKKiqYOnMGJx922CaL66YSx+eL1kPKPHgkaQMGEC4pxt/dzoKrTZIm1yZJMolA9+7RFqlA587kXX4Fvtb5djB4ZSVORgZpgweTefjh+Dt3JrDzzrSaZCiaPJnKd2YDUPrwIxAMkn/95HpLGKjN6VVSSinlaW3y8ti/X3/87ht7SXk5U2fMYENJSZIj236Ozxdt2fHv3IFAjx7RLrFwZSUld95F1bx50ZakQCSJiuk287dvZ8cwFRdT+vgTlNz3X3x5eeT9/VJyTj7J7uTz0eqaa8gYOTJ6XOmjj7HhH1dFW7bUlmmipJRSyvPatWrF/v364XOTpaKyMp6c8RZFpaVJjmz7xRsrVL14MZVz5+LfdVdaXXsNgR494p4jVFJC+auvUvb445Q99RTVixbhuDMGw+Ewjs+HEwjQ6uqryDjk4OhxZU88wYbLr9BkqQE0UVJKKZUS2ue3Zr899sDnJhgbS0t5cuYMimOmzTcH4cpKwqWlpA0cQFqvXnZbPeOKQiUllL/0MqX/vR+nVStyL/oraf37Rx+PTcScQIBWV15JxqGHRreVTX2KDX+/TJOlrdBESSmlVMro0LoN+/bdI5oErC8uZurMGZSUlyc5ssbja90ap3Vrqr9cRPXSZcDmdZaiSdIDD+BkZ5Nzxulkjx0L1NZVqssmS/8g8/DDo9vKnn6GDZdcGvcYpYmSUkqpFLNz27bs06dvNFlaW1TEU2/PpKyiIsmRNY60vn3JPf00gj/9ROkDD1C9aBFQ20K0WZJ09llkH300YAtURhbYjRVJshy/n7wrLifziFHRx8qefY71f7tEk6U4NFFSSimVcnZp1469eveJ3l+9YQNPvT2T8srKJEa14yIJTdaYMeScew5V8+dT/eWX0ce3lCSBbTUCCK5aRXDNmmjpAMdxait4+/3kXX45mUceGT2u/PnnWX/R37a47lxLpeUBlFJKpaRd27cnHO7NJ8ts99Rv69fz9Ntvc8Ihh0TXi0s1kTpLjs9HzgknEOjenXS38OzWkqTgb6uomDGDqnnzqPnmG8KhEOl77UXGAcPIGj3aVvB2azQ5Ph95f78UfD4qXnkFgPIXpkEwSJt//yuacClNlJRSSqWw3XbqQDAUZsE3XwOwct1anpk1i+MPPji6Xlyqia2zlOEuchsqLqZ82ouUPvZYvUlSzY8/UnzrbVR/8QWEw/jat8ffti3Vn39O1bx5BH/8kdzzzosud+L4fDZZuuRiHL+P8hdfAqD8pZchFKLN3f+Ozp5r6TRRUkopldK67Lwz4XCIz7/9FoCf16zm2XdmMWHkyOh6cammbjHI4C+/UPrQQ5CRQe4555A15o/Rx2p+/pmi6yZTs2wZgb59yTz8cDIOGIa/Qweqly6l9NHHKHv6GZz8fHJOPHGTczs+H7l/+xs4PsqnTQOg/JVXCQdDtP3PPZosoWOUlFJKNQNdO+7CwG7do/d/XLWK/82eTXUzGXOT1qcPeRdfTO6ZZ0STpHAoRKi4mLIpU6hZtoy0gQPI++uFZI0+En+HDoRrakjr04fcM8/A36kTFa+8Ss2PP212bsdxyL3or2Qde2x0W8X06aw773zCVVUJe45epYmSUkqpZqF7p07079o1en/Fr7/y/LuF1KT4bK5InaOsMX8k+7jj7LZgEMfnI7RhI1VfLMTXoQM5f/oTgb59cSLjs9wxSYHu3ckYeRDBX34h9Nuv9f4Mx3HIvfAvZI0fH91W8fobrDv3vBafLGmipJRSqtnouetu7NG5S/T+d7/8wrR33yWYwslSfWuyRUoAVH30IaFffyXQpQtpAwZs2q3mONH9QuvWAxBcuRKov4Cl4zjkXvBnsiZMiG6rePMt1p19DuEUn024IzRRUkop1az03n13+uy+e/T+1z//xItz3yPUDCtQR1p70g8YhpOVtcn0/kgyFNqwgeCPP4LPh79Ll/rP414bx3HIPf88sk84IfpYxYyZrD3rHMLNpE7VttJESSmlVLPTZ/fO9Nx1t+j9pT/8wMtz5za7ZCngJj6hdesAW0cpHAzadd7cApUVM2dSvXAh/k6d8Ldvb/dzHwuuXWvvuzPtIo/lnHsO2ZGFdYHKt99m7ZlntchkSRMlpZRSzY7jOPTr0oXuu3SKblv8/Qpe+2Bevd1OqcrfsSO+Dh2oePOtaGFKx++PJkLlL79Myd33AJB9/AT8nWqvR82331J03WRK7r3XHlen2y7nrLPIPvXU6LbKd2az9vQzCDej5WIaQhMlpZRSzZLjOAzo1o2uHXeJblv43Xe8/uEHzSZZCnTvTs6ppxD69VeK/+8/VMyaRXD1airefpviu++h+PY7AMg54wyyjjoqelz1119T+tjjVC9YQNWnnxFcvTr62CYtS2ecTvbEidHHKgvfZe1pZxBqQcmS1lFSSinVbDmOw6Du3QmHQ3z/228ALPjmG/w+P4fts0+05SUVRbrXso46inBVFSX/vZ8iuQ7S0qC6Orpf7vnnkR0zQLvm228pe/xxquZ/jJOZSdqgQdQsXUa4rIxAly62Gy5SwdtxyD39NByfQ+nDjwBQOWcO6/50Gm2nPIwvOzvhzzvRNFFSSinVrDmOw+969CQUCvPj6lUAfLJsKX6/j4P33Ctlk6XY5U6yjz2WQJcuVH22gOrFiyEUIm3QQNIGDIhW9wabJJU+MoXKuXPBcfC1b0/NkiVUvPoqTm4umUf+gdzTT9+kgjdAzsSJ4PNT+uCDAFTOncvaUyfS7rEpzT5Z0kRJKaVUs+c4Dr/v1YtQOMTPa9YA8NGSJfh9PgoG/z51k6WY5U7S996b9L33rl0It856bdEkac4c0vr3J/Pww8k8YhROejrVS5ZQ+sQTlD36GI7jI+e0iZuVJcg59RTwOZTe/wAAVfPmsfbkU2j3+GP4cnIS84STQMcoKaWUahEcx2HPXr3ZpV276LZ5ixYx54svkhjVjotNaMLhME4gEJ39FrFJkjR4MDlnnUnmkX/ASU+3Fbz32IPc00/Ht9NOlD3zDFULF9b7s3JOPpmcc8+J3q/68CPWnnwKoZKSpnuCSaaJklJKqRbD5/Oxd+8+dGzTNrrtvYVf8P6X9ScGqSa2ZSxSbLLmu+82TZJOm0ja734XbXFyAgHCNTUEevQgY9gwwuXlhLeQ+OSceCK5558fvV/10XzWnnQKoeLiJnpWyaWJklJKqRbF5/Oxd9++dGjdOrpt9oIFfLh4cRKjahrVy5ZRcv/9VM6dW5skDRpUbytUqLiY6q++stu2kvRkHz+B3Av+HL1f9fHHrDnxZEJFRU3zRJJIEyWllFItjt/nY9++e9A+Pz+67e1PP+HjpV8lMarGF1q7lqp5H5DWvx85p58WTZIi5REiM+fC5eWUv/QSNcuW4e/alfRhw7Z67uzjjiP3wr9E71d/+ilrTjyJ0MaNTfZ8kkETJaWUUi2S3+9nvz360a5Vq+i2t+bP57OvlyUxqsaVMWQIra67jpzTTiNt4MBokuQ4Tu1tRQUVM2ZQ/tLLOHl5ZI8fjy8np0G1prLHjSP3ooui96s/W8CaE04ktGFDUz6thNJESSmlVIsVcJOlNnl50W2vf/ghX3z7bRKjahyRwpGZI4aTvtde9SdJlZVUvPkWpU9OJVxaSvYxY8k4wLYmNXQmYPYxY8m75OLo/erPv2DN8ScSWr++8Z9UEmiipJRSqkVLCwQY0q8/rXNzo9tenfc+i5YvT2JUO67u9H5g8yTpjTcpffJJwsXFZI07lsyjjsIXM3arobLGjCHv0kui96sXLmTNhBMIrkv9ZEkTJaWUUi1eJFnKj6kH9PL7c1ny/fdJjKppRLvb3nrLJkklJWSNO5asMWPwx5RO2FZZf/wjeZddBm5LVPWiRaydcDxBd8HeVKWJklJKKQWkp6UxpP8A8txK0+FwmJfem8OyH39McmSNKxwMUv7qq5Q+MoVweXmjJEkRWaOPJO/ymGRp8WLWHDeB4Nq1O3zuZNFESSmllHJlpKUxtP8AcrOyAAiFw7ww512+/fnnJEfWeBy/Hycnh9DatWT98ahGS5Iisv7wB/KuuCKaLNUs+comS25F9FSjiZJSSikVIzM9naH9B5CTmQlAKBTif4WzWb5yZZIjazxZRxxBm3v/Q9bYsY2aJNWefxStrroS3HFSNV8tZc34CQRXr270n9XUNFFSSiml6sjKyGDogAFkZ2QAEAyFeG72O3z/229JjmzHRWbDpfXrh799+yb7OZmHHbZpsrRsGWvGHUcwxa6hJkpKKaVUPbIzMhk6YCCZ6ekA1ASDPPvOLH5avSrJke2Y+mbDNZXMQw+l1TXXQGQ5lW++scnSr78mLIYdpYmSUkopFUdOZibDBgwkIy0NgOqaGp6ZNYtfUnS8TTJkHjySVtfGJEvffcfqcccRTJGuTE2UlFJKqS3Izcpi2ICBpLvJUmV1NU/PeptfU3zaeyJlHnQQrSZNiiZLweXLWT1uPDU//5LcwBogkOwAlGoqIrIC6BLn4d+MMR3rOWYocDWwP5AJfAM8DNxtjAnG+TmjgUuB3wN+YBHwH2PMozv6HJRS3pCXnc2w/gOY++VCqmpqqKiqYurMGZx86GF0aNMm2eGlhMwRw3GuEzaaSVBTQ3DF96wZP572zz1LYNddkx1eXJooqeZuI3BXPdtL6m4QkTHA80AF8AywDjgKuBMYBoyv55gLgLuBtcATQBUwDpgiIgONMZc2ztNQSiVbq5wchvQfwPtfLqQ6GKSiqoonZrxF91068c0vP1NVXU16WhoDunZjv36bLouirIwDDyT/uuvYeO21Nln6/gdWjxlLxpD9qXhrBuHSUpycHLKPGUvuOWcT6No12SHjNGTRO6VSkduihDGmawP2bYVtPcoHhhljPna3ZwKzgCHACcaYp2OO6Qp8BZQCexljVrjb2wDzgR7AUGPMvG2MezYwokuXLkycOHFbDqWiuJj577xDXnbO1ndWSm2X9cXFvL/oS2qC9TYy43Mc/D4fxwwfQQ8Pt5QkU+X777Pxmmuhurr+HQIBnLQ02t7/XzJHHtTQ0zZscbptpGOUlLLGATsBT0eSJABjTAW2Kw7gvDrHnA5kAPdEkiT3mPXAje7dc5sqYKVUcrTJy2Nwj55xHw+Fw1QHg7zwbiHri4sTGFnqyBg6lNy//S3+DjU1hMvLWXf2OdSsWJGwuOqjXW+qucsQkZOBztiWny+Ad+sZbzTSvX2jnnO8C5QBQ0UkwxhT2YBjXq+zj1KqGVlTtHGr+wRDIT5aspjD990vARGlnpplS22NJbeuU33C1dWU3P8grW+8PoGRbUoTJdXcdQQer7NtuYicZowpjNnWx71dVvcExpgaEVkO9Ae6A0sacMxKESkFdhORbGNMWd19RGQiMLGemAfHfzpb4TiE/X6q0S51pZrSTw2oMB0Kh/ly+XJGHXhgAiJKPZUzZmwxSQKgpoayF57XREmpJvIIMAc7C60Ym+RcAJwNvC4iQ4wxn7v75ru38T4mRra3jtnWkGNy3P02S5SArsCILT+FbZOWlUX7bt2ojtfvr5RqFPHGJ9VVVVNDYLfdmjia1BQuK2/YfiWlTRzJlmmipJotY4zU2fQlcK6IlACXAJOAsQ08XWSQ4LY01WztmBVAYT3be7Zr127Xjh03q16wVX6/n379+m3zcUqpbTN9+nSqqqq2ul+6W9Vbbc7JySFcstkE5M33y03u5BRNlFRLdB82URoesy3SKpS/+e4AtKqzX+T79u4xa7dwTFF9JzTGTAGmxPl52nemlIcNGjSITz/9lNAWuo58Ph+DBg1KYFSpJfuYsZROfQpqauLvFAiQfcyxiQuqHjrrTbVEkYWaYj+mLHVve9fdWUQCQDegBviugcfs4p7/p/rGJymlUtuQIUPwu1Wm4/H7/ey///4Jiij15J5zNo5b7TweJy2N3LPPTFBE9dNESbVEQ9zb2KRnlns7qp79hwPZwPsxM962dswRdfZRSjUjbdu2Zfz48aSlpeGrs8isz+cjLS2N8ePH07Zt2yRF6H2Brl1pe/9/cbKyIFCngysQwMnKou39/0160UlNlFSzJCL9RWSzVygR6QLc4959Iuah/wFrgONFZO+Y/TOByHSLe+uc7hGgErjALT4ZOaYNcKV7977tfxZKKS/r1asX5557LnvttRcZGRk4jkNGRgZ77bUX5557Lr169Up2iJ6XOfIgOsx8i5yTTsLJywXHwcnLJeekk+gw861tKTbZZLQyu3Iv/AAAHghJREFUt2qWRGQScAXwDrAcO+utB3Akdg236cBYY0xVzDFHYxOmCuBp7BImf8SWAfgfcJwxZpN/GBH5C/Bv7BilZ6hdwmQ34PYdWMJE/zGVUmrbNEllbk2UVLMkIiOwVbF/j62llANsABZg6yo9XjfpcY8bBlyF7Z6LXRT331tYFPco7KK4e2JbaRdjq3XvyKK4+o+plFLbRhMlpVoQ/cdUSqlto2u9KaWUUkolkiZKSimllFJxaMFJpZqRN954g19//TXZYSil1A7p2LEjo0bVV3kl8TRRUsqbtquv/cMPP/yK2sV6lVIqJX3//fdLR40a1TfZcYAmSko1N7nu7UbsDL+WYjB2KRkvP+9UiNFrUumapVKsXha5jrlb2zFRNFFSqnn5BtgVWGCMKUhyLAkjIrOBEXj4eadCjF6TStcslWL1spjr+E2SQ4nSwdxKKaWUUnFooqSUUkopFYcmSkoppZRScWiipJRSSikVhw7mVqp5mQLMBlYkNYrEm4L3n/cUvB+j10whda7ZFFInVi+bgseuo671ppRSSikVh3a9KaWUUkrFoYmSUkoppVQcmigppZRSSsWhiZJSSimlVByaKCmllFJKxaGJklJKqWZJRHZLdgwq8USkUXMbTZSUaqFEZJ9kx+BFIuIkO4a6RGS0iOwvIhnJjiVViMizwEMikp/sWFRiiMjpAMaYUGOeVxMlpVogEXkd+ybSNcmhJJ2I9BKRAhE5TETaAOnudk8kTCLyEDAVuAbISXI4KUFEXgLGAd2BfHebJ36fdUXi8mp8qUJE3gD+KSIHNPa5NVFSqoURkenAQcAjwJokh5NUIvIfYJb79QbwGfAvEelnjAk3dhP+dsQ3DRgPPABcZIxZF/OYvrHWw33DHAV8DvQALgUwxniuurKIGGC0iPjdvzf9nW4H9zWtAPgn9vfeqDRRUqoFcVuSDgL+ATxsjClJckhJIyIvAhOBT93bfwPrgLOBmSIyzBgTStabl/smeghwI3CDMebr2Mcjb/z65lrL/fseAfwV+3tcD4yItJx66VqJyP8AA/wNKBARnyZL267Oa9pDxphid3ujXUddwkSpFsL91DUC++L8oDFmQ8xjbYAcY8xPyYovkUTkSuB64Drg/4wxq0UkE/g99lPpgUANMMoYM8t9E2vUcQ9bia818DoQBsa48WUA7YA/AW2AEuAlY0yjf4JORTEtpVcBU4wx60TkSeAE4HRjzJRkxhdLRC7D/p0tB3bFtmReDbwTSc692ALmNSLyMnAwtlt6Sp0W10HYrurlQLkxZuP2/hxNlJRqAURkFrZp+grgDmNMjYhkAwOwn76HAx2BmcC7xpibkhVrIojIm0BvYE9jzHq36yPoJiOXYhMoB6gEDjDGfJLg+AYDHwHXGmP+6Q5IHgdcBvSK2TUEXAA8bowpTWSMXiIiM7DJbaRVocjdfhzwNLY75igvfBAQkZHAw+7dU4FDgb9jk6VrgFmaLG2diLyNTYzvMMZc6m7LA/bDvqYd6e76MzAf+7/05fb8LO16U6qZE5Fc4Hfu3a7GmBr3+4nA/7BjYEqAldiE6QYRuTfRcSaCiPjcKePDgWKgVEQCbpLkN8ZUAm8BpdgVzDOAO0SkY4JDDWOTIL97vwC4Fds1eCJwBHAP9jX839gkylNdS4kiIqcAXbEtMg8ZY4pExA9gjHkWeBU7qHs3d/9kv+91BzoDFxhj3sUmTfdgWzMnAyO1G65Blrm3w0Wkj/v9ScATwBDsuMO3gHLgaOBpEem/PT/IP2nSpB0LVSnlWe4LbmVhYeGDwFHAEYWFhe0KCwuzsW+8K7CJ0o3YT94LsG/KBxYWFq4uKCiYn5zIm0ZBQUG4sLCwFHstdgGeN8asFZF0t5XNj/00uiu2Sf93wP7AWwUFBd+LiFNQUNDkcRYWFrYHzgQyCgsLpwG3Y7sChxpjvigoKPi2oKDg9cLCwhLswOXDCgsLpxljVjd5cB5TWFj4LfA+MN0YU+y2xIQgmjjujm1d2KWwsPD5mA8KSVFQUPBpYWHhh8CcwsLCamPM+sLCwq+wLZhjgD2AFYWFhd+7LUuBgoKChHX7ep2I+AoKCsIFBQWvFRYW5mA/JOxbWFiYge12XQ4cZoy5u6Cg4InCwsJZ2L+BA4CswsLCtwsKCqq35WcmO7NWSjWRyBuG22KyDts1sRTbVfMY8D1wkDHmY2NMqTHmB2PMU9iupzAwLGnBNxE3EfIBXwI7A4+LSEdjTJW7ywTsm9UKIAg8jx3nMBYSN3PKGLMImA7sTe0092nGmGoRSYtpMbkdeBzIZtMuuRbB/SBQaoyZF5mYEPs7cr+/F9v68HugX+S4JMUbcON6wxhTHInVGPMDtmUwtmXpoEgC7x47VAtoAhCO+fu/DPshYl/gbuBH4BBjzA+R37H7v2SwLeb7Y1uJt4kmSko1QyKSFZne7raURJKlYdhPXDXAScaYqnreNCKDg/cWkfap3vwvIqNE5HAAY0zQGFONTQYXYl843xORV0VkJvAQkAWc5Y75mYftlmyVwHgj1/tZ9/ZGbNdSkfscqmPGU4EdfwH2U3OLsrUB9m53ajHwArYF8ZiGHNeY6vz9xW3NipMs7e+e40/YLrrLI8lWSyMio8Emv5Gucvf+34E7seMJLzXGlNcz+eJb7P9PL6DLtv5sTZSUamZE5L/YcTWt3BalusnSXtgZN2ug9k0j8sKDfVEpA5YaY9ak8oBSEXkQmAKcLSId3G1+9zqMBF4B0oA/YGvuvAHs775pAWzEdolU0YRik9GY6/0a8CSQ58YwQUR6xzyHSne/XtgxVQkdcJ5sDUngjTFB99uXsWO+zhSRAU0aWIz6/v62JCZZ+j/cGZgicjNwE3Zc03+S3XWYDO7A7ZdFJDLWkjrJ0iXYsXvfuvcjr2mRVqVi7P/QQmrHNjWYJkpKNSMiMhU4CzsG53IRyauTLPndsgD/NMasjznOF/Omch62u2mOiDip2qIktjrzcdjWhMuMMavc7sigiKQZY9Zip44fiB2PNBQ42Rjzc8xpTsIOqH7bPWejXQsRudGdlUXdgbvu76MMuBw7GLkK2210voj0jPyuRGQMdqDqYtw3ieZsS9dsS4wxHwD3Ae2xY4CafOB7vL+/rf1sN1m6BZsw/Q47Iy4T2NcYs6QpY/YisXWS9sX+L6yIfaxOsjTNGPNrzHG+mITpHOwHijnANo1PAi0PoFSzIiIPYMfYlGBn+dwG3OQOcq23FlBkarz7/dHYF+lq4HAvTKfeHiJyHXARttvqATcp2tL+TkxXZeTFdTRwM7ZJ/w+xL8KNEN/z2HFPHwDXG2Omx8bhfh8pWZCPrfk0DugALMK++fbCzt7LAoYbYxY3Vnxe1JBrtpXjT8TOiFqGvV6rmjDWbfr7izku9n/xYuz/73rgwOb++62PmyQVAFdiC+TWWwsp9rrVvS8ix2D/fzKBkcaYFdsahyZKSjUjInIjthXkfOyLbDfgDmqTpTR3jE59Ly7nYF/c2wMF7iDIlCMirbD1oCqB44wxK93xPB2wJRGy3V0fBn4yxpTXOT4AXAycgq0t1ajXQmqLDX6HHaT9OXBVnGTJ57YIZmNLAkzALQWA7Rb8ELu0yVeNFZ8Xbcs128p5Psf+HQxqqhmCO/r3555jIjbJysQmSSn5v7gj3CTpAEDYvEDuAOy12WCM+cbdttkHQRG5FDt7tA1wsNnOOkqaKCnVDMS0iByJHZA8Cpvw/BfohB3seJux1YrbAevc/f3YLp2bsIXvlgETUvnTq4j8Hjte52JjzF1ii9AdB1wC9MXOZvMD32C7Yx6PfdMUkb8A/8IWfDytMbs7RGQE8Cj2Rf5I92sStizD1VtKlmLO0RfbirQSKDHNfBma7blm9Zwj0jp3CvCBqbMcTCPHu6N/fz2xY9N6Y5Ok7XpzT2Ui8jj2A99Vxi1+KyI52O7xi7AfGsCOsywEzjC2flbkg0XkNe0o7O/ilB35MKFjlJRqBmLeIL7FfnLtaoyZCZwD/IRdT+pcEdkDO0vqNve4IHaQ43rsbJsjUzlJcmW6t5HXt0OwNaOKsOO3/gg8h/2U+Q/gOBEJRMaNGGPuxr4QH93ISZID7IMtSzDR2Grf92G79wYD14vIH9wYwjHx1B2Y+pUx5jNjzK8tIEnarmtWV0zL6ZNNmSS5dvTv7xvs+KT9WmiSlEntNTw+5qHTsGVN9sGOGXwJm3Qeix3onRvzgWIF8B52JYKjd7TFVRMlpZoJt3VoJbZkf29387vAX7A1k67FdtW0Bj6X2pouX2CLLF4dM9srla3EjtE6xL1/BjZZHG6MecgY8zo2gbwJO+Ptz0BuZIwSgDHmzcYck+SeM4xt4fsT9lMw7jiZ27DdSvW98afFHB+S2pmJLcKOXjPYZDZnosoCNMbf35PGmG2enZXq3FbBCmwX5X3AQBFZ4I4XvAL7QXAYMNoYMxbbwrQIO1bv/yLncSdC3AHcWWdyxnbRrjelmhmx67pVYpudQ+4b7InYaco+7PiJCcaYjWIL2jXp1PdEcxPAQuyaT1dhX2BvMsbc4r5pht1rkovt4jgKON7Y5S6aNC4TZ2q32x16iRvrJl1K7uMHGGPea8r4vKjuOLo6j3nymnn17y9VxHST5mAT4nPchz7HzvyLjLFMM7YAa29sN/kv2K7KBg2c3xbaoqRUMyG1hSOX4RYfdF+QO2FnslUAa4ERwF9FpE0zTJLS3GREsLWgJmIHz0ZKIUSqlae53VbPudvTmzo2Y8sz1Pua6764386mrSSHAojIqcA0EbmvqWP0GvcNM153mueumTtGxpN/f6nC/Z0HjC34ein2A95C4M9uYhQpB1Dtth7+DPyKnQW6U7y/lx2hLUpKNRMxA7rHYas6twXygbnYwb/XAl9jB3bvgS3rf31DZgt5kYgMBgZhaz597Y7JijzWDjv+40xsVe1C4AhjTIWIZLrN+4jI3di6UUONMR8lIr6tDDpuh62bcxl2NfnZ2JluOdium4WNGaPXiF2iowewATtQ/Vt3uyevWX0zrWJiSurfX6oQkf2AntjxRiuNMYV1Hs/BjkN6xWxe+y0yfu8b7MDuoU3RvaqJklLNjIgMxXavnQXcgK3sfLUx5l738dHYT7wn7eggx2QRkbuwi/nuErP5bGPMgzH79MFO8x+HHTj7EHBOzIvr0dhxDKuxdZIarcm+IfHFOc7BtkBciX3zD2CThuHNfWCviERmKfXDtsYsB4wx5oWtHJfwayYi/wGmGGM+2kKylLS/v1QhIo9i677FLhE0FXjWGPPyFo6LTZLOw45P+he2KGV1Y3/400RJqWZGRHbFTontgH0RNsB/TUwhQyDDHfCYckTkRWwl7TewC8J2wb5IbgD2BL6Pea69gVOxA2p3xl6XWdhinCOxg2kbtVjj1uIzcQre1Xnx/zN2kc8WUWxQbBXr0djFir/EJpgF2FaCY40xc+Icl/BrJiJPY6f7f+vG9sUWkqWE//2lChF5BlvqYSr2f2VX7KD9QdiutHuxKwiEZdMCkr46yeYN1BaT/L4pYtVESalmSERuwc66eQS4x9SpOp2qxK6ddRx2xtB9kaZ4EbkVO7C3V6S7JuaY9kB/bAG/PbCz/n7DDg5t1GKN2xNfPec4A/vin04LKDYoIvdil5K5Gfeaia09NAlb1uIfxpibt9L9lpBrJiJXYP+OfsImO98Bx2wlWWoLDCQBf3+pwp1c8hC2JMkNxi0m6bbCHYPtRs0CbjbGGPex2AQpHVtU93zs9RzZlC2umigp5XFbeoOoZ9/YF5Mh2OJ6zSVJOgP7ZjMVmGzswraRxx7A1qcZAvQByoH3YmeZiUgWttJ2F2ApUGbiLImQoPjm1J3RJSI9sJ+khwN7t4DutjHY5/sKNiFaFzPWbjgwA1vSoiDe32+irpnYwpdPYZf32Q+byJ1NA5Il9/gm/ftLJSIi2G6yfd3rFp0RKnbJnrHYgfrpwDXGmLvcx3zYxYHvBQ4HPgZObepkU2e9KeVR7mDgbV38MyS1tVjmNaMkKQ/bFbMKuKtOEnIYtkBkOvAW8Bq2e+NxEdnb3SdgjCk3xiw3xsw2xqxs5CRpe+J7QkT2qnOqH7BVqPu3gCQpHVtQcCdsF0s0SXJ3+QxbODAH2NIHhSa/ZmKn/PfHdpVdZGyxz3Pdn9sdeEFEBsX+/9U53teUf3+pIuba9MT+P0TGJkV/v+51eRZbViEEnOEO+I7UwSoBXgSuwSaoTd4ip4mSUh7kjtn4VEQOh21PlrZ0PxUZY4qB+4GTjTHfS+0q7MOwn+w7YBe+PBeblLyEHUR7jnt8vfWLPBDfuZFzuElCtbHFBrfYPdccGFua4nPgfmPMcnccSmxCFMSWtEjHfa+qm4S4CXCTXzP372cWdqzRa+60dIwxpxEnWZLEF7pMBZHf77vubeT1bZMyEO74yWnY/6n+2BamyGNrsOvk3WIStGi3dr0p5TEicg+27x1gHbYY3Vanlscc3wVoZZrpVPKYrpnW2OTjLGCMMeaNmH1+BzyN7eb6XSKvhdfj8xKxy1W0McasjPP4e0A74PdAVUy38u7GmB8TF2k0ntguotjvH8EORI52w8UcMxj4vLFnYqUytyX1fWwL3QRjzHPu9k1e39wW4Texyyz1B35LRtKpLUpKeYiInIBd02gudqBjW+A5ETkEtt6y5A5cfgG7RMmQBISccJEXUncA6GvAEGPMG+6neMdtmfgcW08HateN0vg8xhhTES9JcvmwY4JCMUnSKGC2iJyViBhjxbZMGltANLIMUGzL0jSxCxcjImdSu+aYchm7Zt9l7t0rxS0UGvv65iZNH2NbX1sDmclqmdNESSmPEJGdsWM2soDzjDEXYmdP5dPAZMltll7j3l1d3z7NgdQuIPq6MeZT90U15G6LDJDuhZ2d1NSLoKZcfKnAHcOUBgTdbrrIeK/J2BlnHycxPKDeZOkxoBvwqohcjV3CxAdMj3+WliXmtetJ4EHgd3azjILa9fpiWpbaY8f+bUh4sC7telPKI0SkDfaFdbEx5uGY7ZPd7RuB8bHdcFDbglFnxltH08iLunpdned/JraY33PA+caYyqQGh/fj8yIRmY8d0Ls/cBh2uZIewDAvdVfKpnV+HsYuXQL2f/bA5j4wf3uJSD9sa9vJwDfAjcaYKTGPH4ldHPcz7BCEpNR+0xYlpTzC2Jo7k7EzPiKFITHGXIOtEbNJyxLgq5skxXy6bclJ0lHY+jtrsUu0JD0J8Xp8XuQO3A5iK22PpjZJOsBLSZIrtkvoLfd2HTah0yQpDmMLbd6ALRTaE3hYRJ4WESMi/3a3ZwJ/T1aSBNqipJSn1fmkGtuydLwx5k13+3nY5v5rjbuGVEvkJpYXYtfOagMc5KU3Ka/H5zVi6w59gB3MvQY7/ueA2IHSXiMi52NbSPKwSVKLq7i9PdxZhMdhVxHYGXv91gFfYZf+Sep11BYlpTzMnTZbX8vSUyIyUkTGYqefX4od+J2yGlr+IM6xu2OXh7gJ21LT6N0dXo/Pi3bkmmFbaaqATtgxSU2aJO1grIhd0HciNtZmv+xMPNtzHSMlHrCrCRyA7YobiZ0tmvTrqImSUh5XT7Ik2Fkgz2Nn2gSAQcaYX5IX5faT7SisWY912IG012HX32rMZUk8HZ8XNcY1c7sk38MWGBzeVElSI/1+wS5Lci3QtyUkwXXtyHWMGW/5gzFmoTFmqjHmC+ORhYK1602pFCEi6TGzf6ZhV91ej30TScn1wMQW1jwKOCKmK7HBS7bUc75obZuWEJ8XNeY1E5EOAMaYVY0bZfT8jfr7bama+3XUREkpj4h9YRGRHGNMaZz9TsauKZaLHQexJIFhNhrxeGFNr8fnRal0zVIpVi9rCddRu96U8oA6SdKxwC0i0que/Y7C1h7JxbYkpWqS5OnCml6Pz4tS6ZqlUqxe1lKuoyZKSiVZnSTpKGxr0RnY2W11rQI+IoVnTInHC2t6PT4vSqVrlkqxellLuo6aKCmVZDFJ0hhsrZg87IDQVbL5SuQfA6OMXQIjVVVhq1GfGUn2jDFXUU+tqMiLbOwLbeSaGGMOBzoZY75pYfF5USpds1SK1ctazHXUREkpD3CboB/E1hAZaoxZIbaG0iZrGxljgsksvNYYjMcLa3o9Pi9KpWuWSrF6WUu6jjqYWymPEJFhwK/GmG8lptBkSyAeL6zp9fi8KJWuWSrF6mXN9TpqoqSUx0gLmEJenzgvshuAcdhPp/cBOwG7mSTUjPJ6fF6UStcslWL1suZ4HTVRUkp5Rp0XWYNd0mAj4AeqgRHJHMTu9fi8KJWuWSrF6mXN7TpqoqSU8hTxeGFNr8fnRal0zVIpVi9rTtdRB3MrpRKqzsyXnLqPx7y4ngzshW22PyBRL65ej8+LUumapVKsXtaSrqMmSkqphBGPF9b0enxelErXLJVi9bKWdh01UVJKJYR4vLCm1+PzolS6ZqkUq5e1xOuoiZJSKiGMxwtrej0+L0qla5ZKsXpZS7yOOphbKZUwbmHNJYAD7B1TWNMTNaO8Hp8XpdI1S6VYvazFXcdwOKxf+qVf+pWwr0mTJg2bNGlSD/d7f7LjSbX4vPiVStcslWL18ldLuo5JD0C/9Eu/WubXpEmTAsmOIZXj8+JXKl2zVIrVy18t4Tpq15tSSimlVBw6mFsppZRSKg5NlJRSSiml4tBESSmllFIqDk2UlFJKKaXi0ERJKaWUUioOTZSUUkoppeLQREkppZRSKg5NlJRSSiml4tBESSmllFIqjkCyA1BKKZVcIjIbGFFn80HGmNmJj6Z+IrIByI/dZoxxkhSOakE0UVJKKQ8TkRVAF0CMMZMaa984ioBy9/uq7Ti+bjwHAbPcu/sZYz5qwDFtgF+BdOA8Y8x97kO/ARWAH2i/o7Ep1VCaKCmllIr4qzFmSiOebzbwPTZ5OxXYaqIEHI9NkiqBZyIbjTF9AESkK7C8EWNUaot0jJJSSqkmYYwJA4+5d48XkbQGHHaqe/uyMWZ900SmVMNpoqSUUqopRRKldsAftrSjiPQC9nfvPtqUQSnVUNr1ppRSqsFExAechG35GYwdYL0GmAPcYYz5MHZ/Y8w3IjIXGOYe89IWTh9pTfoNeLORQ1dqu2iLklJKqQYRkTxsAvMYcAi2lagc2AU4DnhfRC6o59BI69Bod7B2fed2gJPdu08aY2oaM3altpcmSkoppRoqkiB9ARwJ5Bhj8oE2wJVADfAvERlW57hnsTPW0oEJcc49HOga83OU8gRNlJRSSm2ViBwCHA2swNZYmm6MKQcwxmwwxtwEXIN9X/lH7LHGmI3Ai+7dU6lfZPsCY8znjRy+UttNEyWllFIN8Sf3dooxZl2cfaa6tweJiL/OY5HutyEi0jP2ARHJAsbV2U8pT9DB3EoppRpiqHv7NxE5byv7ZmPHL62K2TYD+AXoBJwCmJjHjgZaYbvupqKUh2iLklJKqYbYxb3NB3bewldEduzBxpgg8IR79xR38HZEpNvtDWNMbHKlVNJpi5JSSnlbhXub1YB9I8lJ+Rb32j6RD9ZjjDEvb+c5HgUuA7oBBwBzRKQjcGjM40p5irYoKaWUt611b3fZ0k4ikgG0rXNMY/rNve23vScwxiwGPnbvnuLenoRdv2098Mp2R6dUE9FESSmlvO0z93boFveCfbEJR+wxjWmee3vsDp4n0mp0nIhkUtvt9rQxpnIHz61Uo9NESSmlvO1597aHiIzZwn4Xu7fLaZpEaYp7u7eIxJviD0C8opKup4Aq7Finq4FB7nbtdlOepImSUkp5mDHmHeyMMYAnROQcEcmPPC4ifUTkCezMMYCrjTGhJojjDeAF9+7DYkW7A0WkjYiMEZGXgDu2cJ61wGvu3Ui9paV1lz5Ryit0MLdSSnnfidg10oYC9wH3isgGbKXrHHefMHCNMaYpp9efiv2AfTRwLXCtiGwEHOz0/ogpWznPo8BYaj+sa2uS8ixtUVJKKY8zxqwBRmAHQL+GHVid6z68FHgA2NMYc0MTx1FqjBkLjMa2Lv2MnY2XDnyDrYE0Djh/K6eaDqx2vw9RWzZAKc/RFiWllEoB7iKxT+CBpMIY8xq13Wfbc3w10KHxIlKq6WiLklJKKaVUHNqipJRSKuIREXnE/f4gY8zsZAYTyx2Tlb/VHZVqZJooKaWUWkdtQcmIqmQEsgW/UVulXKmEccLhcLJjUEoppZTyJB2jpJRSSikVhyZKSimllFJxaKKklFJKKRWHJkpKKaWUUnFooqSUUkopFcf/A7RJWg7LYq8iAAAAAElFTkSuQmCC\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig = plt.figure()\n", + "ax_pd_left.plot(U_sc_cs, Ts, \"o\", ls=\"-\", color='grey')\n", + "ax_pd_left.fill_betweenx(Ts, U_sc_cs, U_charge_cs, alpha=0.25, color='grey')\n", "\n", - "ax_pd_sc = fig.add_subplot(111)\n", + "ax_pd_left.plot(U_charge_cs, Ts, \"o\", ls=\"-\", color='C1')\n", + "ax_pd_left.fill_betweenx(Ts, U_charge_cs, [min(U_charge_cs)]*len(U_charge_cs), alpha=0.25, color='C1')\n", "\n", - "negative_U_sx_cs = [-ele for ele in U_sx_cs]\n", + "ax_pd_left.set_ylabel('Temperature\\n[Kelvin]', rotation=0, ha='right', multialignment='center')\n", + "ax_pd_left.set_xlabel('U [eV]')\n", + "ax_pd_right.set_xlabel('U [eV]')\n", "\n", - "ax_pd_sc.plot(negative_U_sx_cs, Ts, \"o\", ls=\"-\")\n", - "ax_pd_sc.fill_betweenx(Ts, negative_U_sx_cs, [min(U_sc_cs)]*len(negative_U_sx_cs) , alpha=0.15)\n", + "ax_pd_left.set_yticks(Ts)\n", + "ax_pd_right.set_yticks([])\n", "\n", - "ax_pd_sc.plot(U_sc_cs, Ts, \"o\", ls=\"-\", color='grey')\n", - "ax_pd_sc.fill_betweenx(Ts, U_sc_cs, [min(U_sc_cs)]*len(U_sc_cs), alpha=0.35, color='grey')\n", + "ax_pd_left.set_xticks([np.round(ele,2) for ele in U_sc_cs + U_charge_cs])\n", + "ax_pd_left.set_xticklabels([np.round(ele,2) for ele in U_sc_cs + U_charge_cs], rotation=70)\n", + "ax_pd_right.set_xticks([np.round(ele,2) for ele in U_sx_cs + U_spin_cs])\n", + "ax_pd_right.set_xticklabels([np.round(ele,2) for ele in U_sx_cs + U_spin_cs], rotation=70)\n", "\n", - "ax_pd_sc.set_ylabel('Temperature\\n[Kelvin]', rotation=0, ha='right', multialignment='center')\n", - "ax_pd_sc.set_xlabel('U [eV]')\n", + "ax_pd_left.spines['left'].set_bounds(Ts[-1], Ts[0])\n", + "ax_pd_right.spines['left'].set_visible(False)\n", "\n", - "ax_pd_sc.set_yticks(Ts)\n", + "ax_pd_left.spines['bottom'].set_bounds(min(ax_pd_left.get_xticks()), max(ax_pd_left.get_xticks()))\n", + "ax_pd_right.spines['bottom'].set_bounds(min(ax_pd_right.get_xticks()), max(ax_pd_right.get_xticks()))\n", "\n", - "ax_pd_sc.set_xticks([np.round(ele,3) for ele in U_sc_cs+negative_U_sx_cs])\n", - "ax_pd_sc.set_xticklabels([np.round(ele,3) for ele in U_sc_cs+negative_U_sx_cs], rotation=45)\n", "\n", - "ax_pd_sc.spines['left'].set_bounds(Ts[-1], Ts[0])\n", - "ax_pd_sc.spines['bottom'].set_bounds(min(ax_pd_sc.get_xticks()), max(ax_pd_sc.get_xticks()))\n", + "ax_pd_left.text(0.3, 0.5, \"SC\", transform = ax_pd_left.transAxes, size=22, color='grey')\n", + "ax_pd_left.text(0.07, 0.5, \"CDW\", transform = ax_pd_left.transAxes, size=22, color='C1', rotation=90)\n", "\n", + "ax_pd_right.text(0.35, 0.5, \"in-plane AFM\", transform = ax_pd_right.transAxes, size=22, color='C2', rotation=60)\n", + "ax_pd_right.text(0.89, 0.65, \"out-of-plane AFM\", transform = ax_pd_right.transAxes, size=22, color='C0', rotation=90)\n", "\n", - "ax_pd_sc.text(0.2, 0.3, \"SC\", transform = ax_pd_sc.transAxes, size=22, color='Grey')\n", - "ax_pd_sc.text(0.6, 0.35, \"prediction\", transform = ax_pd_sc.transAxes, size=22, color='C0', rotation=-45)\n" + "ax_pd_left.set_title(r'Hubbard with $\\mu=\\xi$', color='grey', size=24)\n", + "ax_pd_right.set_title(r'Hubbard with $\\mathrm{Zeeman}=\\xi$', color='Grey', size=24)" ] }, { - "cell_type": "code", - "execution_count": 35, + "cell_type": "markdown", "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", - " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", - " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", - "Two-Particle Response Function tool-box \n", - "\n", - "beta = 11.6045250062\n", - "nk = 256\n", - "nw = 100\n", - "norb = 1\n", - "\n", - "Approx. Memory Utilization: 0.00 GB\n", - "\n", - "--> fourier_wk_to_wr\n", - "--> fourier_wr_to_tr\n", - "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", - "--> chi_wr_from_chi_tr\n", - "--> chi_wk_from_chi_wr (r->k)\n" - ] - }, - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 35, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], "source": [ - "_, delta_1 = get_lambda_delta(hubbard.copy(mu=xi, U=U_sc_cs[0]))\n", - "\n", - "plt.imshow(delta_1[Idx(0), :].data.reshape(hubbard.nk, hubbard.nk).real)" + "We can also check the gap function of the superconducting phase and study its symmetry in momentum space.\n", + "There we can see, that it is constant......" ] }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 92, "metadata": {}, "outputs": [], "source": [ - "%%capture\n", - "\n", - "xi = 0.3\n", - "\n", - "Ts = [1000, 750, 500]\n", - "hubbard_models_doped = parameter_scan(hubbard.copy(mu=xi), T=Ts)\n", - "hubbard_models_zeeman = parameter_scan(hubbard_spin_dependent.copy(zeeman=xi), T=Ts)\n", - "\n", - "U_sx_cs = []\n", - "U_sc_cs = []\n", - "\n", - "for hubbard_model_doped, hubbard_model_zeeman in zip(hubbard_models_doped, hubbard_models_zeeman):\n", - " \n", - " U_sx_c = get_phase_transition(hubbard_model_zeeman, S_x, S_x)\n", - " U_sc_c = get_sc_phase_transistion(hubbard_model_doped, guess=-1.2*U_sx_c) \n", - "\n", - " U_sx_cs.append(U_sx_c)\n", - " U_sc_cs.append(U_sc_c)" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.6,0.35,'prediction')" - ] - }, - "execution_count": 37, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig = plt.figure()\n", - "\n", - "ax_pd_sc = fig.add_subplot(111)\n", - "\n", - "negative_U_sx_cs = [-ele for ele in U_sx_cs]\n", - "\n", - "ax_pd_sc.plot(negative_U_sx_cs, Ts, \"o\", ls=\"-\")\n", - "ax_pd_sc.fill_betweenx(Ts, negative_U_sx_cs, [min(U_sc_cs)]*len(negative_U_sx_cs) , alpha=0.15)\n", - "\n", - "ax_pd_sc.plot(U_sc_cs, Ts, \"o\", ls=\"-\", color='grey')\n", - "ax_pd_sc.fill_betweenx(Ts, U_sc_cs, [min(U_sc_cs)]*len(U_sc_cs), alpha=0.35, color='grey')\n", - "\n", - "ax_pd_sc.set_ylabel('Temperature\\n[Kelvin]', rotation=0, ha='right', multialignment='center')\n", - "ax_pd_sc.set_xlabel('U [eV]')\n", - "\n", - "ax_pd_sc.set_yticks(Ts)\n", - "\n", - "ax_pd_sc.set_xticks([np.round(ele,3) for ele in U_sc_cs+negative_U_sx_cs])\n", - "ax_pd_sc.set_xticklabels([np.round(ele,3) for ele in U_sc_cs+negative_U_sx_cs], rotation=45)\n", - "\n", - "ax_pd_sc.spines['left'].set_bounds(Ts[-1], Ts[0])\n", - "ax_pd_sc.spines['bottom'].set_bounds(min(ax_pd_sc.get_xticks()), max(ax_pd_sc.get_xticks()))\n", - "\n", - "\n", - "ax_pd_sc.text(0.2, 0.3, \"SC\", transform = ax_pd_sc.transAxes, size=22, color='Grey')\n", - "ax_pd_sc.text(0.6, 0.35, \"prediction\", transform = ax_pd_sc.transAxes, size=22, color='C0', rotation=-45)\n" + "_, delta_1 = get_lambda_delta(hubbard.copy(mu=xi, U=U_sc_cs[0]))" ] }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 93, "metadata": {}, "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", - " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", - " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", - "Two-Particle Response Function tool-box \n", - "\n", - "beta = 11.6045250062\n", - "nk = 256\n", - "nw = 100\n", - "norb = 1\n", - "\n", - "Approx. Memory Utilization: 0.00 GB\n", - "\n", - "--> fourier_wk_to_wr\n", - "--> fourier_wr_to_tr\n", - "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", - "--> chi_wr_from_chi_tr\n", - "--> chi_wk_from_chi_wr (r->k)\n" - ] - }, { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 38, + "execution_count": 93, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ - "
" + "
" ] }, "metadata": {}, @@ -1896,17 +1499,11 @@ } ], "source": [ - "_, delta_1 = get_lambda_delta(hubbard.copy(mu=xi, U=U_sc_cs[0]))\n", + "delta_plot = delta_1[Idx(0), : ].data.reshape(hubbard.nk, hubbard.nk).real\n", "\n", - "plt.imshow(delta_1[Idx(0), :].data.reshape(hubbard.nk, hubbard.nk).real)" + "plt.imshow(delta_plot, vmin=0.9*np.mean(delta_plot), vmax=1.1*np.mean(delta_plot))\n", + "plt.colorbar()" ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { diff --git a/doc/user_guide/plotting_tools.py b/doc/user_guide/plotting_tools.py index 8cfea0dc4..ac8afad10 100644 --- a/doc/user_guide/plotting_tools.py +++ b/doc/user_guide/plotting_tools.py @@ -43,14 +43,11 @@ def __bsplot_impl(top, obj, path, xticks_fct, xticklabels_fct, *opt_list, **opt_ k_vecs, k_plot, K_plot = k_space_path(k_paths, bz=obj.mesh.domain) kx, ky, kz = k_vecs.T - get_gf_on_path = np.vectorize(lambda kx, ky, kz : obj([kx, ky, kz])[(0,0)].real) - gf_on_path = get_gf_on_path(kx, ky, kz) - - plot_min, plot_max = np.min(gf_on_path), np.max(gf_on_path) - y_ticks = [plot_min, plot_max] - plt_fct = getattr(top, 'plot') + get_gf_on_path = np.vectorize(lambda kx, ky, kz : obj([kx, ky, kz]).real) + gf_on_path = get_gf_on_path(kx, ky, kz) + plt_fct(k_plot, gf_on_path, *opt_list, **opt_dict) if isinstance(top, types.ModuleType): @@ -62,3 +59,5 @@ def __bsplot_impl(top, obj, path, xticks_fct, xticklabels_fct, *opt_list, **opt_ mpl.axes.Axes.bsplot = lambda self, obj, path, *opt_list, **opt_dict: __bsplot_impl(self, obj, path, self.set_xticks, self.set_xticklabels, *opt_list, **opt_dict) + + From 0c9aa7f4ece648fc285ff2478a8240e52c3aabce Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 10 May 2019 13:43:20 +0200 Subject: [PATCH 017/121] [tb] get rid of model class in favor of function Lose the unnecessary model class and make `SquareLattice` a function called `create_square_lattice`. --- doc/reference/python_reference.rst | 2 + python/triqs_tprf/tight_binding.py | 141 +++++++++++++---------------- 2 files changed, 66 insertions(+), 77 deletions(-) diff --git a/doc/reference/python_reference.rst b/doc/reference/python_reference.rst index 8b28293a1..285834cef 100644 --- a/doc/reference/python_reference.rst +++ b/doc/reference/python_reference.rst @@ -91,6 +91,8 @@ Tight binding lattice model .. autoclass:: triqs_tprf.tight_binding.TBLattice :members: +.. autofunction:: triqs_tprf.tight_binding.create_square_lattice + .. autoclass:: triqs_tprf.super_lattice.TBSuperLattice :members: diff --git a/python/triqs_tprf/tight_binding.py b/python/triqs_tprf/tight_binding.py index 19f03ee74..609adf84a 100644 --- a/python/triqs_tprf/tight_binding.py +++ b/python/triqs_tprf/tight_binding.py @@ -21,9 +21,6 @@ # ################################################################################ -import numbers -from collections import namedtuple - import numpy as np from pytriqs.lattice.lattice_tools import BrillouinZone as BrillouinZone @@ -134,83 +131,73 @@ def on_mesh_brillouin_zone(self, n_k): return e_k # ---------------------------------------------------------------------- +def create_square_lattice(norb, t, tp=0.0, zeeman=0.0, spin=False, **kwargs): + r"""Retuns TBLattice that represents a model on a square lattice + + The model is described by the Hamiltonian -Parameter = namedtuple('Parameter', ['name', 'type', 'default']) -Parameter.__new__.__defaults__ = (None,) - -class Model(object): - """Base class for models to check for characterizing parameters - """ - mandatory_parameters = [Parameter('norb', int)] - optional_parameters = [Parameter('spin', bool, True)] - - def __init__(self, **kwargs): - - for key, value in kwargs.iteritems(): - self.__setattr__(key, value) - - for parameter in self.mandatory_parameters: - - if not hasattr(self, parameter.name): - raise AttributeError('The parameter %s has to be given.'%parameter.name) - - if not isinstance(getattr(self, parameter.name), parameter.type): - raise TypeError('The parameter %s needs to be of %s type.'%(parameter.name, - parameter.type)) - for parameter in self.optional_parameters: - - if hasattr(self, parameter.name): - continue - - # -- If the default is the name of another parameter set it to its value - if isinstance(parameter.default, str) and hasattr(self, parameter.default): - setattr(self, parameter.name, getattr(self, parameter.default)) + .. math:: + H=-t \sum_{\langle j, l\rangle \sigma}\left(c_{j \sigma}^{\dagger} + c_{l \sigma}+c_{l \sigma}^{\dagger} c_{j \sigma}\right) - + t' \sum_{\langle\langle j, l\rangle\rangle \sigma}\left(c_{j \sigma}^{\dagger} + c_{l \sigma}+c_{l \sigma}^{\dagger} c_{j \sigma}\right) + + \xi \sum_j \left(n_{j \uparrow} - n_{j \downarrow} \right)\,, - else: - setattr(self, parameter.name, parameter.default) + where the angular bracket describes a sum over nearest neighbors and the double + angular bracket over next-nearest neighbors. - if self.spin: - self.norb = 2*self.norb -class SquareLattice(Model, TBLattice): - """Square lattice with nearest neighbor and next-nearest neighbor hopping + Parameters + ---------- + norb : int, + Number of orbitals excluding spin + t : complex, + Kinetic energy of nearest neighbor hopping. + Corresponds to :math:`t`. + tp : complex, optional + Kinetic energy of next-nearest neighbor hopping. + Corresponds to :math:`t'`. + zeeman : complex, optional + Strength of Zeeman term. + Corresponds to :math:`\xi`. + spin : bool, + True if spin index should be used explicitly, False otherwise. + The Zeeman term can only be applied if spin=True. + + Returns + ------- + square_lattice : TBLattice """ - mandatory_parameters = [Parameter('t', numbers.Number)] - mandatory_parameters += Model.mandatory_parameters - - optional_parameters = [Parameter('tp', numbers.Number, 0.0), - Parameter('zeeman', numbers.Number, 0.0)] - optional_parameters += Model.optional_parameters - - def __init__(self, **kwargs): - - Model.__init__(self, **kwargs) - - if self.zeeman != 0.0 and not self.spin: - raise AttributeError('There can not be a zeeman term in a spinless model.') - - t_matrix = -self.t * np.eye(self.norb) - tp_matrix = -self.tp * np.eye(self.norb) - zeeman_matrix = self.zeeman * np.diag([(-1)**orb for orb in range(self.norb)]) - - hopping = { - # Zeeman term - ( 0, 0): zeeman_matrix, - - # nearest neighbour hopping - ( 0,+1): t_matrix, - ( 0,-1): t_matrix, - (+1, 0): t_matrix, - (-1, 0): t_matrix, - - # next-nearest neighbour hopping - ( +1,+1): tp_matrix, - ( -1,-1): tp_matrix, - (+1, -1): tp_matrix, - (-1, +1): tp_matrix, - } - - units = [(1, 0, 0), (0, 1, 0)] - orbital_positions = [(0, 0, 0)] * self.norb - TBLattice.__init__(self, units, hopping, orbital_positions) + if zeeman != 0.0 and not spin: + raise AttributeError('There can not be a Zeeman term in a spinless model.') + if spin: + norb *= 2 + + t_matrix = -t * np.eye(norb) + tp_matrix = -tp * np.eye(norb) + zeeman_matrix = zeeman * np.diag([(-1)**orb for orb in range(norb)]) + + hopping = { + # Zeeman term + ( 0, 0): zeeman_matrix, + + # nearest neighbour hopping + ( 0,+1): t_matrix, + ( 0,-1): t_matrix, + (+1, 0): t_matrix, + (-1, 0): t_matrix, + + # next-nearest neighbour hopping + ( +1,+1): tp_matrix, + ( -1,-1): tp_matrix, + (+1, -1): tp_matrix, + (-1, +1): tp_matrix, + } + + units = [(1, 0, 0), (0, 1, 0)] + orbital_positions = [(0, 0, 0)] * norb + + square_lattice = TBLattice(units, hopping, orbital_positions) + + return square_lattice From e4866469d7c935bef5fc3bb13fdda61adcf4b25c Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 10 May 2019 15:35:44 +0200 Subject: [PATCH 018/121] [eli] refactor eliashberg_fft product, add test --- c++/triqs_tprf/lattice/eliashberg.cpp | 55 ++++++++-------- c++/triqs_tprf/lattice/eliashberg.hpp | 1 + python/triqs_tprf/eliashberg.py | 2 +- test/python/eliashberg/CMakeLists.txt | 1 + .../fft_product_constant_vs_full.py | 62 +++++++++++++++++++ 5 files changed, 90 insertions(+), 31 deletions(-) create mode 100644 test/python/eliashberg/fft_product_constant_vs_full.py diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index de731d0ea..49792982c 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -105,19 +105,36 @@ std::tuple dynamic_and_constant_to_tr(chi_wk_vt Gamma_pp_dy return {Gamma_pp_dyn_tr, Gamma_pp_const_r}; } -gk_iw_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const_r, - gk_iw_vt g_wk, gk_iw_vt delta_wk) { +ek_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, gr_tau_t F_tr) { auto _ = all_t{}; + auto delta_r_out = make_gf(std::get<1>(F_tr.mesh()), F_tr.target()); + delta_r_out *= 0.; + + for (const auto r : std::get<1>(F_tr.mesh())) { + auto F_t = F_tr[_, r]; + for (auto [A, a, B, b] : Gamma_pp_const_r.target_indices()) + delta_r_out[r](a, b) += -Gamma_pp_const_r[r](A, a, B, b) * F_t(0)(A, B); + } + + auto delta_k_out = make_gf_from_fourier<0>(delta_r_out); + + return delta_k_out; +} + +gk_iw_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const_r, + gk_iw_vt g_wk, gk_iw_vt delta_wk) { + auto F_wk = eliashberg_g_delta_g_product(g_wk, delta_wk); auto F_tr = make_gf_from_fourier<0, 1>(F_wk); + auto [tmesh, rmesh] = F_tr.mesh(); + // Dynamic part - auto delta_tr_out = make_gf(F_tr.mesh(), delta_wk.target()); + auto delta_tr_out = make_gf(F_tr); delta_tr_out *= 0.; - auto [tmesh, rmesh] = delta_tr_out.mesh(); auto gamma_tmesh = std::get<0>(Gamma_pp_dyn_tr.mesh()); // Test if the tau meshs of delta and gamma are compatible. If not raise an error, because @@ -127,7 +144,7 @@ gk_iw_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_cons " (" << gamma_tmesh.size() << ") must be the size of the mesh of Delta (" << tmesh.size() << ")."; - for (const auto [t, r] : delta_tr_out.mesh()) { + for (const auto [t, r] : triqs::utility::product(tmesh, rmesh)) { for (auto [A, a, B, b] : Gamma_pp_dyn_tr.target_indices()) delta_tr_out[t, r](a, b) += -Gamma_pp_dyn_tr[t, r](A, a, B, b) * F_tr[t, r](A, B); } @@ -137,16 +154,7 @@ gk_iw_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_cons auto delta_wk_out = make_gf_from_fourier<0, 1>(delta_tr_out); // Constant part - auto delta_r_out = make_gf(std::get<1>(F_tr.mesh()), delta_wk.target()); - delta_r_out *= 0.; - - for (const auto r : rmesh) { - auto F_t = F_tr[_, r]; - for (auto [A, a, B, b] : Gamma_pp_dyn_tr.target_indices()) - delta_r_out[r](a, b) += -Gamma_pp_const_r[r](A, a, B, b) * F_t(0)(A, B); - } - - auto delta_k_out = make_gf_from_fourier<0>(delta_r_out); + auto delta_k_out = eliashberg_constant_gamma_f_product(Gamma_pp_const_r, F_tr); // Combine dynamic and constant part for (const auto [w , k]: delta_wk_out.mesh()) @@ -159,25 +167,12 @@ gk_iw_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_cons gk_iw_t eliashberg_product_fft_constant(chi_r_vt Gamma_pp_const_r, gk_iw_vt g_wk, gk_iw_vt delta_wk) { - auto _ = all_t{}; - auto F_wk = eliashberg_g_delta_g_product(g_wk, delta_wk); auto F_tr = make_gf_from_fourier<0, 1>(F_wk); - auto rmesh = std::get<1>(F_tr.mesh()); - - auto delta_r_out = make_gf(std::get<1>(F_tr.mesh()), delta_wk.target()); - delta_r_out *= 0.; - - for (const auto r : rmesh) { - auto F_t = F_tr[_, r]; - for (auto [A, a, B, b] : Gamma_pp_const_r.target_indices()) - delta_r_out[r](a, b) += -Gamma_pp_const_r[r](A, a, B, b) * F_t(0)(A, B); - } - - auto delta_k_out = make_gf_from_fourier<0>(delta_r_out); + auto delta_k_out = eliashberg_constant_gamma_f_product(Gamma_pp_const_r, F_tr); - auto delta_wk_out = make_gf(F_wk.mesh(), delta_wk.target()); + auto delta_wk_out = make_gf(F_wk); delta_wk_out *= 0.; for (const auto [w , k]: delta_wk_out.mesh()) diff --git a/c++/triqs_tprf/lattice/eliashberg.hpp b/c++/triqs_tprf/lattice/eliashberg.hpp index 16d04e15e..5a14daf6d 100644 --- a/c++/triqs_tprf/lattice/eliashberg.hpp +++ b/c++/triqs_tprf/lattice/eliashberg.hpp @@ -95,6 +95,7 @@ namespace triqs_tprf { gk_iw_t eliashberg_g_delta_g_product(gk_iw_vt g_wk, gk_iw_vt delta_wk); std::tuple split_into_dynamic_wk_and_constant_k(chi_wk_vt Gamma_pp); std::tuple dynamic_and_constant_to_tr(chi_wk_vt Gamma_pp_dyn_wk, chi_k_vt Gamma_pp_const_k); + ek_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, gr_tau_t F_tr); /** Gamma particle-particle singlet diff --git a/python/triqs_tprf/eliashberg.py b/python/triqs_tprf/eliashberg.py index 8cc0d18f7..7349baab5 100644 --- a/python/triqs_tprf/eliashberg.py +++ b/python/triqs_tprf/eliashberg.py @@ -79,7 +79,7 @@ def semi_random_initial_delta(g_wk, nr_factor=0.5, seed=None): return delta -def preprocess_gamma_for_fft(Gamma_pp_wk, Gamma_pp_const_k): +def preprocess_gamma_for_fft(Gamma_pp_wk, Gamma_pp_const_k=None): r""" Prepare Gamma to be used with the FFT implementation Parameters diff --git a/test/python/eliashberg/CMakeLists.txt b/test/python/eliashberg/CMakeLists.txt index d02665b61..cbecb83cc 100644 --- a/test/python/eliashberg/CMakeLists.txt +++ b/test/python/eliashberg/CMakeLists.txt @@ -6,3 +6,4 @@ set(PREFIX eliashberg-) add_python_test(product_summation_vs_fft ${PREFIX}) add_python_test(eigenvalue_solver ${PREFIX}) add_python_test(previous_implementation ${PREFIX}) +add_python_test(fft_product_constant_vs_full ${PREFIX}) diff --git a/test/python/eliashberg/fft_product_constant_vs_full.py b/test/python/eliashberg/fft_product_constant_vs_full.py new file mode 100644 index 000000000..558bc7f80 --- /dev/null +++ b/test/python/eliashberg/fft_product_constant_vs_full.py @@ -0,0 +1,62 @@ +# ---------------------------------------------------------------------- + +""" Compare the implementations of the eliashberg products that use FFT. + +One can only handle Gammas that are constant in frequecny space while the +other can also treat dynamic Gammas. +Here we test if bot implementations give the same result for a Gamma that +is constant in momentum space. +This also tests the function 'split_into_dynamic_wk_and_constant_k', to +see if the split is done correctly. +""" + +# ---------------------------------------------------------------------- + +import numpy as np + +# ---------------------------------------------------------------------- + +from pytriqs.gf import Gf, MeshImFreq, MeshProduct +from triqs_tprf.lattice import lattice_dyson_g0_wk +from triqs_tprf.lattice import eliashberg_product_fft, eliashberg_product_fft_constant +from triqs_tprf.eliashberg import semi_random_initial_delta, preprocess_gamma_for_fft + +from triqs_tprf.tight_binding import create_square_lattice +from triqs_tprf.ParameterCollection import ParameterCollection + +# ---------------------------------------------------------------------- + +if __name__ == '__main__': + + p = ParameterCollection( + norb = 1, + t = 2.0, + mu = 0.0, + beta = 5, + U = 1.0, + nk = 4, + nw = 200, + ) + + H = create_square_lattice(**p) + e_k = H.on_mesh_brillouin_zone(n_k=(p.nk, p.nk, 1)) + + wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nw) + g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh) + + wmesh_boson = MeshImFreq(beta=p.beta, S='Boson', n_max=p.nw) + gamma_pp_wk = Gf(mesh=MeshProduct(wmesh_boson, g0_wk.mesh[1]), + target_shape=g0_wk.target_shape*2) + gamma_pp_wk.data[:] = np.random.rand(p.nk**2, 1, 1, 1, 1) + gamma_pp_dyn_tr, gamma_pp_const_r = preprocess_gamma_for_fft(gamma_pp_wk) + + initial_delta = semi_random_initial_delta(g0_wk) + + delta_1 = eliashberg_product_fft_constant(gamma_pp_const_r, g0_wk, initial_delta) + delta_2 = eliashberg_product_fft(gamma_pp_dyn_tr, gamma_pp_const_r, g0_wk, initial_delta) + + np.testing.assert_allclose(delta_1.data, delta_2.data) + + print('The functions eliashberg_product_fft and eliashberg_product_fft_constant' + ' yield the same result for a Gamma that is only constant in momentum space.' + '\nThe function split_into_dynamic_wk_and_constant_k therefore also worked correcty.') From d0e2e8cac44e58785750d440f4f3607462170baa Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 13 May 2019 13:58:16 +0200 Subject: [PATCH 019/121] [eli] change types to new style --- c++/triqs_tprf/lattice/eliashberg.cpp | 16 ++++++++-------- c++/triqs_tprf/lattice/eliashberg.hpp | 10 +++++----- python/triqs_tprf/lattice_desc.py | 10 ++++++---- 3 files changed, 19 insertions(+), 17 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index 49792982c..885a4a134 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -26,7 +26,7 @@ namespace triqs_tprf { // Helper function computing F = GG \Delta -gk_iw_t eliashberg_g_delta_g_product(gk_iw_vt g_wk, gk_iw_vt delta_wk) { +g_wk_t eliashberg_g_delta_g_product(g_wk_vt g_wk, g_wk_vt delta_wk) { auto [wmesh, kmesh] = delta_wk.mesh(); auto gf_wmesh = std::get<0>(g_wk.mesh()); @@ -48,8 +48,8 @@ gk_iw_t eliashberg_g_delta_g_product(gk_iw_vt g_wk, gk_iw_vt delta_wk) { return F_wk; } -gk_iw_t eliashberg_product(chi_wk_vt Gamma_pp, gk_iw_vt g_wk, - gk_iw_vt delta_wk) { +g_wk_t eliashberg_product(chi_wk_vt Gamma_pp, g_wk_vt g_wk, + g_wk_vt delta_wk) { auto [wmesh, kmesh] = delta_wk.mesh(); auto gamma_wmesh = std::get<0>(Gamma_pp.mesh()); @@ -105,7 +105,7 @@ std::tuple dynamic_and_constant_to_tr(chi_wk_vt Gamma_pp_dy return {Gamma_pp_dyn_tr, Gamma_pp_const_r}; } -ek_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, gr_tau_t F_tr) { +e_k_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, g_tr_t F_tr) { auto _ = all_t{}; @@ -123,8 +123,8 @@ ek_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, gr_tau_t F_t return delta_k_out; } -gk_iw_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const_r, - gk_iw_vt g_wk, gk_iw_vt delta_wk) { +g_wk_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const_r, + g_wk_vt g_wk, g_wk_vt delta_wk) { auto F_wk = eliashberg_g_delta_g_product(g_wk, delta_wk); auto F_tr = make_gf_from_fourier<0, 1>(F_wk); @@ -164,8 +164,8 @@ gk_iw_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_cons } // optimized version if there is only a constant term -gk_iw_t eliashberg_product_fft_constant(chi_r_vt Gamma_pp_const_r, - gk_iw_vt g_wk, gk_iw_vt delta_wk) { +g_wk_t eliashberg_product_fft_constant(chi_r_vt Gamma_pp_const_r, + g_wk_vt g_wk, g_wk_vt delta_wk) { auto F_wk = eliashberg_g_delta_g_product(g_wk, delta_wk); auto F_tr = make_gf_from_fourier<0, 1>(F_wk); diff --git a/c++/triqs_tprf/lattice/eliashberg.hpp b/c++/triqs_tprf/lattice/eliashberg.hpp index 5a14daf6d..0bc273b1e 100644 --- a/c++/triqs_tprf/lattice/eliashberg.hpp +++ b/c++/triqs_tprf/lattice/eliashberg.hpp @@ -44,7 +44,7 @@ namespace triqs_tprf { */ - gk_iw_t eliashberg_product(chi_wk_vt Gamma_pp, gk_iw_vt g_wk, gk_iw_vt delta_wk); + g_wk_t eliashberg_product(chi_wk_vt Gamma_pp, g_wk_vt g_wk, g_wk_vt delta_wk); /** Linearized Eliashberg product via FFT @@ -90,12 +90,12 @@ namespace triqs_tprf { */ - gk_iw_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const_r, gk_iw_vt g_wk, gk_iw_vt delta_wk); - gk_iw_t eliashberg_product_fft_constant(chi_r_vt Gamma_pp_const_r, gk_iw_vt g_wk, gk_iw_vt delta_wk); - gk_iw_t eliashberg_g_delta_g_product(gk_iw_vt g_wk, gk_iw_vt delta_wk); + g_wk_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const_r, g_wk_vt g_wk, g_wk_vt delta_wk); + g_wk_t eliashberg_product_fft_constant(chi_r_vt Gamma_pp_const_r, g_wk_vt g_wk, g_wk_vt delta_wk); + g_wk_t eliashberg_g_delta_g_product(g_wk_vt g_wk, g_wk_vt delta_wk); std::tuple split_into_dynamic_wk_and_constant_k(chi_wk_vt Gamma_pp); std::tuple dynamic_and_constant_to_tr(chi_wk_vt Gamma_pp_dyn_wk, chi_k_vt Gamma_pp_const_k); - ek_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, gr_tau_t F_tr); + e_k_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, g_tr_t F_tr); /** Gamma particle-particle singlet diff --git a/python/triqs_tprf/lattice_desc.py b/python/triqs_tprf/lattice_desc.py index 0eafb52b9..cd040f2f9 100644 --- a/python/triqs_tprf/lattice_desc.py +++ b/python/triqs_tprf/lattice_desc.py @@ -411,7 +411,7 @@ out GW self-energy :math:`\Sigma_{ab}(\tau, \mathbf{r})`""") -module.add_function ("triqs_tprf::gk_iw_t triqs_tprf::eliashberg_product (triqs_tprf::chi_wk_vt Gamma_pp, triqs_tprf::gk_iw_vt g_wk, triqs_tprf::gk_iw_vt delta_wk)", doc = r"""Linearized Eliashberg product +module.add_function ("triqs_tprf::g_wk_t triqs_tprf::eliashberg_product (triqs_tprf::chi_wk_vt Gamma_pp, triqs_tprf::g_wk_vt g_wk, triqs_tprf::g_wk_vt delta_wk)", doc = r"""Linearized Eliashberg product Computes the product @@ -439,7 +439,7 @@ out Gives the result of the product :math:`\Delta^{(out)} \sim \Gamma^{(pp)}GG \Delta`""") -module.add_function ("triqs_tprf::gk_iw_t triqs_tprf::eliashberg_product_fft (triqs_tprf::chi_tr_vt Gamma_pp_dyn_tr, triqs_tprf::chi_r_vt Gamma_pp_const_r, triqs_tprf::gk_iw_vt g_wk, triqs_tprf::gk_iw_vt delta_wk)", doc = r"""Linearized Eliashberg product via FFT +module.add_function ("triqs_tprf::g_wk_t triqs_tprf::eliashberg_product_fft (triqs_tprf::chi_tr_vt Gamma_pp_dyn_tr, triqs_tprf::chi_r_vt Gamma_pp_const_r, triqs_tprf::g_wk_vt g_wk, triqs_tprf::g_wk_vt delta_wk)", doc = r"""Linearized Eliashberg product via FFT Computes the product @@ -494,14 +494,16 @@ out Gives the result of the product :math:`\Delta^{(out)} \sim \Gamma^{(pp)}GG \Delta`""") -module.add_function ("triqs_tprf::gk_iw_t triqs_tprf::eliashberg_product_fft_constant (triqs_tprf::chi_r_vt Gamma_pp_const_r, triqs_tprf::gk_iw_vt g_wk, triqs_tprf::gk_iw_vt delta_wk)", doc = r"""""") +module.add_function ("triqs_tprf::g_wk_t triqs_tprf::eliashberg_product_fft_constant (triqs_tprf::chi_r_vt Gamma_pp_const_r, triqs_tprf::g_wk_vt g_wk, triqs_tprf::g_wk_vt delta_wk)", doc = r"""""") -module.add_function ("triqs_tprf::gk_iw_t triqs_tprf::eliashberg_g_delta_g_product (triqs_tprf::gk_iw_vt g_wk, triqs_tprf::gk_iw_vt delta_wk)", doc = r"""""") +module.add_function ("triqs_tprf::g_wk_t triqs_tprf::eliashberg_g_delta_g_product (triqs_tprf::g_wk_vt g_wk, triqs_tprf::g_wk_vt delta_wk)", doc = r"""""") module.add_function ("std::tuple triqs_tprf::split_into_dynamic_wk_and_constant_k (triqs_tprf::chi_wk_vt Gamma_pp)", doc = r"""""") module.add_function ("std::tuple triqs_tprf::dynamic_and_constant_to_tr (triqs_tprf::chi_wk_vt Gamma_pp_dyn_wk, triqs_tprf::chi_k_vt Gamma_pp_const_k)", doc = r"""""") +module.add_function ("triqs_tprf::e_k_t triqs_tprf::eliashberg_constant_gamma_f_product (triqs_tprf::chi_r_vt Gamma_pp_const_r, triqs_tprf::g_tr_t F_tr)", doc = r"""""") + module.add_function ("triqs_tprf::chi_wk_t triqs_tprf::gamma_PP_singlet (triqs_tprf::chi_wk_vt chi_c, triqs_tprf::chi_wk_vt chi_s, array_view,4> U_c, array_view,4> U_s)", doc = r"""Gamma particle-particle singlet Computes the particle-particle vertex for singlet pairing in the RPA limit From 9a7d018d62ccacaf2335be8080c8a61ebc3254b6 Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 13 May 2019 14:10:08 +0200 Subject: [PATCH 020/121] [rpa] change kanamaori function and add to test - norb is now the number of orbitals EXCLUDING spin to make the function less error prone. --- python/triqs_tprf/rpa_tensor.py | 15 +++++++++++---- ...nteraction_tensor_charge_spin_factorization.py | 5 ++++- 2 files changed, 15 insertions(+), 5 deletions(-) diff --git a/python/triqs_tprf/rpa_tensor.py b/python/triqs_tprf/rpa_tensor.py index 4070bda83..a0933dccd 100644 --- a/python/triqs_tprf/rpa_tensor.py +++ b/python/triqs_tprf/rpa_tensor.py @@ -196,12 +196,18 @@ def kanamori_quartic_tensor(norb, U, Up, J, Jp): .. math:: - \hat{U}_{\text { Kanamori }} = U \sum_{i} \hat{n}_{i, \uparrow} \hat{n}_{i, \downarrow}+\sum_{i>j, s, s^{\prime}}\left(U^{\prime}-J \delta_{\sigma, \sigma^{\prime}}\right) \hat{n}_{i, \sigma} \hat{n}_{j, \sigma^{\prime}} - \\ J \sum_{i \neq j}\left(\hat{c}_{i, \downarrow}^{\dagger} \hat{c}_{j, \uparrow}^{\dagger} \hat{c}_{j, \downarrow} \hat{c}_{i, \uparrow}+\hat{c}_{j, \uparrow}^{\dagger} \hat{c}_{j, \downarrow}^{\dagger} \hat{c}_{i, \uparrow} \hat{c}_{i, \downarrow}+\mathrm{h.c.}\right) + \hat{U}_{\text { Kanamori }} = U \sum_{i} \hat{n}_{i, \uparrow} \hat{n}_{i, \downarrow}+ + \sum_{i>j, s, s^{\prime}}\left(U^{\prime}-J \delta_{\sigma, \sigma^{\prime}}\right) + \hat{n}_{i, \sigma} \hat{n}_{j, \sigma^{\prime}} - + \\ J \sum_{i \neq j}\left(\hat{c}_{i, \downarrow}^{\dagger} \hat{c}_{j, \uparrow}^{\dagger} + \hat{c}_{j, \downarrow} \hat{c}_{i, \uparrow}+\hat{c}_{j, \uparrow}^{\dagger} + \hat{c}_{j, \downarrow}^{\dagger} \hat{c}_{i, \uparrow} \hat{c}_{i, \downarrow}+ + \mathrm{h.c.}\right) Parameters ---------- norb : int, - Number of orbitals including spin up and down as seperate orbs. + Number of orbitals excluding spin. U : complex, Strength of intra-orbital interaction. Up : complex, @@ -213,10 +219,11 @@ def kanamori_quartic_tensor(norb, U, Up, J, Jp): Returns ------- - np.ndarray + U : np.ndarray, + shape = (2*norb, 2*norb, 2*norb, 2*norb) """ - U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(int(norb/2), U, Up, J, Jp) + U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(norb, U, Up, J, Jp) U = quartic_tensor_from_charge_and_spin(U_c, U_s) return U diff --git a/test/python/interaction_tensor_charge_spin_factorization.py b/test/python/interaction_tensor_charge_spin_factorization.py index 1e276c387..6e1cad2a8 100644 --- a/test/python/interaction_tensor_charge_spin_factorization.py +++ b/test/python/interaction_tensor_charge_spin_factorization.py @@ -23,6 +23,7 @@ from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors from triqs_tprf.rpa_tensor import split_quartic_tensor_in_charge_and_spin from triqs_tprf.rpa_tensor import quartic_tensor_from_charge_and_spin +from triqs_tprf.rpa_tensor import kanamori_quartic_tensor # ---------------------------------------------------------------------- def print_tensors(T1, T2): @@ -60,7 +61,9 @@ def print_tensors(T1, T2): U_c_ref, U_s_ref = kanamori_charge_and_spin_quartic_interaction_tensors( norb, U, U - 2*J, J, J) + U_abcd_ref_2 = kanamori_quartic_tensor(norb, U, U - 2*J, J, J) + np.testing.assert_array_almost_equal(U_abcd, U_abcd_ref) np.testing.assert_array_almost_equal(U_c, U_c_ref) np.testing.assert_array_almost_equal(U_s, U_s_ref) - + np.testing.assert_array_almost_equal(U_abcd, U_abcd_ref_2) From f3c661bfe3c1101a65f85b50917f6de6ba0f9d69 Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 13 May 2019 14:16:03 +0200 Subject: [PATCH 021/121] [plot] add plotting tools to triqs_tprf --- {doc/user_guide => python/triqs_tprf}/plotting_tools.py | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename {doc/user_guide => python/triqs_tprf}/plotting_tools.py (100%) diff --git a/doc/user_guide/plotting_tools.py b/python/triqs_tprf/plotting_tools.py similarity index 100% rename from doc/user_guide/plotting_tools.py rename to python/triqs_tprf/plotting_tools.py From e7213df12a8c5ee121b9fe84c679c42698ee6d6b Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 13 May 2019 16:04:45 +0200 Subject: [PATCH 022/121] [plot] improve plotting_tools - high symmetry points are no longer part of the bsplot implementation and the user gives now the k-points himself. - axes tuning added - dos implementaion added --- python/triqs_tprf/plotting_tools.py | 94 +++++++++++++++++++---------- 1 file changed, 61 insertions(+), 33 deletions(-) diff --git a/python/triqs_tprf/plotting_tools.py b/python/triqs_tprf/plotting_tools.py index ac8afad10..2c914de9d 100644 --- a/python/triqs_tprf/plotting_tools.py +++ b/python/triqs_tprf/plotting_tools.py @@ -8,56 +8,84 @@ from triqs_tprf.lattice_utils import k_space_path -hs_to_k = { - 'G' : np.array([0.0, 0.0, 0.0]), - 'X' : np.array([0.5, 0.0, 0.0]), - 'Y' : np.array([0.0, 0.5, 0.0]), - 'Z' : np.array([0.0, 0.0, 0.5]), - 'M' : np.array([0.5, 0.5, 0.0]), - 'R' : np.array([0.5, 0.5, 0.5]), - } - -hs_to_latex = { - 'G' : r'$\Gamma$', - 'X' : r'$X$', - 'Y' : r'$Y$', - 'Z' : r'$Z$', - 'M' : r'$M$', - 'R' : r'$R$', - } +from scipy.stats import gaussian_kde + +# ========== Bandstructure ========== def bsplot(obj, path, *opt_list, **opt_dict): """ - Plot stuff like bs lol + Plot Gf objects like bandstructure """ - __bsplot_impl(plt, obj, path, plt.xticks, plt.xticks, *opt_list, **opt_dict) + __bsplot_impl(plt, obj, path, *opt_list, **opt_dict) +def __bsplot_impl(top, obj, path, *opt_list, **opt_dict): -def __bsplot_impl(top, obj, path, xticks_fct, xticklabels_fct, *opt_list, **opt_dict): - - hs_points = path.split('-') - hs_labels = [hs_to_latex[hs_point] for hs_point in hs_points] - hs_k = [hs_to_k[hs_point] for hs_point in hs_points] + hs_labels, hs_k = zip(*path) k_paths = zip(hs_k, hs_k[1:]) k_vecs, k_plot, K_plot = k_space_path(k_paths, bz=obj.mesh.domain) kx, ky, kz = k_vecs.T - - plt_fct = getattr(top, 'plot') + + # -- If top is plt do now access the currently used Axes object + if isinstance(top, types.ModuleType): + top = top.gca() get_gf_on_path = np.vectorize(lambda kx, ky, kz : obj([kx, ky, kz]).real) gf_on_path = get_gf_on_path(kx, ky, kz) - plt_fct(k_plot, gf_on_path, *opt_list, **opt_dict) - + top.plot(k_plot, gf_on_path, *opt_list, **opt_dict) + + top.set_xticks(K_plot) + top.set_xticklabels(hs_labels) + + # -- Make x-spine cut off at starting and ending high symmetry point + top.spines['bottom'].set_bounds(top.get_xticks()[0], top.get_xticks()[-1]) + + # -- Make y-spine cut off at highest and lowest value + lower_limit = np.min([line.get_ydata() for line in top.get_lines()]) + upper_limit = np.max([line.get_ydata() for line in top.get_lines()]) + + top.spines['left'].set_bounds(lower_limit, upper_limit) + top.set_yticks([lower_limit, upper_limit]) + +mpl.axes.Axes.bsplot = lambda self, obj, path, *opt_list, **opt_dict : \ + __bsplot_impl(self, obj, path, *opt_list, **opt_dict) + +# ========== DOS ========== + +def dosplot(obj, *opt_list, **opt_dict): + """Plot density of states for dispersion relation objects + """ + + __dosplot_impl(plt, obj, *opt_list, **opt_dict) + +def __dosplot_impl(top, obj, *opt_list, **opt_dict): + + lower_limit = np.min(obj.data.real) + upper_limit = np.max(obj.data.real) + + dos = gaussian_kde(obj.data[:,0,0].real) + xs = np.linspace(lower_limit, upper_limit, 500) + + dos.covariance_factor = lambda : .1 + dos._compute_covariance() + + # -- If top is plt do now access the currently used Axes object if isinstance(top, types.ModuleType): - xticks_fct(K_plot, hs_labels) - else: - xticks_fct(K_plot) - xticklabels_fct(hs_labels) + top = top.gca() -mpl.axes.Axes.bsplot = lambda self, obj, path, *opt_list, **opt_dict: __bsplot_impl(self, obj, path, self.set_xticks, self.set_xticklabels, *opt_list, **opt_dict) + top.plot(dos(xs).real, xs, *opt_list, **opt_dict) + top.fill_betweenx(xs, dos(xs).real, [0]*len(xs), alpha=0.25, *opt_list, **opt_dict) + # -- Make y-spine cut off at highest and lowest value + lower_limit = np.min([line.get_ydata() for line in top.get_lines()]) + upper_limit = np.max([line.get_ydata() for line in top.get_lines()]) + top.spines['left'].set_bounds(lower_limit, upper_limit) + top.set_yticks([lower_limit, upper_limit]) + # -- No x-ticks + top.set_xticks([]) +mpl.axes.Axes.dosplot = lambda self, obj, *opt_list, **opt_dict : \ + __dosplot_impl(self, obj, *opt_list, **opt_dict) From 2f26f233315c596d24f8e3799e544bea9d1275f1 Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 13 May 2019 17:21:26 +0200 Subject: [PATCH 023/121] [bench] move PHT Hubbard notbeook to benchmark --- .../eliashberg_benchmark_k_mesh_2.h5 | Bin .../tprf_implementation.py | 0 .../PHT_Hubbard_Model.ipynb | 284 +++++++----------- 3 files changed, 107 insertions(+), 177 deletions(-) rename benchmark/eliashberg/{ => comparison_to_previous_impl}/eliashberg_benchmark_k_mesh_2.h5 (100%) rename benchmark/eliashberg/{ => comparison_to_previous_impl}/tprf_implementation.py (100%) rename {doc/user_guide => benchmark/eliashberg/particle_hole_transformation}/PHT_Hubbard_Model.ipynb (52%) diff --git a/benchmark/eliashberg/eliashberg_benchmark_k_mesh_2.h5 b/benchmark/eliashberg/comparison_to_previous_impl/eliashberg_benchmark_k_mesh_2.h5 similarity index 100% rename from benchmark/eliashberg/eliashberg_benchmark_k_mesh_2.h5 rename to benchmark/eliashberg/comparison_to_previous_impl/eliashberg_benchmark_k_mesh_2.h5 diff --git a/benchmark/eliashberg/tprf_implementation.py b/benchmark/eliashberg/comparison_to_previous_impl/tprf_implementation.py similarity index 100% rename from benchmark/eliashberg/tprf_implementation.py rename to benchmark/eliashberg/comparison_to_previous_impl/tprf_implementation.py diff --git a/doc/user_guide/PHT_Hubbard_Model.ipynb b/benchmark/eliashberg/particle_hole_transformation/PHT_Hubbard_Model.ipynb similarity index 52% rename from doc/user_guide/PHT_Hubbard_Model.ipynb rename to benchmark/eliashberg/particle_hole_transformation/PHT_Hubbard_Model.ipynb index 8a0608f2a..4e7600da1 100644 --- a/doc/user_guide/PHT_Hubbard_Model.ipynb +++ b/benchmark/eliashberg/particle_hole_transformation/PHT_Hubbard_Model.ipynb @@ -17,13 +17,13 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 12, "metadata": { "nbsphinx": "hidden" }, "outputs": [], "source": [ - "plt.style.use('./notebook.mplstyle')" + "plt.style.use('../../../doc/user_guide/notebook.mplstyle')" ] }, { @@ -47,7 +47,7 @@ "The Hamiltonian of the Hubbard model on a square lattice is given by\n", "\n", "$$\n", - "H=-t \\sum_{\\langle j, 1\\rangle \\sigma}\\left(c_{j \\sigma}^{\\dagger} c_{1 \\sigma}+c_{1 \\sigma}^{\\dagger} c_{j \\sigma}\\right)+U \\sum_{j} n_{j \\uparrow} n_{j \\downarrow}-\\mu \\sum_{j}\\left(n_{j \\uparrow}+n_{j \\downarrow}\\right)\\,,\n", + "H=-t \\sum_{\\langle j, l\\rangle \\sigma}\\left(c_{j \\sigma}^{\\dagger} c_{l \\sigma}+c_{l \\sigma}^{\\dagger} c_{j \\sigma}\\right)+U \\sum_{j} n_{j \\uparrow} n_{j \\downarrow}-\\mu \\sum_{j}\\left(n_{j \\uparrow}+n_{j \\downarrow}\\right)\\,,\n", "$$\n", "\n", "here $c_{j\\sigma}^{\\dagger}$ creates an electron on site $j$ with spin $\\sigma$ while $c_{j\\sigma}$ destroys such an electron, further the operator $n_{j\\sigma}$ count the number of electrons on site $j$ with spin $\\sigma$.\n", @@ -68,7 +68,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 13, "metadata": {}, "outputs": [ { @@ -81,10 +81,12 @@ "norb = 1\n", "nw = 50\n", "spin = False\n", - "t = 1.0" + "t = 1.0\n", + "tp = 0.0\n", + "zeeman = 0.0" ] }, - "execution_count": 3, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" } @@ -100,6 +102,10 @@ " T=1000, # Temperature.\n", " spin=False, # Treat indices only for orbital character.\n", " \n", + " # -- Model Parameter which will be used later\n", + " tp=0.0, # Hopping to next-nearest neighbor\n", + " zeeman=0.0, # Strength of zeeman term\n", + " \n", " # -- Technical parameter\n", " nk=32, # Number of points in one dimension considered in the Brillouin zone.\n", " nw=50, # Number of Matsubara points in positive dimension.\n", @@ -111,34 +117,57 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "A representation of the kinetic part of the Hubbard model can be constructed using the `SquareLattice` class in `triqs_tprf.tight_binding`.\n", - "This class needs information about the number of orbitals `norb` and the hopping energy `t`, so we can construct it with the parameters stored in `hubbard`. \n", - "From this `SquareLattice` object we can then obtain the dispersion relation as a mesh over the Brillouin zone via its member function `on_mesh_brillouin_zone`.\n", + "A representation of the kinetic part of the Hubbard model can be constructed using the `create_square_lattice` function in`triqs_tprf.tight_binding`.\n", + "This function needs information about the number of orbitals `norb` and the hopping energy `t`, so we can construct it with the parameters stored in `hubbard`. \n", + "It returns a `TBLattice` object from which we can obtain the dispersion relation as a mesh over the Brillouin zone via its member function `on_mesh_brillouin_zone`.\n", "\n", - "The dispersion relation is stored in a `Gf` object and we can plot its bandstructure via the `bplot` function in `plotting_tools`." + "The dispersion relation is stored in a `Gf` object and we can plot its bandstructure via the `bsplot` function in `plotting_tools`." ] }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 14, "metadata": {}, "outputs": [], "source": [ - "from triqs_tprf.tight_binding import SquareLattice\n", + "from triqs_tprf.tight_binding import create_square_lattice\n", "\n", - "H = SquareLattice(**hubbard)\n", + "H = create_square_lattice(norb=hubbard.norb, t=hubbard.t)\n", "\n", "e_k = H.on_mesh_brillouin_zone(n_k=(hubbard.nk, hubbard.nk, 1))" ] }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 39, + "metadata": {}, + "outputs": [], + "source": [ + "path = [(r'$\\Gamma$', np.array([0.0, 0.0, 0.0])), \n", + " ('X', np.array([0.5, 0.0, 0.0])),\n", + " ('M', np.array([0.5, 0.5, 0.0])), \n", + " (r'$\\Gamma$', np.array([0.0, 0.0, 0.0])), \n", + " ]" + ] + }, + { + "cell_type": "code", + "execution_count": 16, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -149,42 +178,20 @@ ], "source": [ "from matplotlib import gridspec\n", - "from scipy.stats import gaussian_kde\n", - "from plotting_tools import bsplot\n", + "from triqs_tprf.plotting_tools import bsplot, dosplot\n", "\n", "gs = gridspec.GridSpec(1, 2, width_ratios=[3, 1]) \n", - "gs.update(wspace=0.025, hspace=0.05)\n", + "gs.update(wspace=0.2, hspace=0.05)\n", "\n", "# -- Bandstructure\n", "ax_bs = plt.subplot(gs[0])\n", - "\n", - "lower_limit = np.min(e_k.data.real)\n", - "upper_limit = np.max(e_k.data.real)\n", - "\n", - "path = 'G-X-M-G'\n", "ax_bs.bsplot(e_k, path)\n", - "\n", - "ax_bs.spines['left'].set_bounds(lower_limit, upper_limit)\n", - "ax_bs.spines['bottom'].set_bounds(ax_bs.get_xticks()[0], ax_bs.get_xticks()[-1])\n", - "\n", "ax_bs.set_ylabel('$\\epsilon(\\mathbf{k})$', rotation=0, ha='right')\n", "\n", "# -- Density of states\n", "ax_dos = plt.subplot(gs[1])\n", - "\n", - "dos = gaussian_kde(e_k.data[:,0,0].real)\n", - "xs = np.linspace(lower_limit, upper_limit , 500)\n", - "dos.covariance_factor = lambda : .1\n", - "dos._compute_covariance()\n", - "\n", - "ax_dos.plot(dos(xs).real, xs)\n", - "ax_dos.fill_betweenx(xs, dos(xs).real, [0]*len(xs), alpha=0.25)\n", - "ax_dos.set_xlabel('DOS')\n", - "\n", - "ax_dos.set_yticklabels([''])\n", - "ax_dos.set_xticks([])\n", - "\n", - "ax_dos.spines['left'].set_bounds(lower_limit, upper_limit)" + "ax_dos.dosplot(e_k)\n", + "ax_dos.set_xlabel('DOS')" ] }, { @@ -206,7 +213,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 17, "metadata": {}, "outputs": [ { @@ -244,7 +251,7 @@ " \"\"\"Return the non-interaction susceptibility for model parameters in a ParameterCollection\n", " \"\"\"\n", " if not e_k:\n", - " H = SquareLattice(**p)\n", + " H = create_square_lattice(**p)\n", " e_k = H.on_mesh_brillouin_zone(n_k=(p.nk, p.nk, 1))\n", "\n", " wmesh = MeshImFreq(beta=temperature_to_beta(p.T), S='Fermion', n_max=p.nw)\n", @@ -278,7 +285,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 18, "metadata": {}, "outputs": [], "source": [ @@ -303,7 +310,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 19, "metadata": {}, "outputs": [ { @@ -312,13 +319,13 @@ "Text(0.55,0.18,'$\\\\chi^{(c)}$')" ] }, - "execution_count": 8, + "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -330,21 +337,11 @@ "source": [ "from pytriqs.gf import Idx\n", "\n", - "fig = plt.figure()\n", - "\n", - "ax_bs = fig.add_subplot(111)\n", + "ax_bs = plt.subplot(111)\n", "\n", "ax_bs.bsplot(chi_s_wk[Idx(0), :], path)\n", "ax_bs.bsplot(chi_c_wk[Idx(0), :], path)\n", "\n", - "lower_limit = np.round(np.min(chi_s_wk.data.real), 2)\n", - "upper_limit = np.round(np.max(chi_s_wk.data.real), 2)\n", - "\n", - "ax_bs.set_yticks([lower_limit, upper_limit])\n", - "\n", - "ax_bs.spines['left'].set_bounds(lower_limit, upper_limit)\n", - "ax_bs.spines['bottom'].set_bounds(ax_bs.get_xticks()[0], ax_bs.get_xticks()[-1])\n", - "\n", "ax_bs.set_ylabel(r'$\\chi(\\nu=0, \\mathbf{k})$', rotation=0, ha='right')\n", "ax_bs.text(0.62, 0.6, \"$\\chi^{(s)}$\", transform = ax_bs.transAxes, size=22, color='C0')\n", "ax_bs.text(0.55, 0.18, \"$\\chi^{(c)}$\", transform = ax_bs.transAxes, size=22, color='C1')" @@ -366,7 +363,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 20, "metadata": {}, "outputs": [], "source": [ @@ -406,7 +403,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 21, "metadata": {}, "outputs": [], "source": [ @@ -428,7 +425,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 22, "metadata": {}, "outputs": [ { @@ -437,7 +434,7 @@ "Text(0.625,0.3,'AFM')" ] }, - "execution_count": 11, + "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, @@ -570,7 +567,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 23, "metadata": {}, "outputs": [], "source": [ @@ -590,7 +587,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 24, "metadata": {}, "outputs": [ { @@ -599,7 +596,7 @@ "Text(0.125,0.3,'AFM')" ] }, - "execution_count": 13, + "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, @@ -660,13 +657,13 @@ }, { "cell_type": "code", - "execution_count": 54, + "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "hubbard_next_nearest_neighbor_hopping = hubbard.copy(tp=-0.05)\n", "\n", - "H = SquareLattice(**hubbard_next_nearest_neighbor_hopping)\n", + "H = create_square_lattice(**hubbard_next_nearest_neighbor_hopping)\n", "\n", "e_k_nn = H.on_mesh_brillouin_zone(n_k=(hubbard_next_nearest_neighbor_hopping.nk,\n", " hubbard_next_nearest_neighbor_hopping.nk, 1))" @@ -674,12 +671,22 @@ }, { "cell_type": "code", - "execution_count": 55, + "execution_count": 26, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -691,47 +698,20 @@ "source": [ "# -- Bandstructure\n", "ax_bs = plt.subplot(gs[0])\n", - "\n", - "lower_limit = np.min(e_k_nn.data.real)\n", - "upper_limit = np.max(e_k_nn.data.real)\n", - "\n", "ax_bs.bsplot(e_k, path, color='grey', ls=\"dotted\", alpha=0.5)\n", "ax_bs.bsplot(e_k_nn, path)\n", - "\n", - "ax_bs.spines['left'].set_bounds(lower_limit, upper_limit)\n", - "ax_bs.spines['bottom'].set_bounds(ax_bs.get_xticks()[0], ax_bs.get_xticks()[-1])\n", - "\n", - "ax_bs.set_yticks([lower_limit, upper_limit])\n", - "\n", "ax_bs.set_ylabel('$\\epsilon(\\mathbf{k})$', rotation=0, ha='right')\n", "\n", "# -- Density of states\n", "ax_dos = plt.subplot(gs[1])\n", - "\n", - "dos_nn = gaussian_kde(e_k_nn[0,0].data.real)\n", - "xs_nn = np.linspace(lower_limit, upper_limit , 500)\n", - "dos_nn.covariance_factor = lambda : .1\n", - "dos_nn._compute_covariance()\n", - "\n", - "ax_dos.plot(dos(xs).real, xs, color='grey', ls=\"dotted\", alpha=0.5)\n", - "\n", - "ax_dos.plot(dos_nn(xs_nn).real, xs_nn)\n", - "ax_dos.fill_betweenx(xs_nn, dos_nn(xs_nn).real, [0]*len(xs), alpha=0.25)\n", - "\n", - "\n", - "\n", - "ax_dos.set_xlabel('DOS')\n", - "\n", - "ax_dos.set_yticks([lower_limit, upper_limit])\n", - "ax_dos.set_yticklabels([''])\n", - "ax_dos.set_xticks([])\n", - "\n", - "ax_dos.spines['left'].set_bounds(lower_limit, upper_limit)" + "ax_dos.dosplot(e_k, color='grey', linestyle='dotted')\n", + "ax_dos.dosplot(e_k_nn)\n", + "ax_dos.set_xlabel('DOS')" ] }, { "cell_type": "code", - "execution_count": 56, + "execution_count": 27, "metadata": {}, "outputs": [], "source": [ @@ -751,7 +731,7 @@ }, { "cell_type": "code", - "execution_count": 60, + "execution_count": 28, "metadata": {}, "outputs": [ { @@ -760,7 +740,7 @@ "Text(0.08,0.1,'AFM')" ] }, - "execution_count": 60, + "execution_count": 28, "metadata": {}, "output_type": "execute_result" }, @@ -868,7 +848,7 @@ }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 29, "metadata": {}, "outputs": [], "source": [ @@ -895,7 +875,7 @@ }, { "cell_type": "code", - "execution_count": 62, + "execution_count": 30, "metadata": {}, "outputs": [], "source": [ @@ -918,7 +898,7 @@ }, { "cell_type": "code", - "execution_count": 67, + "execution_count": 31, "metadata": {}, "outputs": [ { @@ -927,7 +907,7 @@ "Text(0.07,0.15,'CDW')" ] }, - "execution_count": 67, + "execution_count": 31, "metadata": {}, "output_type": "execute_result" }, @@ -991,7 +971,7 @@ }, { "cell_type": "code", - "execution_count": 68, + "execution_count": 32, "metadata": {}, "outputs": [ { @@ -1037,7 +1017,7 @@ }, { "cell_type": "code", - "execution_count": 69, + "execution_count": 33, "metadata": {}, "outputs": [], "source": [ @@ -1086,7 +1066,7 @@ }, { "cell_type": "code", - "execution_count": 70, + "execution_count": 34, "metadata": {}, "outputs": [], "source": [ @@ -1097,7 +1077,7 @@ " \"\"\"Solve the linearized eliashberg equation for model parameters in a ParameterCollection\n", " \"\"\"\n", " if not g0_wk:\n", - " H = SquareLattice(**p)\n", + " H = create_square_lattice(**p)\n", " e_k = H.on_mesh_brillouin_zone(n_k=(p.nk, p.nk, 1))\n", "\n", " wmesh = MeshImFreq(beta=temperature_to_beta(p.T), S='Fermion', n_max=p.nw)\n", @@ -1116,7 +1096,7 @@ "def get_sc_phase_transistion(p, guess=None):\n", " \"\"\"Return U at which model p transitions to superconducting order via root search\n", " \"\"\"\n", - " H = SquareLattice(**p)\n", + " H = create_square_lattice(**p)\n", " e_k = H.on_mesh_brillouin_zone(n_k=(p.nk, p.nk, 1))\n", "\n", " wmesh = MeshImFreq(beta=temperature_to_beta(p.T), S='Fermion', n_max=p.nw)\n", @@ -1136,7 +1116,7 @@ }, { "cell_type": "code", - "execution_count": 71, + "execution_count": 35, "metadata": {}, "outputs": [], "source": [ @@ -1155,7 +1135,7 @@ }, { "cell_type": "code", - "execution_count": 78, + "execution_count": 36, "metadata": {}, "outputs": [ { @@ -1164,7 +1144,7 @@ "Text(0.07,0.15,'SC')" ] }, - "execution_count": 78, + "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, @@ -1226,19 +1206,19 @@ }, { "cell_type": "code", - "execution_count": 95, + "execution_count": 37, "metadata": {}, "outputs": [], "source": [ "hubbard_spin_dependent = hubbard.copy(spin=True)\n", "\n", - "H = SquareLattice(**hubbard_spin_dependent.copy(zeeman=1.0))\n", + "H = create_square_lattice(**hubbard_spin_dependent.copy(zeeman=1.0))\n", "e_k = H.on_mesh_brillouin_zone(n_k=(hubbard_spin_dependent.nk, hubbard_spin_dependent.nk, 1))" ] }, { "cell_type": "code", - "execution_count": 96, + "execution_count": 41, "metadata": {}, "outputs": [ { @@ -1247,13 +1227,13 @@ "Text(0.52,0.6,'$|\\\\downarrow \\\\rangle$')" ] }, - "execution_count": 96, + "execution_count": 41, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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+ "image/png": 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\n", "text/plain": [ "
" ] @@ -1266,17 +1246,9 @@ "# -- Bandstructure\n", "ax_bs = plt.subplot(111)\n", "\n", - "lower_limit = np.min(e_k.data.real)\n", - "upper_limit = np.max(e_k.data.real)\n", - "\n", - "path = 'G-X-M-G'\n", - "\n", "ax_bs.bsplot(e_k[0,0], path)\n", "ax_bs.bsplot(e_k[1,1], path)\n", "\n", - "ax_bs.spines['left'].set_bounds(lower_limit, upper_limit)\n", - "ax_bs.spines['bottom'].set_bounds(ax_bs.get_xticks()[0], ax_bs.get_xticks()[-1])\n", - "\n", "ax_bs.set_ylabel('$\\epsilon(\\mathbf{k})$')\n", "\n", "ax_bs.text(0.52, 1., r\"$|\\uparrow \\rangle$\", transform = ax_bs.transAxes, size=22, color='C0')\n", @@ -1293,7 +1265,7 @@ }, { "cell_type": "code", - "execution_count": 82, + "execution_count": 42, "metadata": {}, "outputs": [], "source": [ @@ -1304,7 +1276,7 @@ " if not chi0_wk:\n", " chi0_wk = get_chi0(p)\n", " \n", - " U_abcd = kanamori_quartic_tensor(2*p.norb, p.U, 0, 0, 0) # Two time norb to take spin int account\n", + " U_abcd = kanamori_quartic_tensor(p.norb, p.U, 0, 0, 0) # Two time norb to take spin int account\n", " \n", " chi_rpa_wk = solve_rpa_PH(chi0_wk, U_abcd)\n", " \n", @@ -1346,7 +1318,7 @@ }, { "cell_type": "code", - "execution_count": 83, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -1383,30 +1355,9 @@ }, { "cell_type": "code", - "execution_count": 99, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.5,1,'Hubbard with $\\\\mathrm{Zeeman}=\\\\xi$')" - ] - }, - "execution_count": 99, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "fig = plt.figure(figsize=(11,7))\n", "\n", @@ -1465,7 +1416,7 @@ }, { "cell_type": "code", - "execution_count": 92, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -1474,30 +1425,9 @@ }, { "cell_type": "code", - "execution_count": 93, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 93, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "delta_plot = delta_1[Idx(0), : ].data.reshape(hubbard.nk, hubbard.nk).real\n", "\n", From 7ea6c58113508623b6343be45343b689f07cdc11 Mon Sep 17 00:00:00 2001 From: Stefan Date: Tue, 14 May 2019 10:36:53 +0200 Subject: [PATCH 024/121] [paramcol] make copy a true copy and add fct --- .../PHT_Hubbard_Model.ipynb | 203 +++++++++++------- python/triqs_tprf/ParameterCollection.py | 19 +- test/python/eliashberg/eigenvalue_solver.py | 2 +- .../eliashberg/product_summation_vs_fft.py | 2 +- 4 files changed, 145 insertions(+), 81 deletions(-) diff --git a/benchmark/eliashberg/particle_hole_transformation/PHT_Hubbard_Model.ipynb b/benchmark/eliashberg/particle_hole_transformation/PHT_Hubbard_Model.ipynb index 4e7600da1..f0f374a0b 100644 --- a/benchmark/eliashberg/particle_hole_transformation/PHT_Hubbard_Model.ipynb +++ b/benchmark/eliashberg/particle_hole_transformation/PHT_Hubbard_Model.ipynb @@ -17,7 +17,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 2, "metadata": { "nbsphinx": "hidden" }, @@ -68,7 +68,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -77,7 +77,7 @@ "T = 1000\n", "U = 1.0\n", "mu = 0.0\n", - "nk = 32\n", + "nk = 8\n", "norb = 1\n", "nw = 50\n", "spin = False\n", @@ -86,7 +86,7 @@ "zeeman = 0.0" ] }, - "execution_count": 13, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } @@ -107,7 +107,7 @@ " zeeman=0.0, # Strength of zeeman term\n", " \n", " # -- Technical parameter\n", - " nk=32, # Number of points in one dimension considered in the Brillouin zone.\n", + " nk=8, # Number of points in one dimension considered in the Brillouin zone.\n", " nw=50, # Number of Matsubara points in positive dimension.\n", " )\n", "hubbard" @@ -126,9 +126,17 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 4, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Starting run with 1 MPI threads at : 2019-05-14 10:35:41.957241\n" + ] + } + ], "source": [ "from triqs_tprf.tight_binding import create_square_lattice\n", "\n", @@ -139,7 +147,7 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ @@ -152,7 +160,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -161,13 +169,13 @@ "Text(0.5,0,'DOS')" ] }, - "execution_count": 16, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -213,7 +221,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -227,11 +235,11 @@ "Two-Particle Response Function tool-box \n", "\n", "beta = 11.6045250062\n", - "nk = 1024\n", + "nk = 64\n", "nw = 100\n", "norb = 1\n", "\n", - "Approx. Memory Utilization: 0.01 GB\n", + "Approx. Memory Utilization: 0.00 GB\n", "\n", "--> fourier_wk_to_wr\n", "--> fourier_wr_to_tr\n", @@ -285,7 +293,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 8, "metadata": {}, "outputs": [], "source": [ @@ -310,7 +318,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 9, "metadata": {}, "outputs": [ { @@ -319,13 +327,13 @@ "Text(0.55,0.18,'$\\\\chi^{(c)}$')" ] }, - "execution_count": 19, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -363,7 +371,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 10, "metadata": {}, "outputs": [], "source": [ @@ -376,7 +384,7 @@ " \n", " def one_over_spin(U):\n", "\n", - " _, chi_s_wk = get_chiRPA(p.copy(U=U), chi0_wk)\n", + " _, chi_s_wk = get_chiRPA(p.alter(U=U), chi0_wk)\n", " \n", " # -- If any value is below zero we are already in an ordered phase\n", " if np.any(chi_s_wk.data[np.abs(chi_s_wk.data) > 1e-3] < 0.0 ):\n", @@ -394,7 +402,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "To scan through some parameters we will copy our base model `hubbard`, which parameters are stored as a `ParameterCollection`, and only change the specific parameters.\n", + "To scan through some parameters we will alter our base model `hubbard`, which parameters are stored as a `ParameterCollection`, and only change the specific parameters.\n", "We do this with the function `parameter_scan` which outputs us a `ParameterCollections` objects which is a container for multiple `ParameterCollection`.\n", "We can then loop over the `ParameterCollections` object to access the individual `ParameterCollection` objects.\n", "\n", @@ -403,7 +411,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 11, "metadata": {}, "outputs": [], "source": [ @@ -425,7 +433,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 12, "metadata": {}, "outputs": [ { @@ -434,13 +442,13 @@ "Text(0.625,0.3,'AFM')" ] }, - "execution_count": 22, + "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", + "image/png": 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4gXCYnHnzSNt9N38TkyY1WwgZY/rGi1trXwEGAY8YY0Z3fFoiIiLdS9X777PmzLNx1rr9A4GMDHIuuojUXXb2OTNpjsYISUKy1o4G7m3hsDpjTMg7fhtgeTPHPmKMGd7EtUYBU4BdgVrgfeB6Y8y/2pa1iHRXlW+9Rd7Zo3BKSgAIRCLkzJ9P6g7b+5yZtGSjFULW2tOAscAAoAfu7bP/An82xiyJc/xM4AbgKWPMydbascBkYGegDFgMXGyMWeYd3w+Yjzs+ZjNgBXA7cJMxxml07r1wf1itNcb0sNYOBuYC+wLpwOde23sat210ngHADNzesT5eXh8C9wP3G2PqWrju4cAsYH+gN3C5MeZS79h9gJOBwcDW3nsqAj4A7gP+1jA3a20PoKDB5U6KM8Zrb2PMB43zaOK9nQw8AXxojNmr0b5CIBfY28vpIuBoYHPgv43Hh3mf72TgQGBTr807wB3GmCfjXb8DfADYJvYdChwJPBtn34dAvJw+iXcia+31wGxgJXAXkAYMB5621k4zxtzSxrxFpAurWbGCkjsXUfb4EzilpQQiEdIOOpDKJUuhshKAQHY2uQsXkPLb3/qcrbRGpxdC1toM4CHgpAbhItzCYSgw1Fo73xhzVTPnuAOYCFQDlbhFwTDgMGvtAUBP4AXqi4VUYCfgRi82v5lzjwHuBoJAIRDGLYjuBgZZa0fFK4astfOBy4HoCnklQA5uUTQIONVaO9QYU93EdccDdza4bl2jQ94CQt7va3CLrF7A77xfx1lrRzbIrQ53TFcmkO19ToWNzhk3lw2wN26xmguUennGWGuDwC24RVBUEe4Ys2OAY6y1i4wxEzs4L4wxH+AWQ+ux1r7h/XZRnN0fRIvRllhrD8Itgr4F9jPGFHjx64B3geuttf8yxqxoW/Yi0hVVvLyY/AkTcaqrocb9584pKaHy+RdixwRyc8m9ZCEpW2/tV5rSRsGNcI3bcIugL4FTgIgxJhf3h+f5uD/gr7TW/r6J9ocDo4AJuIVGDm4Pyne4PRBX4hZanwC7NDj3tV77uV5vUTyZwK24PR9bGmN64v6QjvYknM26P8SB2K2QK3B/qM8CNjXGZHvnOwG3N+o475imrnsL8GCD60ZY91bOC9773gpI995XDnAubm/acGB89GBjTJE3pusSL/ScMaZvo1+fNpFPe92E+70OMMZkGWMyG+YELMT9/H7C7Q3M9d5HFnAOsAaYYK1d7zPuLNba3XAHlP8I/HsDTzfJ214ZLYIAvMLnVtyieswGXkNEuoCaFSvcIqi8PFYExZM1bZqKoG6mU3uErLX7AqOB1cARxphV0X3GmCLgRmttGW7PyHzi36rIBWYaY+5qEHvbWjsN+CdusfIT7g/jcu/cJcA875bMPriF2E1xzp0KvAcMM8bUNsjrUu9W0wxgoddrUeO9p3TgOq/9KcaYlxu8p0rgX9baFd55p1lrr/TO2fi6zxpjRjVoW4Vb3EVfr1cYGmOKgbuttT977/083NsxfikGjjHGxHqejDHfAFhrNwcuxi10j25YhBljyoAHvPfxH+Bia+0dzd2G7EDR3qe/RL/zRn5jrZ2I2/uWB7xhjPmoiXMd6W2fi7PvWdxC8Ejcp/hEpBsruXOR2xPUnGCQqrffJrznHhsnKekQnX1rbLS3fbhhEdTIQ8AdwEBrbZZXxDRUiDtep7GXAAf31tSN0SIozjH7AM09t3hNEz8QrwamAX2BQ4BXvPhxuON5PmhYBDVkjPnEWvsR7i22g4lf4F0XJ9Za/8G9zbVHE5/ZxnJXwyKokZG442WeaaonyhjzvLU2D9gSd+zX552Tpsu7TXsW7m3Eu5s47CjvV8N2rwCjjDHfN4hFgC2Akib+bH/tbXdsJp/R1P8daUiTjYh0MWWPP9FsTxAAdXVULV0K48dtnKSkQ3R2IXSQtx1rrR3RwrEh4DfAV43iX3m9JeswxpRZa0txb7PEHchK/TxIPZu57ivxgsaY1dbaL4FdcIup6HHR97SztXZ1M+eNDkLeKs4+B/hfM22j42tGAiOAPXEHGYfjHNoX+Ka5c3WiN5rZF/2cjmrhc8r1tlvRyYUQcAbu9/JvY8wPjfaV4Y75ehJY5sX2AC4FjgBestbuZYwp9fZF8443j1bDeNzB6J5tcMeTiUgX55SWtnwQ4FRUdHIm0tE6uxDa3NtGx/a0JDNOrKmeJHAfVW7umOj+1Cb2lzcc2xHHj7iFUO8Gseh7Svd+tSTeeyptogcLiN1++yfr9kxU4I6pib6nzXB7wyKtyKGz/NrMvujnFKF1Ocb7nDraBG97Z+MdxphfqB9fFbXUWns08BpwAO74pz+38ZrN3e5bAaz3xCRuj1BunLiI+CSQmdmqYiiQ3pofC9KVdHYhFB2MPcoY89dOvlZnCMSJRd/TvcaYse08b7xbcQ2dj1sErcV9rP/pxrdfrLXFuL1h8XLcWJp7H9HPyRhjLtsYyTTHWrsrbi/VSuCZ1rYzxtRYa+/GLYQOo74Qivb4NFWwtNRjhDHmPtypEBrn+grqKRLpMqo//azZ/9HEhEKkaVX5bqeznxqL3pratZOv014Z3qDopkR7NRr2fGyM93S6t73QGLMoThEUwS2C2it6o7u5/7psaI9EV/vuWxok3Zzo9x/r2fJukf0IZHkDwxvbwds2vtUrIt1I+TPP8utJJ0Nrbo2lpJB5/HGdn5R0qM4uhKJjSIZaa/3suWhO3P95W2v74M5FBO4TYFHR9zTAWttZz0hu6W3fb2L/75ppG52PqLnPOzrAOWyt3bSJY/Zrpn1rRD+nY7zCzTfercazcT+bv7TjFAO97bJG8ehg+SFx2vy+0TEi0o04jkPRDTeSf+4E95F5gLQ0SE2FUGjdg0Mhd02x2bMI9Y27MpV0YZ1dCEXnxdkR9wmsJllrmxvQ3JnmWWtDceJzcQdwr8YdIxL1NO5j1SHghuYKvA14T9HbKbvHOWcYdwBvU6KP6jfZ02WMWUn9LNQnNd5vrd0C9+mqDfE33CfbeuAOQm7SRvjuT8cdMP9MnEHS0RwOsNamxYkfiXurEtx5nxq6w9vOb/gevOU6puBOatnSMh8i0sXUlZdTMOk8iq//YywW7NOHHldfTc8//ZHw4MEEMjIgECCQkUF48GB6Xn8daXvv7WPW0l6dOkbIGPOmtfYe3Mn0brTWboW75MUPANbaHNxH00fjFhandmY+cVTjDkx9yFp7vjHmR2ttNu4PvlneMZdH5xAC95aItfZ84K+4E0Q+ba1daIx5H8D7Ybo37oSHpxH/qbGWvABsD1xlrf0BeMEYU2et3QN3PqQdgCrcx9Mbiz6qPsBau7sx5uMmrvF33MHDV1lrv8NdsqQOdxzMnaw/03WbGGN+sNZeDlwGnO8VCn8wxnwFYK3NxB13cyZuwXfAhlyvBdFB0vFmko66Bujvjc9Z6cX2oH6uoIXGmP82bGCM+a+19k+4f1Y+stY+hvudDMOdmHOaZpUW6V5qfvyJ/LHjqP6k/mHk1N12I3vW+QSzswHIHj9Oj8gnkI2x1th5uD8czgIuAC6w1hbhPk2TQ/0tnM5ac6o5ZbhFz93Aad4aWjnUL23xAHHmMDLGPOD9YP8T7rxCx1lry4Fy3LE10fZNzbHTksuBE3HnqXkOqLTWVuEunVGN+0j9X4hfCL2Du17Wnrg/nNfgLn8BcKwx5jPv95cCx+NOWfAC7lNpdbhPb32J2yO2oZM1XoE7lmkubrE72pvyoAr3c4r2SMZdCqMjWGt3wS22Wxok/QDuki/74d7WSsUd5/QocIsx5tV4jYwxs705o6biFlx1uLdSr9OiqyLdS+U775I//lzqfq0fFpp+zDFERo8ikKI1yhNVp3+z3mzLZ1tr7wfG4U4w2Ae3EFqB+4P7ccCXHxrGmHu9Xpe5uAvCVgGf4d72+EtTsx0bY26y1j4HTMcds7MVbqHyK/Ax7i20f7Qzp1XW2v1xe1OOxZ1DqAR3YsZrjTHvWmvjjnUxxjjW2iG4RchRuAO+o+OA0hoct8paO9C7xu9xbx2t8nK+nPqekHbzPrt51tq/4xbEg7x8Irizgb8PPEUnFsHGmM9pxZN1xpi/0L7xQxhj7sddaFdEuqnSRx6l8MKLoMqbti4UIjJuLBlHHdV8Q+n2Ao6zMVY16Fpas/q6iF+ij8/369eP0aNH+5yNSGJzamspuuJKShbVd4AHsrPJmT2b1P5d5aHX5JG6+26xW5Dt0K6HstTXJyIiSamuqIj886ZQufiVWCy01VbkzJtHqM9m/iUmG5UKIRERSTo1y5aTN3oMNd9+G4ulDRhA1vRpBDMyfMxMNjYVQiIiklQqli4lf9J5OGvrJ37PGDqUzOHDCAQ7e1YZ6WpUCImISFJwHIfSe+5lrb0Mar0J5lNTyT5vMuFDDvE3OfFNUhZCxpgP8HeNLhER2YicqioK5y+g7P8eisWCPXuSPXcOqdtv72Nm4rekLIRERCR51OblkX/uBKrefCsWS9l+e7LnXEBok018zEy6AhVCIiKSsKo//Yy8seOoXbkyFgsfeghZEycRCMebk1aSjQohERFJSOXPPkvB9Jk4ZWVuIBAg88yRZJx4IoGARkeIS4WQiIgkFMdxKL7xz+ssmhrIyCB7xnTS9t3Xx8ykK+o2hZC1dr0psI0xXaakt9auxF0b7FBjzGstHd+K86XgrisGsJW3YvwGs9YOAN5uFH7JGDO4I84vIuKnuvJyCs+fRfnT9as2Bfv0IWfeXFK2as8a2JLouk0h1MAaoDbeDmvt4birqAP8tqmVv621VwPzvJdXGGMWdnCOXVk17mKiABm4i8yKiHR7NT/+RP648VR//HEsltq/P9mzZ23Isg2S4LpjIbRfUwVOa1hrbwBmei/nG2Ou6pCsOp6Duwo81PcMbTBjzIdAXwBr7Xg2fIV5ERHfxV85/mgio0dr5XhpVtL86bDWBoDbgEleaJYx5gYfU2qWMaYW2NnvPEREurrSR/9O4bwL1105fuwYMo4+2t/EpFtIikLIWhsE7gbG4Pa0TDHG3O5vViIisiGc2lqKrvoDJXfcGYsFsrPJnj2LtP79fcxMupOEL4S8Qcf3AyOBOmC8MebeFtr8FpgNHA1sCdQAXwGPArcYY8paee37gFHAI8aY4c0ctxC4DHjbGLN/g7zjDpa21l4BzAf+YowZb60dA0wGdsUdP/UOcJUx5qXW5Cki0t3UFRWRP2UqlS8vjsXclePnEurTx8fMpLtJ6NXlrLWpwMO4RVANcHYriqDTgc+BKcAOXjgM7AtcA/zXWtu7lSn8n7c9wVqb1cxxIxod32rW2nuBe4C9cQu9HOBI4Hlr7UltPZ+ISFdXs2w5v55w0jpFUNq++5J7xeUqgqTNErkQCgOPA6fi9qwMM8Y0W2hYawfiFiMh4A/A1saYTCATOAi3p2VP4L5W5vAS7hNamUDcosRauyewC24R80grzxt1KjAMmAjkGmNygO2A13C/21ustaE2nlNEpMuqWPoqv5xwAjXffBOLZQw9mey5cwhmZvqYmXRXiVwIPQQcD1QCQ40xj7eizQ24twtnGWMuNsb8AO7AZWPMG8AQYDVwrLV2r5ZO5g14ftR7ObKJw6K9QYuNMatakWNDPYAxxphF0dt1xphl3jmrcW/rHdDGc4qIdDmO41Byz73knXU2TuFaN5iaStb06URGjiQQTOQfZ9KZEvlPzt7e9n5jzL9bOthauxMwECgFFsU7xhiTB/zHe3lUK/OI9kIdZa3t1eiaAWB4o+PaYpkxZr1eJG880bvey93acV4RkS7DqaqicN6FrF14CdS608gFe/Yk9zJL+qGH+JyddHeJPFj6TdzekAnW2g+NMbe1cPxB3jYMfGetbeq46FifVk1Raoz5n7X2W9xbVqcDdzS6Zj/cXqt/tOZ8jbzTzL4fvW3PdpxXRKRLiLty/HbbkT13jlaOlw6RyD1C5wDPeb+/xVo7roXjN/e2KUCfZn5FvOPacjP6YW87olE8+voZY8zaNpwvqriZfRXeNrUd5xUR8V31Z5/z67HHr1MEhQ85hFxrVQRJh0nkHqEqYCjwL+B3wCJrbYUx5m9NHB8tCmOPsHegv+E+7n6otXZLY8xKbxDz6d7+9tzHOGZ3AAAgAElEQVQWExFJWOXPPUfBtBnrrhw/cgQZJ52kleOlQyVyjxDGmArgROBV3Pd6v7X2tCYOj66/tVNHP2lljPkc+BBoOCbod8BmQBFusSYikvQcx6Hoxj+TP+7cWBEUSE8ne+4cMk8+WUWQdLiELoQAvKepjgP+h/tY/P9Za0+Mc+gb3jYHt0jpaNFen+jTY9HbYk94BZuISFKrKy+n4LwpFF93fSwW7NOH3KuuJDxggI+ZSSJL+EIIwBhTjPvo+3u4Y2YetdYe0+iYT6gffHyttbbJMUDW2kxrbVob03gId3mPvb25g4Z6cd0WE5GkV/vTKtaccirl/3w6Fkvt358ef7iKlK1a9WyKSLskRSEE4A1GPgr4CPfJsCestUc0Omwq7tiiPYGl1tojo7fJrLVBa+1u1tpLgG9xb2u15fo/4E50CO5M0Lm4t+O0DIaIJLWqd9/jl+OOp/qjj2Ox9KOPJmfBfILZ2T5mJskgaQohAGNMPm4x9DmQATxtrT24wf43cWdrLsZdUuMloMxauwb3KayPAQv0xe3daato788+3vZRb9JFEZGkVPbYP/j19DOo++UXNxAMEhk/nqxzxxNISeTneaSrSKpCCMAY8wvuGKCvcR+Ff8Zau3+D/f/CXWPsKuB93AKoB+6g5teBhcDOxpgfabu/U7+QKui2mIgkKae2lrVXXEnBjJlQWQlAICuLnIULyDjmaJ+zk2QScJz2dGxsfNbaaKK/Ncas8DOXRGGtHQ/cBbxkjBnsdz7ista+Agzq168fo0eP9jkbkY7nrhw/jcqXX47FQltu6a4c37evj5mJ31J3321Dboe265FC9TuKiMhGU7N8OXljxlHz9dexWNq++5I1fZoWTRVfdMdCaHl0+QtjjCaUaCNr7QDgbb/zEJHkU/Hqa+RPmlS/aCqQcfLJZA4fTiCUdCM1pIvoToXQzy0fIq1QzfqfZb4fiYhIcnAch9L77metuTS2aCqpqWRNnkT6oYf6mptItymEjDG6cdwBjDEf4j71JiLS6ZyqKgoXXELZ3+pXNwr27En2nDmk7rC9j5mJuLpNISQiIt1LbX6+u3L8/96MxVK2247sOXMI9dKiqdI1qBASEZEOV/355+SNGUftDz/EYuFDDiFr0iQC4bZOzC/SeVQIiYhIhyr/z3/cleNLS91AIEDmiBFknKyV46XrUSEkIiIdwnEcSm66maJrr4vFAunpZE2fTng/LZoqXZMKIRER2WBOeTkFsy+g/Kl/xmLBzTYjZ95cUrbe2sfMRJqnQkhERDZI7apV5I0dt86iqan9+5M963yCOTk+ZibSMhVCIiLSblXvvU/euPH1i6YC6UcdRWTsGC2aKt2C/pSKiEi7lP3jcQrmzI0tmkowSGTsGDKOOcbfxETaQIWQiIi0iVNbS9HV11By2+2xWCAri+xZs0jbfTcfMxNpOxVCIiLSanXFxe7K8S+9FItp5XjpzlQIiYhIq8RbOT51333Inj5dK8dLt6VCSEREWlT52uvkTZy47srxJ51I5oiRWjleujUVQiIi0iTHcSi9/37WXnLpuivHT5pI+mGH+ZqbSEdQISQiInE51dXuyvEPPhiLuSvHX0DqDjv4mJlIx1EhJCIi66nNzyd/wkSq3vhfLKaV4yURqRASEZF1VH/xhbty/Pffx2JpBx9E9uTztHK8JBwVQiIiErPeyvFA5ojhZAwdqpXjJSGpEBIREXfl+Ftupeiaa8FxgOjK8dMI77efz9mJdB4VQiIiSc4pL6fggjmUP/lULBbs3ZucefNI6aeV4yWxqRASEUlitatWkTduPNUffhSLpey6KzmzZ2nleEkKKoRERJJU1fveyvE/N1w5fjCRMWMJpOrHgyQH/UkXEUlCZY8/QcEFc9ZdOX7MaNKPOUaDoiWpqBASEUkiTm0tRddcS8mtt8VigUiE7NmzSNt9dx8zE/GHCiERkSRRV1xMwdTpVLz4YiwW2mILcubNI7S5Vo6X5KRCSEQkCdSsWOGuHP/VV7FY6t57kz1jBsGIVo6X5KVCSEQkwVW+/l/yJkzEKSyMxbRyvIhLhZCISAIruf+vrL3EQE2NG0hNJWviRNIHaeV4EVAhJCKSkJzqatYuvITSB+pXjg/06EHO3DlaOV6kARVCIiIJxl05fhJVb7wRi6Vsuy3Zc+cQ6tXLx8xEuh4VQiIiCaT6yy/JGz02zsrxkwmEwz5mJtI1qRASEUkQ5c+/QMHUaeuuHD98OBmnaOV4kaaoEBIR6eYcx6Hk1tsouvqa2MrxhMNkz5iuleNFWqBCSESkG3PKyymYM5fyJ56MxbRyvEjrqRASEemmalevdleO/+DDWCxll13ImT2bYK5WjhdpDRVCkrCstSuAfk3s/tkYs96aAtbag4AFwEAgHfgGuAe42RhT28R1jgcuAPYGQsCnwG3GmPs39D2INKXqgw/cleNX/xyLpQ8eTGSsVo4XaQv9bZFEtxa4MU68pHHAWnsS8A+gAngEyAdOAG4ADgZOj9NmKnAzkAc8CFQBpwH3WWt3N8Zc0DFvQ5JVzYoVlNy5iLLHn8ApLSUQiZC2915UvvkWVFW5BwWDREaPJn2IVo5vSeVbb1F83fUApO6xB7kLFzR5bNWnn1J0qW3xnKF+/eh5/XWx1xWLX6HktvpFbbMvmE34gAOabF9XVET+hIlQ6/5fKzxoENlTp7R4XekYKoQk0RUaYy5t6SBrbQ5wF1ALHG6MeceLLwReBk6z1g43xjzcoM02wPW4BdMAY8wKL34Z8DYw21r7D2PMG4i0Q8XLi8mfMBGnujo2M7RTUkLlq6/FjtHK8W1T+cqS2O+rP/6Y2ry8Vs2tFMjOhmD85UiCOc3fhqxcsqTZQqjytddiRZBsfCqERFynAb2Bv0aLIABjTIW1dgHwEjAZeLhBm7FAGLgmWgR5bQqstVcBfwEmASqEpM1qVqxwi6Dy8qYPCgTInqUiqLXqioupeu89CIcJ77cfla+9RuXSV8kcenKLbXtc/QdCm23WpusFIhGoq6PqvfepKy4mmJ0d97jKJUsBd5B73a+/tukasuFUCEmiC1trzwK2BkqBj4Clccb7HOltn4tzjqVAGXCQtTZsjKlsRZtnGx0j0iYldy5ye4KaEwxS+dZbpO2hQqg1oj0v4YEDST9qsFsILVnSqkKoXVJSSNtnHyoXL6by9dfJGDJkvUNqVq6kZtkygr17k7rTTlSqENroVAhJousLPNAottxaO8YYs6RBbCdv+1XjExhjaqy1y4H+wLbA561os8paWwpsaa3NNMaUNT7GWjsaGB0n572afjuSLMoef6J+odSm1NZStXQpjB+3cZLq5qK3xcKHHkrKLrsQ3HRTan/8keqvvyF1h+075Zrpgwa5hdCSpXELoVhOhx1G3S8/r7dfOl/8G54iieFe4He4xVAE2B24E9gGeNZau2eDY3O97domzhWN92hHm9wm9m8DDIrzq6njJYk0nB262eMqKjo5k8RQ88MP1CxbRiA7m9Q99yAQCBA++GAAKpe80mnXTdl1F4K9e1PzzTfU/PjTOvucujq3lwpIH3RYp+UgzVOPkCQsY0zjxz0+ASZZa0uA2cClwNBWni76KI7ThhRaarMCWBInvhcqhpKW4ziUPfJI/QzRLQikp3dyRokh1vNy4IEEUtwffeFDD6X8qaeofP2/REaN7pRpBwKBgHudxx+nculSUkYMj+2r/uQT6vLySNlhB0Kbb97h15bWUSEkyegO3EKo4X/BWuq9yWl0XPT3m3pt8pppUxTvhMaY+4D7Gsetta/g9gxJkqn99VcK586j4vkXWtcgFCLtMPUktMSpraPy1VcBCB9ySCye0m9rQltvTe3331P17juEBw5s8hyFF17U5FNjPW/6M8HMzCbbpg86zC2EXn2VzOHDYlMcRAdJhwfpr7ufdGtMktEv3jbSIPalt92x8cHW2hTgt0ANsKyVbTb3zr8y3vggkcbKn3uOX353VOuLIICUFDKPP67zkkoQ1R99SF1BAcHevUnZead19oUPdQujho/Vx+MUF+OsXRv3V0u9d6Hf/IaUHXag7tdfqf7sM/d8FRVUvvkmpKQQPuigDXh3sqHUIyTJ6EBv27CoeRk4ExgCPNTo+MOATNynzSobtTnYa9P4EfnfNzhGpEl1xcWsvcRQ9ujf14mnDxlC6u67UXzTze6g6YbzzIRCkJJCzuxZhPquN0G6NFIRvS128MHrTTgZPvgQyv7vIao++IC6tUVNLk3S89Zb2vz4/DrXGXQYNV9/TeWSJaT17+8WQZWVpB2wP8HsrHafVzaceoQkIVlr+1trN4kT7wfc4r18sMGux4A1wHBr7YAGx6cDV3gvb290unuBSmCqN7litE1P4GLv5R3tfxeS6CrfeINfBh+9ThEU3GQTchbMJ2vcWML770/P668jPHgwgYwMCAQIZGQQHjyYntdfR9ree/uYffdQV1pG1dtvA+veFosK9d6UlJ13htra2MDlzhA+6GBISaHqf2/iVFbptlgXoh4hSVSnAxdaaxcDy4FiYDvgONw1xJ7BnRUaAGNMkbX2XNyC6BVr7cO4M0afiPuY/GO4y27QoM1ya+0c4CbgHWvtI9QvsbEl8EfNKi3xOBUVFF17HSWL7lrntkr44IOJjB9HMKu+hyDUty/Z48fpEfl2qvrvf8Gbj6nwguZXvKlYsoSM447tlDyC2Vmk7bMPVW+9Rflzz1H9yScEsrNVzHYB6hGSRLUYeAJ3bM9IYBbuAOTXgFHA8caYqoYNjDFPescsBU4FpgHVXtvhxpj1BgIYY27GLZY+Bc4BJgCrgdFaZ0ziqfrkE3459jhK7lwUK4ICkQjZM2eSPXPGOkWQbLiKJc2P/Wmodvlyar77vtNyCXsD28seeggch/BBB8WeYBP/6BuQhORNltj6fwHr270OtOm/hMaYp4Gn23otSS5OTQ0lt91O0Z9uiPVQAKTuuSdZ500mtMl6d3JlA9WuWk3Nl+4zDT2uu5Zg795NHlty8y1UvfsulUteIeWcczoln7R99iGQnY1TXAzotlhXoUJIRKST1SxfTsGM86l69936YDhM5OyzST/6KK0Y30kqvIkSQ/36kbLNNs0em3bggVS9+y4Vr75G5plnEQh1/A2TQGoKkdGjqF2xAsLpnTabtbSNCiERkU7iOA5lDzzI2ssuX2fx1JQddiB72lRNoteJHMehcqk3d1AzK79HpQ3YF0IhnMJCqj/8gLR99umUvNIPOww091OXokJIRKQT1P78MwUXzKHy5cX1wVCIzNNPI+PkkwmEQv4llwSqP/00tpJ72sCWC6FgJELqbrtR/eGHVLyypNMKIel6VAiJiHSw8qf/RcGFF+EUFsZioS22IHvaNFK229bHzJJHdILE0Oabk7LVVq1qEx54ANUffkjVO+9Q18q13qT7CzitXM9GRDaO6BIb/fr1Y/To0T5nI21Rt3YthQsWUv74E+vE0487jsiIEQTCaT5lJtI9pO6+G8Hs7PY2b9dgO/UIiYh0gIqlr1I4aza1q1bFYsFevciaOoW03XbzMTMRaY4KIRGRDVBXXk7RVX+g9J5714mHBx1GZMxYgpGmF+MUEf+pEBIRaaeqDz6gYPpMar79NhYLZGeTNXFCq55UEhH/qRASEWkjp7qa4ptvofjGP6+zGGrqvvuQPXESwZ49fMxORNpChZCISBtUf/MtBTNmUP3Bh7FYID2dyOhRhI88UpMjinQzKoRERFrBqauj9P6/UnTFlTgVFbF4yk47uZMj9unjY3Yi0l4qhEREWlD70yoKZs2m8tVX64OhEJnDh5FxwomdshyDiGwcKoRERJrgOA7lTz5J4fyFOGvXxuKhrbcme/o0Uvr18zE7EekIKoREROKozS9g7cUXU/70v+qDgQAZJ55A5rBhBFJT/UtORDqMCiERkUYqFi+mYPYF1P38SywW3GwzsqdOIXWXXXzMTEQ6mgohERFPXVkZRZddTukDD64TDx95JJHRowhmZPiUmYh0FhVCIiJA5TvvUjBjJrUrVsRigdxcsiZNJDxggH+JiUinUiEkIknNqaqi+IYbKb7lVqiri8XT9t+frAkTCObm+JidiHQ2FUIikrSqv/ySgukzqf7kk1gskJFBZOwYwoMGaXJEkSSgQkhEko5TV0fJXXdTdM21UFkZi6f270/WlPMI9e7tY3YisjGpEBKRpFKzciUFM2dR9cYb9cHUVCIjR5B+7LEEgpocUSSZqBASkaTgOA5lf3+MtZcYnOLiWDz029+SPW0qKVtt5WN2IuIXFUIikvBq8/IonHchFc8+Vx8MBMgYOpTM004jkKp/CkWSlf72i0hCK3/+BQrnzKVuzZpYLNi3L9lTp5K6044+ZiYiXYEKIRFJSHUlJay91FL20MPrxNOPPprI2WcRSE/3KTMR6UpUCIlIwql8800KZs6i9vvvY7Fgz55kTZ5M2t57+ZiZiHQ1KoREJGE4lZUUXf9HSm6/AxwnFk878ECyzh1PMDvbx+xEpCtSISQiCaH6s8/Jnz6dms+/iMUCkQiRceMIH3KwJkcUkbhUCIlIt+bU1lJyx50UXXc9VFfH4ql77EHWeZMJ9erlY3Yi0tWpEBKRbqvmu+8omHE+VW+/XR9MSyNy1lmkH3O0JkcUkRapEBKRbsdxHMr+7yHWXmpxyspi8ZTttiNr2jRStviNj9mJSHeiQkhEupXaX36hcM48Kl58sT4YDJJ52qlkDB1KIEX/rIlI6+lfDBHpNsqfeZbCufOoKyiIxUJbbEHWtKmkbredj5mJSHelQkhEury6oiIKFxrKH3tsnXj6739P5MwzCYTTfMpMRLo7FUIi0qVVvvY6BefPovann2KxYK9eZJ03mbQ99vAxMxFJBCqERKRLcsrLWXv1NZTe/Zd14uFDDyUybizBSMSnzEQkkagQEpEup+rjjymYPpOar76KxQJZWWRNmED4wIE+ZiYiiUaFkIh0GU5NDcW33ErxDTdCTU0snrr33mRPnkSwZ08fsxORRKRCSES6hJply8mfMZPq996rD4bDREadQ/rgwVoiQ0Q6hQohEfGV4ziU3v9Xiq64Eqe8PBZP2XFHsqdOJbR5Xx+zE5FEp0JIRHxTu3o1BbMvoPKVJfXBUIjMYWeQceKJBEIh/5ITkaSgQkhEfFH21D8pvPhinMK1sVhoq63InjaNlN9u41teIpJcVAiJyEZVV1hI4fwFlD/5VH0wECDj+OPIHD6cQJomRxSRjUeFkIhsNBVLl1Jw/mzqVq+OxYK9e5M9ZQqp/Xf1MTMRSVYqhESk09WVl1N0xZWU3nf/OvHwEYcTGT2aYGamT5mJSLJTISQinarq/ffdyRGXLYvFAjk5ZE2cQHj//X3MTEREhZCIdBKnupriP99E8U03Q21tLJ42YABZkyYSzM31MTsREZcKIRHpcNVff03B9BlUf/RxLBZITycydgzhww/X5Igi0mWoEBKRDuPU1VF6z72s/cMfoKIyFk/ZZReyp0wh1GczH7MTEVmfCiER6RA1P/5E4azZVL72Wn0wJYXMEcPJOO54AqGgf8mJiDRBhZCIbBDHcSh//AkKFyzEKSqKxUP9+rmTI/bb2sfsRESap0JIRNqtNj+fwgsvpuLf/64PBgJknHwSmaefTiA11b/kRERaQYWQiLRLxUsvU3DBHOp++SUWC/bpQ/bUKaTuvLOPmYmItJ4KIRFpk7rSUtbayyn729/WiacPHkzknHMIZKT7lJmISNupEBKRVqt8+x0KZs6kdsV3sVggN5fsyZNJ23cfHzMTEWkfFUIi0iKnqoqiP/6Jkttuh7q6WDztgAPImnAuwZwcH7MTEWk/FUIi0qzqL76gYNoMqj/7LBYLZGYSGTeW8KGHanJEEenWVAiJSFxObS0ld91F0TXXQVVVLJ66225kTTmP0Kab+pidiEjHUCEkIuup+eEHCmaeT9X/3qwPpqYSOfNM0n8/hEBQkyOKSGJQISQiMY7jUPboo6y95FKckpJYPGXbbcmaNpWULbf0MTsRkY6nQkhEAKhds4bCufOo+M/z9cFgkIxTTiHz1FMIpOifCxFJPPqXTUQo/89/KJwzj7q8vFgstPnmZE2bSuoOO/iYmYhI51IhJJLE6oqLWWsupeyRR9eJpx9zDJGzzyIQDvuUmYjIxqFCSCRJVb7xBgUzZ1G7cmUsFuzZk6wp55G2554+ZiYisvGoEBJJMk5FBUXXXkfJorvAcWLx8MEHExk/jmBWlo/ZiYhsXCqERJJI1SefUjBjBjVffBmLBSIRss49l/DBB/mYmYiIP1QIiSQBp7aWkttup+iPf4Lq6lg8dc89yZo8mVCvTXzMTkTEPyqEJCFZa3sBQ4HjgN2BLYAq4GPgXuBeY0xdg+O3AZY3c8pHjDHDm7jWKGAKsCtQC7wPXG+M+dcGv5EOULN8OQUzZ1H1zjv1wXCYyNlnk370UVoiQ0SSmgohSVSnA7cDq4DFwPdAH+AU4G7g99ba040xTqN2HwJPxjnfJ/EuYq29HpgNrATuAtKA4cDT1tppxphbOuC9tKhmxQpK7lxE2eNP4JSWEohEyDhlKKE+fSi59TacsrLYsSk77ED2tKmENt98Y6QmItKlqRCSRPUVcCLw70Y9PxcDbwGn4hZF/2jU7gNjzKWtuYC19iDcIuhbYD9jTIEXvw54F7jeWvsvY8yKDXsrzat4eTH5EybiVFdDTQ0ATkkJZQ88uM5gaEIhMk8/jYyTTyYQCnVmSiIi3YYWDJKEZIx52RjzdMMiyIuvBu7wXh6+gZeZ5G2vjBZB3jVWALcCYWDMBl6jWTUrVrhFUHl5rAiKaVAEBfv0oceVV5J56qkqgkREGlCPkCSj6Gjhmjj7fmOtnQj0AvKAN4wxHzVxniO97XNx9j0LLPSOMRuQa7NK7lzk9gQ1JxAgdffdSdlu285KQ0Sk21IhJEnFWpsCnOO9jFfAHOX9atjmFWCUMeb7BrEI7gDsEmPMqjjn+drb7thMLqOB0XF27dVUm8bKHn9i/Z6gxhyHqtdfh/MmNX+ciIjffHh4Q4WQJJurgd2AZ4wx/2kQLwMuxx0ovcyL7QFcChwBvGSt3csYU+rty/W2a5u4TjTeo5lctgEGtSX5xpzS0pYPwp1EMXzAARtyKRGRhKRCSJKGtXY67uDmL4CzG+4zxvwCXNKoyVJr7dHAa8ABwHjgz228bOOn0hpaASyJE9++V69eW/Tt27fFkwciEZySkpaPy4q0eIyISDJSISRJwVo7BbeI+Qz4nTEmvzXtjDE11tq7cQuhw6gvhKI9PrlxG7bcY4Qx5j7gviZ2N1dAxWSeMpTS/3uo+dtjKSlknnJqa04nIpJ09NSYJDxr7UzgFty5gI7wnhxri1+9baxbxbtF9iOQZa2NNyHPDt72qzZeq02yJk4gkJra7DGB1FSyJozvzDRERLotFUKS0Ky184AbgA9wi6Bf2nGagd52WaP4y952SJw2v290TKdI2WYbNll0J4GMDEhp1MGbkkIgI4NNFt1JyjbbdGYaIiLdlgohSVjW2oW4g6Pfxb0dtqaZYw+w1qbFiR8JnO+9fLDR7uh8RPOttT0btNkGd8mNStzlPDpV+pFHsNmLzxM580wC2VkQCBDIziJy5pls9uLzpB95RGenICLSbQUcp1VDEUS6FW/9r/tw1/66mfhjdVZ443Sij8j3B17BXS4D3KfGonMFLTTGXBHnOn8EZnltHsNdYmMY7jxEG7LEhv5iioi0TbuevddgaUlUv/W2IWBmE8csoX6w8gO4i7Tuh3tbKxX4GXgUuMUY82q8ExhjZltrPwKmAhOAOuA94LqusuiqiIg0TT1CIl2T/mKKiLRNu3qENEZIREREkpYKIREREUlaGiMkkmCee+45Vq9u61RJIiL+6tu3L0OGxJuNpHOpEBLpmtq98uCbb775BbBTB+YiItLpvvvuuy+HDBmy88a+rgohkcST5W3X4k4kKYlhL9ylW/S9di36XjZc9DPMaunAzqBCSCTxfANsAXxgjDnc51ykg3hzXQ1C32uXou9lwzX4DL/x4/oaLC0iIiJJS4WQiIiIJC0VQiIiIpK0VAiJiIhI0tJgaZHEcx/u4rErfM1COtp96Hvtiu5D38uGug8fP0OtNSYiIiJJS7fGREREJGmpEBIREZGkpUJIREREkpYGS4t0IdbaLYHLgCFAL2AV8CRgjTEFrTzHHOAIYFdgU6AO+A54AfiTMWZlM21PBCYDA4Ac4BfgfeAqY8z/2vm2klpHfKcNzrU7EP1+N8Nd1uFz4C/GmL82Ora5AaBvGmMGtuXaiaajvhdr7VBgGrAPkA4sBx4CrjXGVDTRZlfgUuBw3L9n3wEPA1cbY8rb9442LmvtabizQe8F7AlkA38zxpy1Mc5jrT0IWAAMxP3cvwHuAW42xtS2JQf1CIl0Edba7YB3gTHAW8ANwDJgBvCGtbZXK081EfgNsAS4DfgLkAecD3xqrd07zrWD1tpFwFNAf+Bx4I/A88B2wL7tf2fJqwO/U6y1o3GL0pOBV3G/n8dwF+g9tolm3wE2zq+72/5uEkdHfS/W2stx/67sh1tE3QoU4X7GL1prM+K0OQB4G/d7fBH4s9fmEuAFa214g97cxrMAmIpbwPy4Mc9jrT0JWAocBjyB+7mn4X6PD7c1AfUIiXQdt+H+L3+6MebmaNBa+yfcIuZKYFIrzrNbvP+JWmvPBRZ552n8g3M2cC7wADDeGFPVqG1qG96H1OuQ79RaOxC3ePkEGGKMWd1of1PfzwpjzKXtSz2hbfD34v2HYj5QCOxrjFnmxQPATbg/3Ofh9vxE24SAe4FM4CRjzD+9eBB4FDjVu/7VHfEmO9n5wErcnphBwOKNcR5rbQ5wF1ALHG6MeceLLwReBk6z1g43xrS6IFKPkEgXYK3dFjgadx6NWxvtNkApcLa1NtLSuYM5TfkAAAsuSURBVJrqjsf9hxZgh0bXzsH93+hK4NzGRZB3zuqWrivr6sjvFLgWCAFnNS6CQN9PW3Tg9zIUtzfu7mgRBGCMcYCLAQeY7BU/UYOAXYCl0SLIa1MHzPVeTvKKqS7NGLPYGPO193435nlOA3oDD0eLIO88Fbi9S+De3m819QiJdA1HetvnvX8UY4wxxdba13H/8R4IvNTOa5zgbT9qFD8RyALuAILePfvtgWLgNWPMh+28XrLrkO/UG8tyKPAO7q3NI3BvVTrAB8DixudvoIe1dizQF3c80bsa69Vhf9f6ettljXd451mD2+u0O+731PDaz8Vps8xa+xWwI7At8P/t3XuMVOUZx/EvWlCxuqU1WmoTUCxSFGspikKjJaI1XhEs0lrARlIvvRjFmF7Up0/TS9qkmPqPGKIioWqb1Ygt1saEQlUsVtuKqQkCAdv0glxEW0UEpH8879kdhpndM7tndkfO75OQd8/9zBxm5jnved73XZ/v5ZRO3feQeFz2NjDB3Q8xs515dqhASKQ1nJjKV+osX0t8OY8kZyDk7nOAjxNBzhhgMpEz8q2qVU9L5S4i8XZY1X4eBmaZ2dt5jisdirqm2fVZS1T9f65q+UvuPtXM1tXY9lNEjlgHd38RmGlmL3VxzANZUddlSyqPq17g7kcQDRUARtEZCOU59sj0T4FQbXXfQzPb7e4biDzH44nvs27p0ZhIa2hL5Rt1lmfzP9TAPucQVf1ziS/2F4DJZra2ar2jU3kLsBkYT7TcGE/UQkwjciqkMUVd0+z6TCceq0xN+z6ByOkaAyx190FV280DJhKPEY4gAqp2Ijha5u7H5nsZB5yirstvUjnH3YdXLfsB8dgMYEgTjl1mhb+HqhESeX/IvlRzP4/PmkenFjBjiQTQF9z9CjOrrFbOchh2ABdX5KA8l5rTv0LkTHzXzHrTOkT2lfeaHlxRzjGz7Af4TXefTQRH44iA9cFsIzObW7Wf54EvuHt7WvdmIlFV9pXrupjZSne/m2iluTrVnG4jgs/TgL8RNRONNOVu+HMu+2n4PVSNkEhryO5i2uosP7JqvdzMbKuZPUnUCu0AFlU16836TPljdSKumf0bWEV8V4xr9NglV9Q1za7PTuDxygUpwXRJmjw953nNT+VZOdc/0BT2WTOza4GrgZeJGrtrgXeBzwPZo8fXmnHsEiv8PVSNkEhrWJPKkXWWZy296uUWdMvMtrv7s0T/JScRNQSVx95eZ9Psh3i/PlGkS0Vd02w//62TFN3o9dmcyjyt1Q5EhX7WzOxeoiO/fbh71lfTn5p17JJaQ9yUjSQe93dw9w8QOVu7qZHEXo9qhERaQ9Z3xnmpT5EOKfFyIlGb09sWP1leyO6KeVlC6El1tsnmb+zlscumqGu6mkjMPcrdj6mx/ORUbsx5XlmP0rl/KA4wTf+suft5RKODFVWPk5el8vwa2xxP/Li/SnmvTR5130OilnMwsDJvizFQICTSEsxsPdGL83Dga1WLnbh7X2Rmb3XMdB/l7qP2WdF9WPpC3Y+7X0PkLvyDzmp7UvP4Z4BPppZmldvMIXJQ1rPvna10o6hrama7gbvT5E8rf7zTkBtXEYFte8X8sbX6wXH3U4hcMYDFPXph73NFXZc0/8ga80YQHZfuYf8WmiuIlkxnpfy7bJuDgJ+kyfm97Zun1bj7wPQejihgd+3EjcEMd+94XO/uhxJJ6gB3NbJDPRoTaR3XAyuBO939HOILczwxrtQrRC+2lbKmoZWdr30aeMTdV6ZtNhHjKJ1BtC76H9F0ujqB82rgaWCBu08lEj1HEz1Qvw1c1ej4PQIUc00BfgScA8wCxrj7cqI12DRinKW5Vc3nvwlMdfdlROC7k2jGfT6RdL2AisTqEirqutzj7sOIRzSvEy35LgYGEont+9Qqmdked/8KUavRnhLX/05c23HEDckdhbzCJnP3KcRjdujsU+lMd1+Y/t5iZjenv48l3sNXiQC0p/vBzN5MveS3A8vd/SEiSf0Soml9O/DLRl6LaoREWkS6Ux0HLCS+lOcS43zdCZxpZltz7ObPxBfpIOBComXQF4kWFD8DRpvZihrHXkO0LLuHaF59A9Fp34PAODN7ujevrawKuqakPpzOIWosBhM1GZcQP+YXmNm8qk0eJcaxOhmYTQRGnwF+Swzt8NUDrdahEUVdF6IJ/S4iUfpmYALwMDDWzBbWOfYqomZ2CdGA4UYi8ff7wLmNPNLpZ6cS/7dmE8nhEH33ZPMub9Z+zOxRopfuPxA3A98grsNNwIxG/28P2Lu3tJ8FERERKTnVCImIiEhpKRASERGR0lIgJCIiIqWlQEhERERKS4GQiIiIlJYCIRERESktBUIiIiJSWgqEREREpLQ0xIaISMmlITvOrpo9ycyW9/3Z1Obu24kemDuYWfWQFyINUyAkItLC3H0jMZK5m9n3ilq3jjeJkdcB3u3B9tXnM4nO0cLHm9lzObYZAvyHGCbmOjObnxZtAt4hxko7qrfnJpJRICQiIpkb6o2R1UPLiYE2hxEDxnYbCAEziCBoJxWDZ5rZiQDuPhzYUOA5SskpR0hERJoiDX65KE3OcPeBOTablcrHzOz15pyZSCcFQiIi0kxZIPQR4IKuVnT3TwBnpMn7m3lSIhk9GhMRkdzc/SDgSqLm5lQigXkL8BQwz8xWVa5vZuvc/RlgYtpmSRe7z2qDNgG/K/jURWpSjZCIiOTi7kcQAcoiYDJRy7MDGApMB1a6+9drbJrV7lyUkqFr7XsA8OU0+Qsz213kuYvUo0BIRETyygKg1cCFwOFm1gYMAb4D7AZ+7u4Tq7b7FdHiaxBwRZ19nwUMrziOSJ9QICQiIt1y98nAFGAj0cfQ42a2A8DMtpvZj4HbiN+Vb1dua2ZvAI+myVnUls3/q5m9WPDpi9SlQEhERPKYncqFZratzjoPpHKSux9ctSx7PHamu59QucDdDwMur1pPpE8oWVpERPKYkMob3f26btYdTOQPvVYx70ngX8DHgJmAVSybAhxJPFp7AJE+pBohERHJY2gq24BjuviXGVy5sZntARanyZkpOTqTPRZ7wswqgyeRplONkIhIa3snlYflWDcLPnZ0uVbPZDfOl5rZYz3cx/3ALcBxwGeBp9z9o8C5FctF+pRqhEREWtvWVA7taiV3PwT4cNU2RdqUytE93YGZvQw8nyZnpvJKYvyw14Ff9/jsRHpIgZCISGv7SyondLkWnE4EFJXbFOnZVE7r5X6yWp/p7n4onY/FHjKznb3ct0jDFAiJiLS2h1M5wt0v7WK9m1K5geYEQgtTOc7d6zWBBzpGkK/nQWJk+zbgVuCUNF+PxaRfKBASEWlhZvZ7osUVwGJ3v8bd27Ll7n6iuy8mWl4B3Gpm7zXhPJ4AHkmT93roeFzn7kPc/VJ3XwLM62I/W4GlaTLrb2hN9dAcIn1FydIiIq3vS8QYXROA+cBd7r6d6Kn58LTOXuA2M2tm8/NZxA30FOB24HZ3fwMYQDR/zyzsZj/3A5fReTOu2iDpN6oREhFpcWa2BTibSDBeSiQufzAtXgMsAMaa2Q+bfB5vmdllwEVE7dA/idZsg4B1RB9AlwPXd7Orx4HN6e/36GxWL9LnVCMkIvI+kAYhXUwLBA1mtpTOx1s92X4XcHRxZyTSc6oREhERkdJSjZCIiGTuc/f70t+TzGx5f55MpZQT1dbtiiINUiAkIiLb6OwwMfNuf5xIFzbR2cu2SGEG7N27t7/PQURERKRfKEdIRERESkuBkIiIiJSWAiEREREpLQVCIiIiUloKhERERKS0FAiJiIhIaf0fl8JsSsJyquMAAAAASUVORK5CYII=\n", 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" ] @@ -567,7 +575,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ @@ -587,7 +595,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 14, "metadata": {}, "outputs": [ { @@ -596,13 +604,13 @@ "Text(0.125,0.3,'AFM')" ] }, - "execution_count": 24, + "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -647,7 +655,7 @@ "\n", "Such a model is therefore not symmetric in its AFM phase for $\\mu=0$, which we can test.\n", "\n", - "We make a copy of our `ParameterCollection` `hubbard` where we have stored the parameters of our Hubbard model and give this copy the additional parameter `tp`.\n", + "We alter our `ParameterCollection` `hubbard` where we have stored the parameters of our Hubbard model and give this new one the additional parameter `tp`.\n", "This parameter stands for the energy gain of next-nearest neighbor hopping processes.\n", "The `SquareLattice` class knows about this parameter and we can proceed as before to obatin the dispersion relation.\n", "Plotting it, we already see, that the density of states is no longer symmetric.\n", @@ -657,11 +665,11 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 15, "metadata": {}, "outputs": [], "source": [ - "hubbard_next_nearest_neighbor_hopping = hubbard.copy(tp=-0.05)\n", + "hubbard_next_nearest_neighbor_hopping = hubbard.alter(tp=-0.05)\n", "\n", "H = create_square_lattice(**hubbard_next_nearest_neighbor_hopping)\n", "\n", @@ -671,7 +679,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 16, "metadata": {}, "outputs": [ { @@ -680,13 +688,13 @@ "Text(0.5,0,'DOS')" ] }, - "execution_count": 26, + "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -711,7 +719,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 17, "metadata": {}, "outputs": [], "source": [ @@ -731,7 +739,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 18, "metadata": {}, "outputs": [ { @@ -740,13 +748,13 @@ "Text(0.08,0.1,'AFM')" ] }, - "execution_count": 28, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -848,7 +856,7 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 19, "metadata": {}, "outputs": [], "source": [ @@ -859,7 +867,7 @@ " \n", " def one_over_charge(U):\n", "\n", - " chi_c_wk, _ = get_chiRPA(p.copy(U=U), chi0_wk)\n", + " chi_c_wk, _ = get_chiRPA(p.alter(U=U), chi0_wk)\n", " \n", " # -- If any value is below zero we are already in an ordered phase\n", " if np.any(chi_c_wk.data[np.abs(chi_c_wk.data) > 1e-3] < 0.0 ):\n", @@ -875,7 +883,7 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 20, "metadata": {}, "outputs": [], "source": [ @@ -898,7 +906,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 21, "metadata": {}, "outputs": [ { @@ -907,13 +915,13 @@ "Text(0.07,0.15,'CDW')" ] }, - "execution_count": 31, + "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -971,7 +979,7 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 22, "metadata": {}, "outputs": [ { @@ -985,11 +993,11 @@ "Two-Particle Response Function tool-box \n", "\n", "beta = 11.6045250062\n", - "nk = 1024\n", + "nk = 64\n", "nw = 100\n", "norb = 1\n", "\n", - "Approx. Memory Utilization: 0.01 GB\n", + "Approx. Memory Utilization: 0.00 GB\n", "\n", "--> fourier_wk_to_wr\n", "--> fourier_wr_to_tr\n", @@ -1017,7 +1025,7 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 23, "metadata": {}, "outputs": [], "source": [ @@ -1066,7 +1074,7 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 24, "metadata": {}, "outputs": [], "source": [ @@ -1103,7 +1111,7 @@ " g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh)\n", " \n", " def lambda_minus_1(U):\n", - " lamb, _ = get_lambda_delta(p.copy(U=U), g0_wk) \n", + " lamb, _ = get_lambda_delta(p.alter(U=U), g0_wk) \n", " return lamb - 1.0\n", " \n", " upper = 1.1*guess\n", @@ -1116,7 +1124,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 25, "metadata": {}, "outputs": [], "source": [ @@ -1135,7 +1143,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 26, "metadata": {}, "outputs": [ { @@ -1144,13 +1152,13 @@ "Text(0.07,0.15,'SC')" ] }, - "execution_count": 36, + "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -1206,19 +1214,19 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 27, "metadata": {}, "outputs": [], "source": [ - "hubbard_spin_dependent = hubbard.copy(spin=True)\n", + "hubbard_spin_dependent = hubbard.alter(spin=True)\n", "\n", - "H = create_square_lattice(**hubbard_spin_dependent.copy(zeeman=1.0))\n", + "H = create_square_lattice(**hubbard_spin_dependent.alter(zeeman=1.0))\n", "e_k = H.on_mesh_brillouin_zone(n_k=(hubbard_spin_dependent.nk, hubbard_spin_dependent.nk, 1))" ] }, { "cell_type": "code", - "execution_count": 41, + "execution_count": 28, "metadata": {}, "outputs": [ { @@ -1227,13 +1235,13 @@ "Text(0.52,0.6,'$|\\\\downarrow \\\\rangle$')" ] }, - "execution_count": 41, + "execution_count": 28, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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DosKNeYmJuupK8l94EU9mJp5Dhyj6cgFRQ4cYEovwntz6E8IgxT/+RMmPP2qDo/X8FMXQmA7kFDF+wSaGvPE7X6zed8wkZTYpNE6KwmL+d6yHcov5dv1Bnl+wievfXsrqXUcCEfa/KBERxNxysz4ueO89VPW/E64IbnJFJYQBVJeL3Mr1/IZdh7VrV8PiySt08dYP21i07gBuT9UX9E6N4+nVMpmWDWJomRJD0+RowiwmikvdbE7PY93uHNbuyWHDvlyKS9368w7lFjPmw9Vc3bMJYwa1JdIa2Jeb6BtGUPDmW6iFhZRt+ZuSX34h4txzAxqD8A1JVEIYwDFlKu7yyglKXFyV8z+Btv1QAY98spYDOUVVHj+1aQK39m9Nz5ZJx7zSiwgz06N5Ej2aJwFQ5vaw9WA+a9Ky+WhpGvlFZQDMW7WP1WnZPD2kK+1OifP/P6icKTGRqGHX4ZwyFQDHO+9Joqql5NafEAHmzsig4LXX9bGR9fx+2HiQ2z5YWSVJ9WieyKSRp/PuLb3o1Sq52rcjLWYTnRoncGO/lsy+6yz6tUvRP7cny8mtk1cwa2kaHk/gbsHF3DYKzGYASpYuxbVhQ8DWFr4jiUqIAMt7bnxFPb82bYgeeVPAY3B7VN78fitj56zXb9dFWc2Mv7Ybb9/ci9NaVD9BHUu92HBeGNadJy7vRKRVSxRlbpU3v9/GPTNXk5FffIIZfMPSpAmRl16ijx3vvheQdYVvSaISIoBKVq2maO5cfWxEPb+8Qhf3f7SGWUt36481SY5iym19OLdjA5+toygKg3s05sM7+tKhUcUtv9W7srnhnWVs3Jfrs7WOp/IB4KKvFlK2f39A1hW+I4lKiABR3W7ynhyrjyMuvoiIs88OaAy5The3T/2DP3ZW7MY7s20KU2/rQ4v6MX5Zs2lyNJNH9eamfi04epGWV1jKPTNXByRZWbt2xXrGGdrA7cbxvrSrr20kUQkRIIWzZlO6caM2iAgPeD0/Z0kZ93+0ht2ZTv2xW85pyYvDuhMb6d+rOovZxOjz2zJpZE8So7WDt4Ulbh6c/Sf7jjhP8GzvxY6+Q/+48OOP8eQG5mpO+IYkKiECwJ2dQ97EF/Rx7JgxWBo3Dtj6JaVuHv54LVsOaHXvFAXGXd2F/53XBpMpcGe3ejRPYtLIniREaYkxr7CUB2b9SV6hf8sxhZ/bH0v7dgCohYU4Z37k1/WEb0miEiIA8ie+gFr+W7y5aVNiK71v4m9lbg9j565nTVq2/tjDl3Tkwq6NAhZDZS3rx/DS9T0It2gvP/uOFPLIJ+twlXn8tqaiKMTcXvHf3DF1GmpJid/WE74liUoIP3OtX0/hrFn6ON5uQ4kMTE08j0fl+QWb+O3vDP2x0QPacGXPJgFZ/790bpKA7aou+njdnhyenb/Rr9Ujoq64HFNDbbOIJyODws+/8NtawrckUQnhR6rHQ96TT0H5C3D4eecSMXBgYNZWVd74fiuL1h3QHxt+RnNu7NciIOufyHmdGjJmYFt9/P2Gg0z+eYff1lOsVmJuvVUfO959D9Xjv6s44TuSqITwo8K583CtWaMNrFYS7IGr5/fF6v18snyPPh7cI5Uxg9oaXk+wsuFnNufK0yveq5v66y6+Xpfut/WiRwxHidF2N5bt2EHx4h/9tpbwHUlUQviJJz+f/Oee18cx/7sNS8vAXM38fSCPV7/Zoo/P7diARwd3CqokBdp7Rw9e3IE+rSsqc4xfsIk1af4pZmuKiyN6+PX6+Gh5JRHcJFEJ4Sf5L7+CJysLAFPDhgFriJhfVMrjn/2lVz5v0zAW21VdMAdwd9/JsJhNPDf0VFo3KL/Scas8+sm6f9Ue9JXoW28Bk/bSV7JkCaXbt/tlHeE7kqiE8IPSv//GOW26Po5/amxAGiKqqsqz8zfqL/JR4Waeu+ZUIsLMfl/bG9ERFl4ZfhopseEAFBSX8eScvyj1w05AS2oqEYMq3id0fjjD52sI35JEJYSPqR4PuY89Dm6thp61b18iLxsckLVnL9tdZYffk1d0pmly8HQMPp768RGMv66bfuW3OT2PGUt2+WWt6JEj9Y8LP5uDp6DAL+sI35BEJYSPOWd+hOuPVdrAYiHh2acD8t7Quj05vL244jbWtX2acl7Hhn5f15c6N07gzvPb6OPpv+0iLdPh83XCzzoTS+vWAKhOJ4Xz5vl8DeE7kqiE8CH3gYPkPz9eH8eMvoOw9u39vm62o4Sxc/7Smx52bhzPmIHt/L6uP1zXtzmdGscDUOpWmfjVZp+3BlEUpUrVeuf0GdIBOIhJohLCR1RVJfexxytaeLRqRdx99wZk3WfnbySzQKu0EBcZxrNDTyXMUjt/vM0mhUcHd9JvAa7bk8OCP31f8TxqyNUo5e8blm3fjmvpMp+vIXyjdn4nCxGEihYsoHjxYn2c8OJElIgIv6/79boDLNuepY/HXd2FhgmBqXzhL20axjLizOb6+K0ftpFV4NuSR6bYWKKGDtHHjunTfTq/8B1JVEL4gDs7h7yxNn0cfeMNhPfu7fd1M/KLee3bv/XxNb2bckablOM8o/a4+ZxWNE6KAsBRXMYri7ac4BknL/qmG/WPi7/7nrJ0/x02FjUniUoIH8izP43niHZI1XzKKcQ9/pjf11RV7f0bR3EZAKmJkYyutBGhtosIM/Po4I76+KfNh6vsaPSFsLZtCT/zTG3g8UhV9SAliUoILxX/8kvVrr3jn8cUG+v3db/56wBLt2Xq4yeu6Eyk1eL3dQPp9JbJXNo9VR+/+PVmnOWJ2Veib67YVFE4azZqcbFP5xfek0QlhBc8+fnkPlJx9RR5+WVEDjzf7+tm5hfz6jcVt/yG9m5Kj+ZJfl/XCHcPaqs3W8zML+GdH31bSSJi4EDMjbSWJ57sbIoWfu3T+YX3JFEJUUOqqpL7yKO492s70pSEBOKftgdk3Qlfbaag0i2/O0Polt8/xUdZuf+iii3+81btZYMPW9grFgvRN96gjx3TP/TZ3MI3JFEJUUOFn35K0YKv9HHihPGY69U7zjN849v1B6vc8nv88tC75fdPAzs3pG8b7b+tqmqFa31ZXinq+mFg1a7aSteuxbVunc/mFt6TRCVEDZTu2KH1mSoXNfx6Igdf6vd1jzhKqlRFH9KrCae1CM1bfpUpisJDl3TUaxbuynDw0dI0n81vTk4mcnBFmSunXFUFFUlUQpwktbiYnNF3oRZphV8tbdoQbx8XkLXf/G4r+UXaLb9GiZHceX7bEzwjdDRKjOT281rr4+m/7SIjz3cbH2Iqb6pY8BXu7GyfzS28I4lKiJOU9/x4Sjdv1gbh4SS9PQlTAFrLr0k7wrfrD+rjRy7tSFR4aN/y+6dr+jSj7SnajsqSMg/Tftvps7mt3bsT1u1UbVBSQuHHn/hsbuEdSVRCnISi73+o0mwv/qknCevYwe/ruso8vLCw4pbf+Z0b0ru1/98PO54yt4eSUneNa+TlOF1M/GoTn6/aV+3nmE0Kd1W6ilzwZzr7jjhrtP6xRN9Uqf7fhzNQyyvgC2NJohKimtwHD5L7wIP6OOKCQVVe2Pxp1tI09mRpL8hR4WbuvcC7grNr0rLpY/uOp7/YUOM5HvlkHec8u5iDuTW7/ZYQFcaSbZm8/9N2vZhudfRqlUyP5okAuD0qk3/23VVV1GWDMSWWz52eXqUkljCOJCohqkF1u8m+5z48OTmA1rE34aWXAtK+Iz27kOm/VfRluv28NqTE+b+GoL8pikK/dvXJLSw9qe3miqIwutJV1Q8bD7L9kG/6SSkREURVblUvmyqCgiQqIU5AVVXybONwLSuvrm0ykfTWG5iTEgOy/ivf/E1J+VbstqfEcnXPJgFZNxDObl8f4KRLI3VpksBZ7bSahqoK7/3ku0PA0TeMqGhV/9vvlO7Y4bO5Rc1IohLiBByT3q7SVj723nsI79s3IGsv25apn5lSFG0DhcUcOj+2pzVPIjrcUqMafref14ajF7RLtmayfm+OT2KyNG5MRKXqIs4ZM30yr6i50PmOF8IPnJ9+Rv74Cfo4cvClxD5wf0DWLi3z8GqlyuiDu6fSqXFCQNYOlDCLiT6t67E/u5BdGSfXybdNw1gGdj5FH7/z43afNT+s3FSxcM5cPIWFPplX1IwkKiH+Q/FPP5P70MP62Nq3L4mvv4ZiCsyPzacr9rDviPYCGRNh4Y4BoVkm6ZwONbv9B3Dbua30Botrd+fwx84jPokp/KyzMLdoAYCan0/R/C99Mq+oGUlUQhyDa+1asv93O5RvTw7r2JHkqR+ghIcHZP0jBSVMrXRGaFT/ViTFBGbtQDujTT0sZqVGiapJcjSX9aioru6rqyrFZNLeqyrnnDFTWtUbSBKVEP9QumMnR24cqVeeMDduTPJHMzDFxQUshrcXb6OwREuSzVOiGdKracDWDrSYiDC6N0tiy4E8MvNPfqv7zee0ItyivZT9fSCfn7cc9klc0dcMhQjtl4PSDRsolfp/hpFEJUQlJX/8QdYVV+IpL59jSkwkedZHmBs0CFgMG/fn8vW6A/r4/ovah9QGimM5u30KqqptijhZ9eMiqiTy937ccVLnsv6LKTGRqMsu08fOD2d4PaeomdD+7hfiJBTOmUvWtcP0s1JKRATJMz4krHWrgMXg8ai8sqhiA8XZ7evTu5WxFSgCoUG8VoLqcA2uqABuOKsFUeFawdo9WU6+XX/gBM+onsrtPwq/+kr/3hCBJYlK1Hmqx0P+xBfIue9+cLkAMCUnk/zJx1h7dA9oLIv+OsDm9DwArBaT1xUofC0tw0GZ+9jtNbYdzK/xvEu2au9PndU2pUbPT4i2MvyM5vp48s87cPmgDUhYt26EdemiDYpLcH42x+s5xcmTRCXqNI/DQfYdd1Lwxpv6Y5Z2bUn5+ivCe54e0FicxWW8vXibPh7WtzmpSVEBjeF4th3M57YpK3ns03X/SlY/bz7Mze+v4K3vt570vKqqsmRbJkkxVjo1jq9xfNf1bU5CVBgAh3KL+XJN9WsI/hdFUYi+6UZ97JwxE9Xjuz5YonokUYk6q3TzFjIvvpTirytaj4ef25+UL+djaRL46g9Tf91JtkO7okuJC+emfi0CHsPxNEqMpGlyNL9vzaySrH7Zcpgn5/yF2aTUqDfWxv15ZDtc9GtX36uSVNHhFm7q11Ifz1q6+z+v/k5G5OWXoZRvpHHv3k3JkiVezylOjiQqUeeU7txF9t33kHHBhZTtrNgCHn3zSJKnT8MUGxvwmPZkOfl05R59PGZg26Br4RETEcYbN55Gx9R4ft+aycryM0tvfLcVs0lhwrXd6Nvm5G/dHd2WfrSckjeu7NmExGitU++hvGJ+3HTI6zlNUVFEDR2ij6VSReBJohJ1Rum2bVqC6n8uRZ9/AeW3cJTISBJfe5WEZ59BsRiTHF779m/K3NpOta5NExjU5ZQTPMMYlZPVUWFmhfHXduOMGr6/9NvfGURazZzug07FEWFmhvSquBqetXS3T84/Vd5UUfzd97gPHDzOVwtfk0QlQpJaWkrptm0UfbWQ/JdeJmvEDWScO6BKggIIP+9cUhYtrPIbc6At3ZbJ8u1ZgFbP74GLOgSkKntNVU5WR5PUmTVMUnuynOzJctKndT3Cy9vMe+vqnk0JD9Ne2rYdKmDVLu879Ya1bo31jDO0gceDc/Zsr+cU1Rdc9xaEOEmq2417715Kt26lbOs2Srdu1T7euQtKS//zeeHnnE3cgw9iPa1HAKP9N1eZh1e/qdiOflmPxrRvFLiDxTUVExHGe7f0wlXmITqi5i8jvrztd1RCtJVLu6Uyr7wh4+xlafRqlez1vDE33kB2eQV95+zZxN57D0pYmNfzihOTRCVqpZLlyymY9Dau5StQi6t/9iZi4PnE3nsP1u6B3Xb+Xz5dsYf92bWznl+YxUSYxbubMr/9nYHZpHBGG9+eFRt2RnO+WL0Pjwordhxh+6EC2jT07r3HiAsvwFS/Pp6MDDyHMyj+7nsiL73ERxGL45FEJWoNVVVxLV1G/quv4lqx8oRfb27UCEv7doS1bYulXTusp51GWKuWJ3xeoGQVlDDt14rNHLf1b61vBKgLsh0lbNqfS7dmicRH+fbf3Tgpiv4dGvC6akT0AAAgAElEQVTTZq2c0uxlu7Fd1cWrOZWwMKKvH0bBa68D2qYKSVSBIYlKBD1VVSn5fQkFr76K649V//q8KSWFsHbtsLRrR1g7LSmFtW0T0Np8NfH2D9sodGn1/FqkRHN1r9BpiFgdSTHhLBt3gd/mv/7M5nqi+n7DQe4Y0FqvgFFTUddfr52583goWbqU0h07CGvd2hfhiuPwOlHZ7fZooAFQD4gEjgBZNpvN+32hos5Ti4rIeeQxiubNq/oJi4WooUOIvetOLC2C67xRdWzcl8uivyrX8+sQ8vX8Aq1z4wS6NUtk3Z4c3B6VT1fs5R4vK31YUhsRMWggxd9+B4BzxkckPD3OB9GK4znpRGW3283ApcAgoB/QEfjXFiW73Z4HLAV+B+bYbLY070IVdU3Z/v1k33obpRs3VjwYFkbUNdcQO+ZOLE1rZ0Vxj0fllW+26ONzOtT3yZv9J+OUhEhu7d+Ktl6+bxPshp/ZnHV7tPp889fs45ZzWhIT4d0GiOgbb9ATVeGcOcQ9+jCmqOCpIBKKqp2o7HZ7M2AMcAOQwjGS0z8kAJcAFwPP2+32n4HJNpvtsxrGKuqQkqXLyL5jtF7FHCDyqiuJe+RhLI0bGxiZ975el87mdK0unlH1/BolRnLbuaF/y+rMNik0qxfNniwnhSVu5q/ez4izvLsCD+/XD3PzZrh379GaKn65gOhh1/koYnEsJ7zXYLfbU+x2+xvAVuBBoD6wHngbuAU4DWgGxAFWtNuA7YELgbHAV4ATGAB8bLfb19vt9sG+/6eIUKCqKo7JH5A17PqKJGWxEP/8cyS+8XqtT1IFRaW8vXi7Pr7+jOY0SpTfxv3FZFKqFKv9dOUeSr0sVqs1Vaw4AOycIe0//K06V1S7gGggDfgQ+Nhms20/ztdnlv/ZBnwPYLfbw9FuF14PXAbMt9vtD9lstle8iF2EGNXtJvehhyn8tOKi25SSQtL77xLeq5eBkfnO5J93kOPU6vk1iI8Iunp+oeiCrqfw7k/byXa4yMwv4fuNB7mkW+qJn3gcUddcQ/4LL0JJCaXrN+Batw5rt24+ilj8U3US1X5gPDDLZrO5a7KIzWYrAeYB8+x2e2vgUbSrLyEA7Uoq97EnqiSpsO7dSZ78HuZTgrOc0MnafqiAuX/s1cf3XNCOSKtsvPW38DAz1/Ruxrs/ar9fz166m4tPbeRV9Q9zUiKRgwdTNHcuoDVVlETlP9XZZtTRZrPNqGmS+iebzbbDZrONAib6Yj4RGvInTKRw1ix9HDV0CCnz5oRMklJVlVcWbeFo49nTWyRxXsfAdQ2u667q2YRIq1aiaWeGg+U7sryeM6ZS+4/CBQukqaIfnTBR2Ww27ys6Ana7vZE/5hW1X8E77+J4a5I+jrzqKhJeeRklPNzAqHxr8cZDrC3ffWY2KTx4cXDX8ws1cZFhXNaj4nbf7KW7vZ4zrHs3wjp31gbFJRTOmev1nOLYanRww263P3CSX98OWFaTtURoc87+mPxnn9PHEQPPJ/GVl1BMoXOmqLCkjDe+q2goeE3vprSoH2NgRHXTtX2aYzZpvxysTsvm7wM170gM5U0VK1VVd0hTRb+p6avBS9VNVna7vSewBKhbx+7FCRUt/JrcRx7Vx9a+fUh65+2QK/Q57bddZBaUAJAUY2VU/9DfFh6MGiVGVrndOmup90c7I6+8AqW8f5k7LY2SJUu9nlP8mze/tr54omRlt9sHAT8CgT3NKIJeyfLlZI+5W2+5EdalC8nTpqJEelfiJtjsyXLy8fLd+njMwLZeVRsX3hl+ZsUuy582H+ZATpFX8/2rqeJMaaroD94kKgUtWT14rE/a7fbrgAVoW9uF0LkzMsgefZfehsPSqhXJs2Ya0lnXn1RV5dVvtugNEbs0SeDCro1O8CzhT+0bxekNGt0elc9W7DnBM04s+oYR+sfF332P+6A0VfQ1bxKVipasXrDb7f9X+RN2u/1e4COqbkH3fpuNqPXUsjKy7xyDJzMTAFNyMskfz8KcHHoX3b9vzWTFDq1du6LA/13SAZNJNlAY7fozm+sfL1yXTpGrzKv5wtq2xdq3rzZwu3HO/tir+cS/1TRR3Y6WqI4mq4lHk5Xdbn8eeKV87qOf3wmc6XW0otbLf+llXMuXawNFIfGtN7Gkenf4MhgVl7qrNES84rQmtDsluKu51xV9WtWjcZJWDcRRXMZ3672/Aqq8qcI5ezbqcZp2ipNXo0Rls9kmA8OBMqomq2XAI+Xjo4+vBPrabLYdPolY1FrFP/6E48239HHsgw8QcXY/AyPyn5m/p3EwV3v/Iy4yjDsGyAaKYGEyKQyp1FJlzh97UVXvTstEXngBppQUADyHDlP8/Q9ezSeqqvGtP5vN9ilwJVBMRVLqTdUkNR8412azyW2/Oq4sPZ3se+7Vx+Fn9yP2nrsNjMh/dmU4+HDJLn08ekAbnzcGFN65pFsqEWHlB4APO/QK6zWlWK1EXz9MHztnyKYKX/LqsIrNZlsEXAQUoCWnoxTgDeBqm81W/T7hIiSpLhfZt49Gzc0FwNSwIYlvvYliNhscme+5PSrPf7lR30DRqXE8l51WuwvphqLYyDAu7FpR9WTuH/u8njNq+HAoP/9XsmQJpTt2nuAZorpOuE/WbrefXY15nkEriXT0aupL4HOgn91u17/IZrP9VrMwRW2W9/x4Steu1QZmM0nvvh2SmycA5v6xl4378wCwmBWeuLyzfshUBJerezVl/pr9APyy5TAZ+cXUj4uo8XyW1EZEnD9Av+3nnDmTBPs4X4Ra51XnQMcvVL1aOp6jP5GXl/+pTK3meiKElCxbjnPyB/o47vHHCO/Z08CI/OdgbpFe+BTgpn4taSkVKIJWm4axdG+WyNryDsBfrt7Pbed5915i9E036omqcM5c4h59BFOInQ00wsnc+lOq8edEXyvqEE9hITkPVpxcCD/vPGJu/5+BEfmPqqpM/GoTRS6tdnOLlGhu6tfS4KjEiVzdq6JL9Pw1+7zuVRV+9tmYmzcDQM3Lo2jBAq/mE5qTSVSqF39EHZQ/fgLuvVpbCyU+nsQXJ4ZsIdZv1x+scmbq8cs7Y7WETr3CUNW/Q33qxWrFj484XPyy5bBX8ykmE9EjKg4AOz+Upoq+UN2fpOpcTVXnSkvUESXLl+OcOk0fJ9jHYW7Y0MCI/CfH6eK1byvOTA3t1ZQuTRIMjEhUl8Vs4srTKza7zKnUL6ymoq69Bsor/5f+tR7XX395PWddd8L3jGw2m/xaKE7Kv275DRhA5JCrDYzIv179Zgt5hdoBz4YJEdwxoI3BEYmTccVpTZj22y7K3Crr9+ay7WA+bb04nG1OSiLy0kspmjcP0LaqW18+1Vfh1kmShITP5U+YiHtP+S2/uDgSJ44P2Vt+360/wPcbDunjRwd3Iipc9gzVJsmx4ZzboaKq+lwfXFVVrlRROH8+7mxpqugNSVTCp0pWrMA5Zao+jh9nC5kuvf+0P7uQiQs36+OLuzWiT+t6BkYkampI74pNFd9tOEheocur+ayn9ajaVPFjqf/nDUlUwmc8RUX/2uUXdc1QAyPyn9IyD0/N/YvCEm2XX+OkKB68uIPBUYma6tokgbYNter9JaUeFq494NV8iqIQfcvN+tg5/UPUMu+K39ZlJ0xUdrvd53ts7Xa7yW63Nz3xV4rapOC113Hv1tomKHFxJL4wIWRv+b3303Y2p2sdYi1mhWeGdCVabvnVWoqiVNmq/vmqvXg83m1Yjrr8MkzlB9vdBw5Q/O13Xs1Xl1Xniupvu93+YXk7ea/Y7fYwu93+P2A7MNLb+UTwKN26Fce77+nj+KfGhuwtv5U7svho6W59PHpAWzqkxhsXkPCJC7qcQmx5U8v0nCJW7PCuRKkSEUH0iOH62DFlilfz1WXV+RXwD+AGYLjdbv8d+ASYa7PZjlRnAbvdrgD9geuAq4AkwAnIns0QoaoquY8/AeW3Nqy9empbdEPQEUcJ9i826OM+rZMZ1reZgREJX4mwmhncozGzl+0GtK3qZ7RN8WrO6BtvoGDS21BWhuuPVbg2bMDapYsPoq1bqrM9/Sy73X4Z8DxwDnA2MMlut28H1gDr0Zoi5gAuIAFIBFoApwPd0br8KkApMAl4xmazZfr8XyMMUThnLq4VK7WBxULC+OdRTKH39qfHo/LMFxvJdmhvtCfFWBl7ZRdphhhCrurZhI+X70ZVYfn2LPYdcdIkueZNys0NGxJ56SUUzf8SAOeUqVhfe9VH0dYd1Xo1sdlsC4AuwCVorTvcQDvgemA8MBmYi9Z6fgbwOnAf0A+IAdKAJ4HmNpvtHklSocOdnUP+M8/q45jbRhHWvr2BEfnPJyv2VLkdZLuyC8kx4QZGJHytcVIUfSvt3Px8lfdV1WNuvVX/uPDLBbgz5eXvZFX73V+bzaYC3wDf2O32JOBctK69vYBTgHpAOJCNdoW1FVgKLLHZbKt9HLcIEvkTJuDJzgbAnJpK7AP3GxyRf6zbk8Pbi7fp4+FnNqe3bEUPSUN6N2XZdu0XkoVr0/nfea2JtNZ8o4y1R3fCunfXOgi4XDg/mkXc/ff5Ktw6oUb/9W02WzYwr/yPqKNcf/1F4eyK8yHxz9gxRUUZGJF/7Mpw8NDsP/UeUx1T47jjPKk+Eaq0VvWR7M8uoqC8Vf0Vpzc58ROPI2bULeTcpTUKdc6YSexdd6JYpZlmddXojQS73S73O+o4VVXJG2uD8hbe4QMGEHnBBQZH5XsZecXcN3MNBcXaRpHEaCvPDj2VMCk4G7JMJoWrelbeqr7P+1b1F1+MqUF9ADwZGRR9tdCr+eqamv60PWu324/Y7fbBPo1G1BpFn3+Ba80abRAWRsI4m7EB+UF+USn3fbSGjHytSXWU1cyrI3rQKDH0rhpFVZd0a0R4+S8j2w4VsKm8GWZNKVYr0TfeqI8dU6Z4nfzqkpomqtPRdvedsCiW3W6/2m63n2+32+WnO0R4HA7ynntOH8fcNgpLyxYGRuR7xaVuHv54LbsyHACYTQrjr+tG+0ZyXqouiI+yMrBLxTlAX2yqiL5hRNWq6mv+9HrOuqKmiaoVWp+pDSf6QrTdgd8Bd9RwLRFkCt58C8/hDABM9esTe+89BkfkW26Pim3eetbtqSgkOvbKzvRuJZsn6pKrela8L7V40yGv6/+Zk5OJuvwyfeyUA8DVVtNElQLk22w2vR2m3W7fbrfblx/ja+ehnaHqX8O1RBApS0vD8f5kfRz/+GOYYkKn3bqrzMPTX2zg1y0Z+mN3D2rHhV0bGRiVMELH1HjaN9LafbjKPCxcm+71nNGVtqoXfb0I94GDXs9ZF9Q0UTn4947BGLSt6v+Uhnb11bmGa4kgkmd/Glzab5Zh3bsTefVVBkfkO7lOF3d/uIrv1le8eAzr24zhZzY3LihhqKsrXVV9sXqf1/X/rJ07Ye3TWxu43TimTj3+EwRQ80S1D4i22+2plR5LALDb7VWOcdtsNheQi3YVJmqx4l9+ofiHxfo44dmnQ6YCRVqmg1snr+Cvvbn6Y5ef1pi7B3ld4lLUYgM7V9T/259dxKpd1aocd1wxt43SP3Z+NAtPfr7Xc4a6mr7KfFP+9+0Adru9H9phX4AqZQnsdrsFiKeGZ7ZEcFBdLvKeGqePo669Bmu3bsYF5EMrd2Zx2wcrSc8pAkBR4O5BbXl0cEcpj1THRVjNXNyt4rbvPB9sqogYNAhLS60phVpQgHPWbK/nDHU1TVTvAcXA43a7/XO0QrUqWt2/u//xtf3L18lA1FqOadMp27kTACU2lrjHHjU4Iu95PCof/raL+2euwVF+TioizMyEa7sx/MwWIduiRJycymeqlmzN4HBekVfzKSYTMaMr9pY5PvgAtaTEqzlDXY0Slc1m24tWUb0EuAKthNI24Ca0Kuuv2e32Dna7/WzgLbQk9odvQhaB5s7MpODV1/Rx7H33Yk6p3XdyN+zLZcyHq3jnx+0cfdshJS6c927txTmV2pIL0axeNKe3SALAo8KXa/Z7PWfUVVdiql9+APjQYQrnz/d6zlBW4zcYbDbb50AbtG3nY4AzbTbbeuAV4B5gI/Az0Lb8Ke94F6owSv6EiagFBQBYWrUiplLn0tpmw75c7pu5mts+WMmfuyu2n3dtmsDU2/rQ7pQ4A6MTwaryVvUv1+ynzO05zlefmBIRQcytt+hjxzvvoXq8mzOUKf44HW232x8C7gUaAQeBJ2022zSfL2QAu93+C3BOs2bNGDlypMHR+J/rr7/IvGSwXiop+aMZRJx7rsFRnZxsRwmb0/P4ZPkeVqdlV/mcSYFhZzRn9IA2WMyhsTFE+F6Z28MVr/5GVoF2i+65a05lQKeGXs3pycvjUM/eqE4nAEnTphI5aKDXsQa5Gt1P98sGB5vN9iLwot1uD7fZbHLztZZSPZ4q9fwizj8/qJNUflEpuzIclf4UkJbpJMf574OaJgUu6NqIm89pSVMv+g2JusFiNnF5j8ZM+VV7n/bzVfu8TlSm+HiiRwzH8d77ADjeeacuJKoa8etOPElStVuVen5WK/HjnjI2oEo8HpVl2zNZk5atJ6bMghN/u5lNChd0OYWbzm5Js3qSoET1XX5aY6b/vgu3R2VNWjZpmQ5apHh32D1m1CgcU6bqHYBLVq0mvOfpPoo4dMiWcXFMHoeDvOef18cxt43C0sL4en4ej8rPWw4z9ded7DzsqNZzIsLMtKwfTZcmCVzTuxmpSVJ2Upy8+vERnNUuRa9a8sWqfTxwcQev5jQ3OoWoK6+gcM5cABzvvkt4zw+8jjXUSKISx1TwxpsV9fwa1Cf2nn+eOggst0flp02HmPrrTtIyncf8GqvFRLN60bSsH0PLlBhaNoihVf0YGsZHynko4RNX9WyiJ6pFfx1g9PltvGqqCBBzx+16oir+7ntKd+wgrHVrr2MNJZKoxL+UpaXhmFzxW138448bWs9v3Z4cxi/YxJ6sqgkq0mrm8h6N6dosgVb1Y0lNjJQNEcKverZIpnFSFPuzC3EUl/H9hkNcflpjr+YMa9+e8AEDKPnxR1BVHO+9T+KLL/go4tAgP9XiX6rU8+vRg8irrjQkDlVVmbNyD3dNX1UlSUVZzdzUrwVf3Hc2913UnvM6NqRZvWhJUsLvtKaKFVvV563a65O+UrF3VhwALpw7D/fhw17PGUrkJ1tUUfzzzxX1/BSFhGfshtTzKyl189yXm3h50d+4y0/kRoWbufnslnxx/9mMPr8tCdHSylsEXpWmigcL2JTuXVNFAGvv3oR1764NXC5tg4XQSaISOrWkhNyxFZ16jarnl5FXzOhpf1Rpq9C+URyz7zyT2we0IT5KEpQwTnyUlQGdK7am+6KpoqIoxN45Wh87p03HnZXl9byhQhKV0Dk+mII7LQ0or+f36CMBj2Hdnhxuem85m9MrKkpffGoj3r2lFw0TIgMejxDHUrn9x48bvW+qCBBxwSAs7bVq/WphIQVvvOX1nKFCEpUAwH3wIAWvva6P4/7vwYDX8/tzdzb3zlitH9A1mxTuv6g9Y6/sTESYOaCxCHE8HVPj9XJbJWUeFq494PWcitlM3MMP6WPnzJmUpXvfrDEUSKISAOQ9+xxqYSEAlvbtiB55U0DX//tAPv83+09KyrR6Z4nRVt686XSu7dNMqpiLoKMois+bKoLWAiSsRw9t4HJR8MqrXs8ZCiRRCUqWL6do/pf6OOGZZ1AsgTu5sDvTwX0zV1NY4gagXmw4k0f1pkfzpIDFIMTJGtilITF6U8VCVqV531RRURTiK91yL/xsDqU7dno9b20niaqOU8vKyH1yrD6OvPwyws/oG7D1D+UWce/MNeQWlgIQF2nh9RtOo7FUjxBBLtJq4eJTK5oqfv6H95sqAMLPPIPwfv20gcdDwYsv+WTe2kwSVR3n/HAGZX9vBUCJjCT+yScDtnaO08W9M9dwOK8Y0EodvTL8NFo1iA1YDEJ4o/KZqt+3ZpBR/r3srbhHH9Y/Llq4ENeGDT6Zt7aSRFWHubOyyH/pZX0ce9+9mBudEpC1ncVl3DdzjX6Q12JWmDisG52bJARkfSF8oXlKDKf5uKkigLVbNyIuulAf57/wok/mra0kUdVh+eMnoOZr28DNLVoQc9uogKyrqipPz9/A1oPa2iYFnr66K71b1QvI+kL4UpWmin9631TxqLiHH4LyjUQlP/1MycqVPpm3NpJEVUe5/lxL4Sef6uOEZ+wo4eEBWfuT5Xv0wp4AjwzuxHle9vYRwijntK9Pcox2CD2roITf/s44wTOqJ6xtWyKvvlof50+Y6JNyTbWRJKo6SHW7yX3iCX0cccGggDVE3LAvl7d+2KaPh/Zu6nVRTyGMZDGbqnwP+6JSxVFx//cAhIUBaP2qfvrZZ3PXJpKo6qDCTz6ldH35m7Ph4cSPsx3/CT6S63TxxGd/6bX7OqbGcfegdgFZWwh/uvy0xhztJLM6LZvdmdXrlXYiliZNiB4xXB/nT3wB1eObW4u1iSSqOsadmVmlIWLsXXdiadrU7+t6PCrjPl9PRr62Kyou0sJz13TDapFvQVH7NYiPpF+7+vr4i9W+u6qKvedulEitfFjppk0UfbXQZ3PXFvIqUcfkjX0KNVer9mxu2rRKIUx/mv77LlbsqDgQabuqK6dI7T4RQipvqvh63QGKXGU+mddcvz7Rt96ij/NffAm1zDdz1xaSqOqQou+/r/LbWMLECfpvav60etcRPvh5hz6+8awWnNk2sHUEhfC3ni2TaZyk/Tw5isv4YcMhn80dO/oOlPh4ANxpaThnfuSzuWsDSVR1hCc/n9zHHtfHUdcMJeLsfn5fN7+olHGfb+BoGbTuzRL533nSZluEHpNJ4crTK26jf+7D23+mhIQqdz/yJ76A+5DvEmGwk0RVR+Q9Nx7PIa1rqKlePeKfGnuCZ/jGa9/8TVZBCaAVmn16SFfpxCtC1qXdG+nvu/59IJ/NPmiqeFTMbaOwtGwJgFpQQJ7N7rO5g528YtQBJcuXU/hRxa2C+GeexpSY6Pd1l2zNYNFfFe0PHh3ckZS4CL+vK4RR4qOsnF/pTOC8P/b6bG4lPJyEiRP0cdHChRQv/tFn8wczSVQhTi0uJuehimrMEYMGEjn4Ur+vm19UysSvNuvjQV0ack6HBn5fVwijXdWrYlPFYh81VTwq/Iy+RF0zVB/nPvEkHqfTZ/MHK0lUIS7/1deqdO1NeP65gPR3ev3bv8msdMvvwYs7+H1NIYJBp9R42p6iFVYuKfOwaJ33TRUrixv7pH5HxL1/f52oAyiJKoS51q7F8c67+jj+iccxn+L/orNLt2XydaUfzkcGdyQ+yur3dYUIBoqicNXpFVdVn/uoqeJR5qSkKof0nVOm4vpzrc/mD0aSqEKUp6CA7LvGgFtrRmjt05uo4df7fd2ColImLNikjwd2bkh/ueUn6pgLup6iN1Xcd6SQlTuzfDp/5NVXEX7O2dpAVcl5+GFUl+9uMQYbSVQhSFVVch99DPce7Y1cJTaWxFdfQTH5/3/3699tlVt+os6LtFq4tFuqPv50he82VYB21ZYwYbx+DrJsy99V7p6EGklUIajwszlVW8tPnBCQMkkrd2SxcG26Pn740o4kRMstP1E3De3d9GiXDlbsyPJZ/b+jLE2baq1AyuW/9jqlO3Yc5xm1lySqEFO6Yyd5T1R06Y0adh1Rl1/m93VLSt28+PUWfTygU0PO7Si3/ETdlZoUxVmVKrDMWenbqyqA6FtvIazbqdrA5SL3oYdDsmitJKoQopaUkHPnXahFRQBYWrcm/unAHAqcsSSN/dmFAMRGWHjg4vYBWVeIYHZNn2b6x4v+OkBBUalP51fMZhJfeAEs2vthrj9WUfjRLJ+uEQwkUYWQvOfGU7qpfCNDeDhJb0/CFBXl93X3ZjmZ8fsufXzHgDYkxwSmCaMQwez0Fkm0qh8DQJHLzVeVbo37SlinjsSMvkMf5z37HGW70ny+jpEkUYWIoh8W45wyRR/Hj32SsE4d/b6uqqq8+PUWSt1He0zFc0WlrblC1GWKojC0d8X7w3NW7tX7sflS3H33VpRXcjrJHn0nanGxz9cxiiSqEOA+eJDcBx7UxxGDBhI98qaArL144yFW7dLad5gU7cyU2eT/A8VC1BYXdm1EXKTWpfdgbhFLtvqmVX1lSkQEiZPeBKu2eal040Zy7rs/ZN6vkkRVy3ny8zly40g82dkAmBo2JOHllwNSfcJZUsbr323Vx0N6NaXdKXF+X1eI2iTCaq7Sqv4zP2yqALB27VrlIHDRVwvJn/iCX9YKNElUtZhaUkL2qP9Rurm8pp7ZTNKbb2BO8n/BWYDpv+3SK6PXiw3n9vPaBGRdIWqbIb2a6Hca1qRls/1QgV/WibnpRqJvuVkfO96ahHPWbL+sFUiSqGop1eMh5777KVm6VH8s4cWJhJ/RNyDr7z3i5OPlu/XxXQPbEl1+El8IUVWD+Ej6d6hoVf/Zyj1+Wyt+nI2Igefr49zHHqf411/9tl4gSKKqhVRVJW/c0xQt+Ep/LO6Rh4m+9tqAxfD6t1spK99A0aVJAhd08X8NQSFqs6G9K7aqf7/+ILlO/5Q8UsxmEie9RVjnztoDbjfZ/7uD0i1bjv/EICaJqhZyvPtelR1+0SNvIubuMQFbf9n2TJZuywRAUeCBi9pjkg0UQhzXqU0T9PdwS8o8zF+z329rmaKjSf5wGuZGjQBQHQ6O3Diy1nYFlkRVyzg//Yz8Z5/TxxEXX0z80/aAbJ4AKC3z8No3f+vjS7un0iE1PiBrC1GbKYrCtX0qtqrPW7WXMrf/duWZGzYkecZ0lBjtHJf7wAGOjLylVvavkkRVS6iqSv6rr1XZhm7t05ukN19HMZsDFsdnK/ey94hWgSI63MLoAbKBQojqOr/zKSSW17/MzC/hp82H/bpeWIcOJL33DpS/RpRu2ED2LXKAtOQAABMlSURBVKPwlFevqS0kUdUCanExOWPupuCll/XHLB3akzx1CkpE4Fq7HykoYcqvFUUvb+3fiiSpQCFEtVktJq7qWXEgftbS3aiq7w8AVxbRvz8Jz1fchSlZsoSsoddQllZ7qldIogpy7sxMsq65rko19PCzziJl7hxM8YG95fbOj9spLNH6WzWrF83QXv6vyC5EqBnSqynhFu2ld+vBfFanZft9zegRw4l75GF9XLp2HRmDLsQ5+2O/J0pfkEQVxFwbNpB56WW41qzRH4saMYLkj2ZgSkgIaCyb9udWaeFx/0XtCbPIt48QJysx2sql3St6VX20JDBXNrH33E28fZxewFYtLCT3oYfJvuVW3Fm+bezoa/JKE4TU0lIc06aTefmVuPeX7wxSFOLH2UiY8DxKWFhA4/F4VF6ptIGiX7sU+rSuF9AYhAglw85oztGNsit3HmHbwfyArBsz6lZSvvoSS+vW+mPF3/9AxoCBFP2wOCAx1IQkqiCilpXh/PQzDvc/l7wnx0KJVvVBiYkhadpUYm4bFbDdfZV9u/4Am/bnARBmVrj3QmnhIYQ3GidFcW7Hhvr4o6W7A7a2tWtXUr5dRPTNI/XHPFlZZI+8mZyHH8VTWBiwWKpLElUQUF0unLM/5vDZ55D7wIO4d1ecWrd06EDKoq+JrHTSPJCcJWVM+mGbPh7WtzmNk/zfOkSIUDfizOb6xz9uOsSBnMDtxDNFRpLw7DMkz5qJqUFFxYzCWbPIGDCQvOfHU7z4Rzx5eQGL6Xik5k2AqSUllO3YSem2rZT+vZWybdtwrV2HJzOzytcpCfHE3n67dhUVGWlQtDDt150ccWgn6FNiwxl5dkvDYhEilHRIjef0FkmsTsvG7VH5ePluHry4Q0BjiOjfn/qLF5P7yKMUL1oEgHvvXhyT3sYx6W1QFMI6dsTapzfhvXtj7d0Lc73A3/aXRBUgro2byLlrjLYl1O3+z69TEuKJGTWKmFG3YoqNDWCE/7b3iJNPVlRc3d05sC1R4fItI4SvjDirhb7rb8Gf+7n1nFYklJ+zChRzUiJJ779L0dx55I59CrWgUsFcVaV00yZKN23COWUqAJZWrYh98H6iLr88YDHKq06AmJOSKNux4z8/b6pXj5g7bif6hhGYyk+SG+2f9fwu7Cr1/ITwpd6tkmndIIYdhx2UlHqYt2ovt/ZvfeIn+piiKEQNHULEoIGULFtGyco/cK1cSenGTfCPnlZlO3eimAObOiRRBYjplIYosbGoBQWYmzUlrF07LG3bEta+HWFt22Fp2ybgu/mOZ9m2qvX8Hry4vSEbOYQIZYqiMOKsFoybtwHQOgAPP6MFEdbAVZupzBQfT+RFFxF50UUAeAoKcK1ZQ8mKlbhWrsS17i9wubD27hXQuCRRBYiiKKR89SXm1FRMUcG9GaG0zMNr31at59e+kdTzE8Ifzu/UkHcXb+dQXjG5haUsXJfOkCA5TG+KjSWif38i+vcHtCo5pZs2Y05JCWwcAV2tjgtr0ybokxRovXKknp8QgWExmxjWt7k+/njZbr8Wq/WGEhGB9bQeAV9XEpWoQqvnt1Mfj5J6fkL43eAeqcRFaje40nOK+GVLhsERBRdJVKKKtxdv0+v5NU+JZmjv4LgFIUQoiwq3cHXPip+16b/txOMJ/hp8gSKJSug27Mvl63UH9PH9F7bHYpZvESECYWjvpoSHaT9vOw47+HFT7Wxy6A/yKiQAcHtUXvq6olX1OR3q01vq+QkRMEkx4VxbqV39ez/tCNr3qgJNEpUAYMGa/WwtL4wZbjFx7wVSz0+IQBtxVgtiIrT3qvZnF1bpWFCXSaIS5BW6eOfH7fr4hrNa0CjRuLJNQtRVcZFhjDizhT6e8utOSkr/u5JNXSGJSvDeTzvILyoF4JSESEac1eIEzxBC+Mu1fZpWaVf/+ap9BkdkPElUddzfB/L5YnXFD8L9F7UnIsyYU/FCCIi0Wri5UvHnD3/fhbOkzMCIjCeJqg7zeFReXrSFo52o+7SuR792gT1xLoT4tytOb0LDhAgAcgtL+WT5bkPjMZokqjrs2/UH2LAvFwCLWeGBi6SenxDBwGoxMapScdpZy3aT63QZGJGxJFHVUY7iUt6q1BDx+r7NaVov2sCIhBCVXXRqI5qnaD+ThSVuZi5JMzgi40iiqqOm/LKT7KMNEeOkIaIQwcZsUvjfeRVXVXP/2EtGfrGBERlHElUdtCvDwWcr9+rjewa1k4aIQgShczs0oH2jOABKyjxMq1SHsy6RRFXHqKrKS19vxl1eR6x780TO79zQ4KiEEMeiKEqV7gUL/kxn3xGngREZQxJVHbPgz3T+3J0DaLcWHry4g2ygECKI9WqVTI/miYBW6mzyz3XvqkoSVR2SmV/Mm99v1cfD+jajdYNYAyMSQpyIoiiMPr+tPv5h40G2lZc7qyskUdUhLy3agqNYOzjYOCmKUee2PsEzhBDBoEuTBM4qP+OoqvDi11vqVBsQSVR1xE+bD/FrpWZsj13WUSpQCFGL3DWwLRazdpt+w75cvlyz3+CIAkcSVR2QX1TKy5VaeFzW4//bu/fgqMo7jOPf3AlJJBcuwUQCQQTDxSACSm0FHWlQ0VLwDoKItdbWlqkjLSO8vt5hvNR6oRrHpiraUkVAVGwRECoWEYVIKKgQCEG5GMIlAQK59I9dNtEBISHZc/bs85nZgXP27O4zZ3f2l33Pe34ng35d0hxMJCKN1aVdIjc16MP5zMIvKNtf5WCi4FGhCgNPvbeBMv85U22T4vjN0O4OJxKRphj742wyU1sDUHGomicWrHc4UXCoUHncyk1lvNXgmjZ3XX42SfExDiYSkaaKi4li0vCcwPLCtdv58ItdDiYKDhUqDzt4uJpH5hUFlofkdGDw2R0cTCQip6p/dhqXnXN6YHn6/HWe766uQuVhj7+znm3lBwFIahXNXZed7XAiEWkOv83rHrhm1Y69h5ix8MsTPCK0qVB51L8//+Y7Q34Th/UgLSnOwUQi0lzatI5l4rAegeU3VpZQWFLuYKKWpULlQdt2H+CRt9YFlof27siwBkMFIhL6Lu2VzqBubQHfuVUPzSvicHWtw6lahgqVx1TX1DL1jcLAmHVGSjyTrshRmyQRj4mIiODuK3KIj/WdD7l5VyUvLdvkcKqWoULlMc8v+oqi0r2Ar5fffaP6kNBKndFFvCg9Of47TWsLlm2ieGeFg4lahgqVh3y8sYyXP6y/uNrtl3SjZ2ayg4lEpKWNHNCJXpltAKiuqePBuWuprvHWEKAKlUfsrqjCzi6kzt/+a2DXNG4Y1NnRTCLS8qIiI5h8Va9Ae6W1pXs912FdhcoDamvruH/O2kD3iZSEWKaO6E1kpI5LiYSD7PaJTBhc32T6b8s2seR/OxxM1LxUqDzgxQ828tGX3waWzc97ayq6SJi56cIuDOha38PTvFFIUekeBxM1HxWqEDd3VSkvLKn/mX/joM6cf2ZbBxOJiBMiIyO4b2SfQC/AqiO13PXqZ3ztP+k/lKlQhbCl63cy7a36Fkn9s9P4ZYMZQCISXpITYnl89Lmc5u/nWV55mN/PXMX+g0ccTnZqVKhCVGFJOVP+uYaj107r3vE0Hrkul5hovaUi4axTWgLTr+9LjH9yRfGuSv44azVHQvhkYH2rhaDiXRXc9epnVPk/eBkp8Tw++lwS4nS+lIhAblYKU0b0Dix/smk30+avo64uNK8KrEIVYnbuO8TEl1exz/9TPiUhlifG9CMtUZMnRKTe0N4due3i+pmA8z/bRsHS0OxcoUIVQkq+reSOgpVs33sIgPjYKB678Vw6pSU4nExE3GjcT7K5PLe+z+dzi77i7dXbfuAR7qRCFSJWFZcx4YX/srXsAOA7ye+ha84hJ6ONw8lExK0iIiL4w/CenNclNbDugTlreXPl1pAaBlShCgHzVpVy50ur2HfQ12g2LjqSB64+hwu6tXM4mYi4XUx0JA9fm8uZHRIBX6f1afPXMXnWGvYeOOxwupOjQuViNbV1PPWvDTw0r4ga//S+tMRYZowfwJAcXalXRE5OUnwMT4/tz1npSYF1i9ft4MZnl/PRl+6/lL1np4lZazsDxT+wyT+MMdcFJ03j7a6oYuobhXyyaXdgXbf0JB69oS8d2sQ7mExEQlFyQizP3TKAP7+3gTc/KQXg2/1VTHzlU0YNOINfX9qdVv5LhriNZwtVA2uAOcdYvzbYQU7GwcPVvP7xVmZ+WMyeA/Un6V3YvR33jexDa01BF5Emio+NZtLwnvzorHY8OLeI8krf0N/rH29l5abd2JG96XG6+457h8O33mpjzL1OhziRyqpq3ly5lZnLNwc+PAARETDux9lMGHImUWoyKyLN4MLu7Zn5qzY8PK+IZRt8Q39bvq3klvwVjL8omyv6Zrhq5CYcCpUr1dXVsWt/FcU7K1hTUs7rH28NnBt1VMfkeCYNz1HvPhFpdqmJcUy/vi/zPt3Gnxas5+DhGmpq68hfvJH8xRtJT25F36xUcrNS6JuVwhlprR27Ung4FKrTrbW3AWlAGfCRMaYw2CHKKqpYVLSdTTsrArf9h6qPuW16m1b+8x8y1BJJRFpMREQEV/XLpF+XVOzsz/l8a3239e17DvHunq95d83XAKQmxpLbKYXcrBQGndUu0Pw2GMKhUF3qvwVYa5cAY40xJcd7kLV2HDDuGHflNiXE7ooqHntn/Q9uk5ESz5gLu3BZbgaxKlAiEiSZqa2ZcXN/5nxSypL1O1i7dS+HjtR8Z5vdFYdZtG4Hi9btoA649vysoOXzcqE6ANyPbyLF0b4hfYB7gSHA+9baXGNM5XEe3xm4qLnCdEpLICoyIjDNHCAhLprs9olkt0/kvC6pDMnpQHSUCpSIBF90VCSjBnZi1MBOVNfUsv6bfazeXM7qknLWbCn/zghQ36yU4GYL6qs1krV2M9CYsj3TGDMawBizE5j6vfuXWmuHAv8BBgITgCeP81ybgQ+Osf7MtLS0jPT09EbEgriYKG4Y1Jnk1jFkt0+ka/sk2p0W59iYr4jI8URHRdIrM5lemcmMpgu1tXVs3FnBmi3lFG3bS9cOSSd+kmYU4eY2Gtba94GMRjxknjHm7pN43glAPjDbGDOyCdHcu9NERNyrSX+Zu/oXlTHmkhZ66qOnYqubq4iIy4XrAZHz/f+GZs97EZEw4tlCZa0daK2NPcb6i4GJ/sVXgptKREQay9VDf6doGtDTPxW91L+uD3Cx//9TjDHLnQgmIiInz8uF6mVgBNAfGAbEADuAWcDTxphlDmYTEZGT5OpZfy6mnSYi0nhNmvXn2WNUIiLiDSpUIiLial4+RuU6CxYsYPv27U7HEBE5Jenp6eTl5QXt9VSomqZJ46wrVqxYD3Rv5iwiIkG1ZcuWDXl5eT2C9XoqVMGV6P93L7DaySAelwu0Qfu5JWkfh6ej73viiTZsTipUwfUVvt6Fq40xgx3O4ln+c+cuQvu5xWgfh6cG7/tXwXxdTaYQERFXU6ESERFXU6ESERFXU6ESERFX02SK4CoAluC7erC0nAK0n1taAdrH4agAB9539foTERFX09CfiIi4mgqViIi4mgqViIi4miZTBIG19mQOBKYYY/a0eBiPsdZOAPKBBcaYYcfZ5m3gMuAOY8yzwcwX6hp8duuAbsaYjcfZbjEw2L94szGmoOXTSTC44ftLhSq47A/cdyhoKTzEGPOCtXY4cKW19g5jzDMN77fW3o6vSL2rItVk1fi+K24BJn//TmttN3xtdY5uJ97k2PeXPlRBZIy51+kMHnUrcAEw3Vq70BizAcBaexbwKFAGjHcwX6jbAXwD3GytnWqMqf7e/RPwXVFgPvCzYIeT4HDy+0vHqCTkGWN24itWrYFXrLXR1tpo4BX/ul8YY3QhsFOTD6QDVzRcaa2NAcYCy4EiB3JJGFChEk8wxswFXgTOA6b6b/2BAmPMbCezecRrQCW+X08NXQl0wFfIRFqECpV4ye+AYnzHUSbjO3v+TicDeYUxZj/wdyDPWpvZ4K5bgX3ALEeCSVhQoRLP8H+Z3gdE+W+3+9dJ88jHt1/HA1hrs4BLgZnGmANOBhNvU6ESz7DWxgOTGqy62qksXmSMWQF8Doy31kbiGwaMRMN+0sJUqMRLpgM9gCfxXR59vH/qujSffCALyANuBlYZYz5zNpJ4nQqVeIK1dihwB76/+CcBY4AqIN9a29bJbB7zMnAQeA7IAJ53No6EAxUqCXnW2lTgr8ARYLQxpsoYsxaYgm9G2l+czOcl/u4DrwOZ+GYBvuZsIgkHKlTiBTOA04F7jDGFDdY/BiwDRlprRzuSzJvuAUYAP9VkFQkGdaaQkGatHQNcAyzFV5gCjDG11tqxQCHwlLV2iTGm1IGYnmKMKQFKnM4h4UO/qCRkWWs7AU/hO4/nJmNM7fe3McYUAxOBZOBFa21EcFOKyKnSFX5FRMTV9ItKRERcTYVKRERcTYVKRERcTYVKRERcTYVKRERcTYVKRERcTYVKRERcTYVKRERcTYVKRERcTYVKRERc7f9r07m0RSJt5QAAAABJRU5ErkJggg==\n", + "image/png": 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gtQJQtHYdRRs3GpyRqCopVEIYJO/Dj3Cd/CEaHKy+M2X2v2/JfakO7nl/Ha8s2U6hy1Pmc45CNw9/tJ6fd6QalN0/WRo2IKxPHy12TJW2SjWd/31XCFELuFNSyJn4ghZHPfgAQWedZWBG/+T2eHn/xz3c+u5q/jqUpY0nJ0Yyrv851IkMBsDp9jJm7h98vTHFqFT/IfLuu7SPCxZ/g/vQIQOzEVUlhUoIH1MUhayxT6Lk5wNgbdmSqPvvMzirsrYfyeb2qWuYtmI3Lo+6dYbVYuLO7snMvPsiep7bkKnDO5MUFwaotwafW7CZWav2G5h1ieB2bQm55BI18HpxvDfD2IRElUihEsLHChYuwvn992pgMhH74mRMISHGJlWs0OXhzWU7GDbtV3Yfd2jjbZJi+PDuixjerQVBVvXHRqP4cKYO70yLepHa172xbAdvfbfTL/aFiryn5Koqf85cvNnZBmYjqkIKlRA+5M3MJPsZmxZH3DqUkI4XGphRid/3Z3DL26v5ZNV+vMV1JiTIzMNXt2L6iM4k14v6xzEJUSG8c0cnzmsap419/Ms+Jizcgttj7PL1kG7dsLZSb6cqeXnklXqhWtQsUqiE8KHs8c/hLW6Yaq5fn+ixY85wRPXLK3QzadFW7vvgNw5n5GvjHZrHM+u+rgy+uBkW87+/1xUVFsSrQztwSau62tii31N48rM/cf5t8YUvqW2VSq6qHDNmoBQVGZaPqDwpVEL4iPOXVeR/+pkWx054DnPUP69SfGn1zjQGv7WKL9eXLDaICLEytk9b3rztQhrFh5drntAgCy8MPI9e5zXUxn7cnsr/PtlAXqFb97zLK7xvX8yJiQB4jx2nYOEiw3IRlSeFSggfUAoKyBw9WotDr72WsKuvNiyfrLwibPM38eis30nNKdTGL21VlzkPdOX6Do0q3B3DajHz1PXtuPniZtrY7/szuW/mb2Q4nHqlXiGmkBAib79Ni3PfneoXz89ExUihEsIHcl59Dc/+AwCYoqOJHW83JA9FUfjur6MMevMXlm46qo3HRQQz/sZzmTz4fBKjK7//ldls4sEeZ3HfVS21sR1Hc7hrxjqOZBrTzTx86FBMYerqRPe2bTh//sWQPETlSaESopoVbd6C4513tTjmqSex1Kvn8zxScwoZNWcjT8/bRFa+SxvveW4D5tzflf+2a6BLj0GTycStl/6HJ/q05eSjrcMZ+dw9Yy17judWef6KssTHET7wJi12TJW2SjWNFCohqpHi8ZA1ahR41EUFwV06Ez54kG9zUBQWrD/E4DdX8fOONG08MTqUKUMuYFz/c4mNCNb9vH06NGLCwPMIsqjVKi3Xyb0frGPTQd+3XIq8cwQUF2HnDz/i2r7d5zmIypNCJUQ1ypvxPq4/N6lBSAixkyb5tE3S4Yx8HvhwPS8s2kqes2RRQ7+OjZlzf1e6nlX3NEdXXbez6/Hq0A6Eh1gAyClw8+BH61m9K+0MR+rL2qwZodf01GLHtOk+Pb+oGilUQlQT96FD5Ex+UYujH36IoBbJPjv/zztSGfrOajbsy9DGGsWH8/YdHRnVuw0RoVaf5NGheR3evr0TccVXbU6Xl5GzN7Jk0xGfnP+k0jsA53/xJZ7jx316flF5UqiEqAaKopA1Zqy2Hbq1dSsi773HZ+ffcjiLMXP/oKBIveVoNsEtXZvxyX0Xc0GzeJ/lcVLrhtFMHdaJ+rHqQg2PV2Hc/L/49NcDPssh5MIOBHfooAYuF44PZvrs3KJqpFAJUQ0KvlyA84cf1cBkIu7FFzEF6/8c6FTcHi8TFm7BU9xeomFcGDPu7MIDPVoRGmTxSQ6n0iQhgmnDO/OfxJKWS698u51pK3b5bMl45D0lV1V5H3+MNz//NF8t/IUUKiF05snIINs2Tosjht1B8AXn++z8n6zaz57iPn2hQRZev/VCzk6K8dn5TycxOpR37ujIOY1jtbH3f9zL5K+3aYW1OoVe3QNLs6YAKFnZZV7AFv5LCpUQOsu2j8eboT4XsjRsSPSokT4798H0PN7/cY8W39m9Rbm7S/hKTHgwr9/agYtaJmhjX64/xDPz/qz27e1NFguRI0ZosWP6dBSPcW2eRPlIoRJCR4U//kjBvHlaHDtxAubIyNMcoR+vV2Hioi3aD/vWDaMZ2KWJT85dUWHBVl4cfD49zmmgjX2/5TiPzfqdfGf1tlwKH3gTplj1CtNz4CCFS5ZW6/lE1UmhEkIn3vx8ssY8ocVh1/ch9KorfXb+RRtT2LhffUfJYjbxRJ+2WC3++y1utZgZ1+8cbuxcUkx/23uCBz78jay86mseaw4PJ2LoUC3OfVdeAPZ3/vuvWIgaJnfKy3gOHgTAFBtDjH2cz859ItfJm8t2aPHgi5pyVoNon52/ssxmE49e05q7urfQxram5HD3++s4llV9LZci77gdihe3uH7/Hedv66vtXKLqpFAJoYOiTZvKvEQa88zTWOpW78u0pb387TZyi7uUJ8WFMaJbizMc4T9MJhPDuiUz8tqzTzaP4EB6HnfNWMe+NMfpD64kS716hN/QV4ulrZJ/k0IlRBUpbjdZI0eDV302FNK1K+E33XSGo/Tz0/ZUvt9S8vLqmD5tCQ02bhl6ZfXv1ITxA9pjLW65lJpTyD3vr2PL4axqOV/pvaoKlyzFvW9ftZxHVJ0UKiGqyDH9PVybN6tBaAixkybq0ty1PPIK3by4eKsWX3teQzr+p45Pzl0drmpXnylDLiCsuNBm57t44MP1rN2Trvu5glq1IqR7NzVQFBzvzdD9HEIfUqiEqAL3/v3kvjRFi6MffRRr8+Y+O/873+8kLUfd6ykuIpiHrm7ls3NXl87JCbx524XEhAcBUFDk4bFZv7N88zHdz1WmrdLcT/Fk+L5hrjgzKVRCVJKiKGSNHotSqG48GNSmDZF33emz8286mMn830p25n30mtbEhPum+0V1a9solneHddL2xnJ7FJ6e9yfz1x3U9Twhl3QlqE0bAJTCQvI//ljX+YU+pFAJUUn5n8/D+UvxJnxmM7EvTcYUFOSTcxe5vUxcuIWTnYcubpnAVe3q++TcvtK8biTTR3SiaUIEAIoCLy7exvs/7NGt5ZLJZCrTVsnxwUztFw/hP6RQCVEJnvR0su3PanHkiOEEt2/vs/N//Mte9qXlARAWbGFU7zY+ey7mS/Viwpg6rBNtkkqW2k9buZv3Vu45zVEVE9bnOsz11SLvTUsjf8EC3eYW+pBCJUQlZI+zo2Spq9EsjRsTNfJxn517X5qDmT/t1eJ7rmhJ/dgwn53f12Ijgnnjto5lFonM+HEPK7bo88zKFBRE5PBhWuyYOt1nTXJF+UihEqKCClespODLkt+6Y1+YgDncN/30vF6FiQu34PKoP0jbJMUwoLN/tknSU0SIlSlDLqBLi5JiNWHhFhyFLn3mH3Izpgj1FqN7506cK3/QZV6hDylUQlSANy+PrDFjtTisXz9Cu3Xz2fkXbDjMpoPFV3JmE09c3xaLOfBu+Z1KsNXMswPa06D46tFR6OarDSm6zG2OiSF88CAtdkhbJb8ihUqICsiZ/CKeFPWHozkujphxz/js3Kk5hbz13U4tvqVrc1rUi/LZ+f/O7fHidHkqfZssM6+ISYu28EWplYtnEh0WxG2Xliz///TXA7g9+nRcjxwxHCzq+1vOVaso2rxFl3lF1UmhEqKcijZuJO/9D7Q4ZpwNSx3fvVw75Ztt5BV3Fm9cJ5xhl/+n0nNt2JdBF9tSnv3yr0rPMXruH1z+3HKOZlVulVxseBC/7Exj2opdFdqL6pr2DbVt7VNzCvlep2dV1saNCbu2lxY7pk7TZV5RdVKohCgHxekkc+SokjZJl19GWP9+Pjv/yq3H+XFbqhaP7dOWEAN369WDyWTi0laJZOW7+OtQ+dskhQRZGNCpsRbPWr1ft8UPpZeqFyxciOfIUV3mFVUjhUqIM/AcOcqJobfh3rYdAFNYGLEv+K5NUm6BiynfbNPiPhckcUGzeJ+cu7pd1joRUPsVVkT/jk0Isao/vnYezeX3/Rm65BPcvj3BXTqrgduN4/33dZlXVI0UKiH+heL1kvfxJxzvfgXOVau08ejRo7A28d1Ku7eX7yQ9V22TFB8ZzAM9an6bpJM6NIsnIsRa4UIVGxFMr/OStHjWqv265VS6rVLeJ7Pw5ubqNreoHClUQpyCe98+0m8aRNaYsSiOkq0moh5/jIgRw32Wxx8HMvly/WEtfrzX2USH+ab7hS8EWc10aZHA4Yx89qZWbEuPwRc11bYFWb0rXbctQUKvuhJrcjIASm4u+XPm6jKvqDwpVEKUorjd5L77Lsev+i9Fa9Zo45bmzUmY/znR/3vEZ7f8nC4PExeWrDy7tFVdurep55Nz+9LlZ1fu9l+ThAgubZWoxXNW79clH5PZXKZno+O9GShuty5zi8qRQiVEMde2baRd35ec8c9DoXqrDYuFyAfup953Swnp0sWn+Xz4814OpKttksJDLIy8NjDbJF3cMgGrxVThQgVw88XNtI+//fMIJxxOXXIK798Pc/GKTk9KCgWLF+syr6gcKVSi1lOcTnJemkJqz164/vhTGw9q04a6Xy8kZuwYTGG+bVG0N9XBR7+UbOR335VnkRgT6tMcfCUyNIjzm8az7Ug2aTkVW+revkksbZJiAHB5FN26q5vCwoi47VYtdrw7VdoqGUgKlajVin7fSOo1vch95VU4eXsnOJjo0aOo+83XBJ97rs9z8ngVJny1GXdxm6RzGsfSr2PjMxxVs13Wui6KAr/sSKvQcSaTqcxV1fzfDlFY5NElp4jbboXQEABcm/6i6NdfdZlXVJwUKlErefPzyRpnJ63P9bh3lHR7CO7QgcRlS4h66EGfbdnxd1/8dpDNh7MBsFpMPNGnLeYAb5NUL0a9Yj1ewSsqgG5nJ2ptlbLzXSz+Q5+2SpaEBML7D9BieQHYOFKoRK1T+PMvpF75X/Kmv8fJDZ1M4eHEjH+WhC/nE9SypWG5Hc8u4J3lu7T4tkv+Q/PESMPy+bt9qY5/bVm082hOpef9ZYf6fOqSs+pW+FirxcygLk21eM6aAxXqdHE6pRdVFH63HNfu3brMKypGCpWoNbzZ2WSOHMWJQYPxHCx5lhFy2aUkrlhO5LA7MFmM6/agKAqTv95GfvGtq6YJEdx2WeXbJOlt59Ec7pyxlrGf/vGPYrVy63HumPYrby7bUeF5FUXhl51pxEcG07ZRTKVy631BElGhVgAOZ+Rrha+qglokE/rfq7TYMe09XeYVFSOFStQKBUuXcrz7FeTPnqONmWJiiH15CnVmz8La2PhnQN9vOc6qnSXPaMb2aUuw1X++RRvGhdGkTgQ/70grU6x+2Hacpz7/E4vZRIfmFe+YsflwNhmOIi5tlVjpVY0RIVb6Xli2rZJeSrdVyp83D096um5zi/Lxn+8CIaqBJz2djHvvI2PYCLzHS37LDu11DfV+WEHEwJv8Ysl3ToGLl78taZN0w4WNOa9pnIEZ/VNkaBCv39qBNkkx/LwjjbV7TgDw+tIdWMwmXhh4Hhe1rPitu5PL0k+2U6qsGzs3wWpR/1tuOpjF5sPl7x94OsGdOxPUvnhRjdNJ3ocf6TKvKD8pVCIgKYpC/vwvOH55dwoWLtLGzXXrEj9tKnWmT8OSWLUfjHp6Y9kOMhxFANSNCuH+/xr3nOx0Sherk4IsJiYOPI+LK/F8CdRCFRZs4cJKXI2VlhgdSo92DbRYtxeATaaybZVmfohSUKDL3KJ8pFCJgONOOcKJW28n86GHte3iAcJvHEC9ld+X2crBH2zYd4JFv5esVHv82rOJDPXfNkmli9XJItW1kkXqQHoeB9Lz6NIiQZdu8INLLVVfufU4RzLzqzwnQNi1vbA0agSANyOD/HnzdZlXlI8UKhEwFK8Xx4cfkdr9CpwrVmjjlqQk6sz6mLhXX8Ec51+30wpdHiYu3KrF3c5O5PKz/b9NUmRoEFOHdWLJqCu4pFXlr0z1uu13Usv6UXRKVjtKeBWYu+aALvOarFYihw/TYse06ShefTZsFGcmhUoEBNeevaQPuJHsJ55EyVPbDmEyEXHH7SSuWO7T7eIr4oMf93A4Q/2tPzLUymO9zjb6npvmAAAgAElEQVQ4o/ILspqJKF5pV1k/bU/FYjZxccsEnbKCIaWuqhZtTCGnwKXLvOE3D8YUHQ2Ae+9eCpcv12VecWZSqESNprjd5L79Dqk9elC0dp02bk1OJuHL+cQ+Nx5zpP+8h1TarmO5fFJqe4r7rzqLutGB2SbpVDIcTrYczqJ9k1hiwoN1m7dTch2S66n/zQuKPCxYX/6t7k/HHBlJxJCbtdjx7lRd5hVnJoVK1FiuLVtJ692HnOcnlG0i++ADJC5bQkjHjsYmeBoer8LEhZu1F1PPaxrH9R0aGZyVb8VHhrB63NW8fUcnXec1mUwMvqiZFn+29iAutz636SKHDQOrehVZtHYdRX/8ocu84vSqdt0O2O32CKAekACEASeAdJvNdqyqcwtxKorTSe5rr5P71tsl/fmAoHbtiJ3yEsHt2hqYXfl8vvYAW1PUTg5BFhNjrmsT8G2SfKnHOQ149/tdpOc6Sc91smzzUa4ttdFiZVkaNiCsTx8KvvgCUNsqxb/zdpXnFadX4UJlt9stQG+gB3Ap0Ab4x3eY3W7PBlYBPwOf22y2fX//GiEqyrl+A1mPj8S9q6TNECEhRD/6PyLvvsuw/nwVcTSrgKkrSlrx3HFZMs3q+vb2ZIPYMIZ3S+as+lE+Pa+vBFvN3NipCe98r/47mb16P73aN9TlnbnIu+/SClXB14txP3HIL14YD2TlvvVnt9ub2u32F4EU4AvgXqBd8RymU/yJBa4FJgK77Hb7d3a7/SZ90xe1hTcvj6xnxpHe94YyRSq4U0cSly0l6oH7a0SRUtskbaWguE3SfxIjGXpJc5/n0TAujDu7t6gRKwwrq++FjQgLVpe87znuYF3xC8pVFdyuLSGXXKIGXi+O92boMq/4d2csVHa7va7dbn8d2AE8BiQCm4C3gWFAB6ApEA0Eo94GbA30BJ4GFgF5wJXAHLvdvslut1+n//8UEagKf/pJbSI7Y0ZJE9mICGKeH0/C/HkEtUg2OMPy+27zMdbsUlvwmEzwRJ+2BPlRm6RAEhMeTO/zS2736dtW6S7t4/w5c/FmZ+s2t/in8tz62wtEAPuAD4E5Nptt12m+Pq34z05gGYDdbg9BvV14M9AHWGC320fabLaXq5C7CHDerCyynx1P/qeflRkP6d6N2BcmYm1UsxYfZOcX8cq327W4f8cmtGsca2BGgW9Ql6bMX3cQrwLr9pxg17FcWupwuzOkWzesrc7CvWMnSl4eebNmE3XfvTpkLE6lPIXqMOrtu1k2m61SO5LZbDYnMB+Yb7fbWwBjUK++hDilgm+/JeuJp/CmlvTnM8XGEmsfR1j/fn7Rn6+iXlu6g8w8tU1SYnQo917ln22SAklSfDjdzq7Hiq3HAZizZj/P3HBOledV2yrdRdajjwPgmDGDyBHDMQXLj7XqUJ57Dm1sNttHlS1Sf2ez2XbbbLYRwCQ95hOBxZOayom77iFjxF1lilRY797U+2EF4QP618gitW7PCb7544gWj+p9NhEhVV50K8rh5q7NtI+X/XW0wtvd/5vwvn0xF/eL9B47XqanpNDXGQuVzWbTZQcyu93esDrmFYFBURTyP5/H8e5XULh4sTZuTkwk/r1pxE99B0vdyvWTM1phkYdJi7Zo8ZVt61ep7ZComHaNYjm3iXqL1e1R+HztwTMcUT6mkBAib79Ni3PfnYqiyI+16lCpp7h2u/3RCn59K2B1Zc4lAp/78GFO3DKUzEf+h5JV8lA6fNBAtYnsNdcYmF3VTf9hNymZarftqFArj17T2uCMap/SbZW+XH+IfKf737+4AsKHDsUUFgaAe9s2nD//osu8oqzKLjd6qbzFym63dwR+AeRFA1GG4vXi+GAmqd2vxPnDj9q4pXFj6syZTdyUlzDH1uzFBjuO5pRpjPpgj1bUiQoxMKPa6ZJWiTSKDwcgt9DNoo0pZziifCzxcYQPLHnrxjFtmi7zirKqsi72xTMVK7vd3gP4HqhThfOIAOQ5cpT0/gPIfupplPzirRhMJiKGDyfx++8IvexSYxPUgdvjZcJXW7Q2SR2ax3PdBVXvjiAqzmI2Meiiplo8d80BbYfiqoq8c4T6rgHgXPkDru3bz3CEqKiqFCoTarF67FSftNvtg4CFqEvbhdC4U1JIva4PRet+08asLVuSsOBLYp8dhzkiMP7JfPrrQXYcVdskBVvNjL6uTY1cCBIoep+XREy4+lL40awCftyeeoYjysfarBmh1/TUYse06brMK0pUpVApqMVqst1uf7z0J+x2+8PAJ5Rdgp5ehXOJAKEoClmjRuM9VtwK0mIh6uGHSFz6LSEXdjA2OR2lZOQzbWXJ64bDL0+mSZ3AKMA1VWiwhX4XljyBmLVqv26LH0rvAJz/xZd4jh/XZV6hqmyhuhu1UJ0sVpNOFiu73T4BeLl47pOf3wN0rXK2osYr+HJByfMok4k6Mz8getRITCGB89xGURQmfb0Vp0u9tdSiXiRDSi2RFsYZ0LkJQRb1qnZrSjZ/Hsw6wxHlE3JhB4I7FP+i5XLh+GCmLvMKVaUKlc1mmw4MAdyULVargdHF8cnxtcBFNptt979MJ2oJT0YG2bZxWhwx7A5Cr+huXELVZMmmo1pfObMJnri+HVaLtEnyB3UiQ+jZvuRNmTm6tlUquarK+/hjvCefvYoqq/R3j81m+xS4ASikpCh1pmyRWgB0t9lscttPkD3uWbwZGQBYGjYketRIgzPSX2ZeEa8uKXmYflPnprRJijEwI/F3N5faq+qnHakcPJGny7yhV/fA0kxdsKFkZf+j9ZeovCr9mmez2b4BrgFyUYvTSSbgdaC/zWbT5zVwUaMV/vgjBfPna3HsxAl+u/NuVby6ZDvZ+erW5/VjQ7nrihYGZyT+rnliJBe3TADUHselXx+oCpPFoq4ALOaYPh3Fo0tDn1rvjD1c7Hb7ZeWYZzxqS6STV1NfoW4Fcqndbte+yGaz/VS5NEVN5s3PJ2vME1ocdn0fQq+60sCMqsevu9NZuumoFo/q3YZwaZPkl4Z0bcbq4i72izemcFf3FsRGVL1PX/hNN5Hz4ksoWdl4DhykcMlSwq7tVeV5a7vyfBf9QNmrpdM5ufb2+uI/pSnlPJ8IMLlTXsZzUG1bY4qNIcY+ztiEqkG+080Lpdok9TinARe3rJktn2qDC5rFc1aDKHYezcXp9vLFb4cY1q3q28WYw8OJGDoUxxtvAuoOwFKoqq4it/5OtTni3/+c6WtFLVO0aVOZ90pinnm6xvbsO51pK3dzLEu9yx0dFsQjPVsZnJE4HZPJxM2l2ip9vu4gTpc+t+ki77gdiruoF23YgPO39brMW5tVpFApVfgjaiHF7SZr5Gjwqsu0Q7p2JfymwNvkeWtKNp/9WvKc45GerYiPDJzl9oHqqrb1SYwOBdRFMEtK3batCku9eoTf0FeLpa1S1ZW3UJXnaqo8V1qiFnFMfw/X5s1qEBpC7KSJAdeZwe3xMnHhFoq7JNEpuQ7XtG94+oOEX7BazAzs0kSLZ6/ej9er1wvAJTsAF367BPe+fbrMW1ud8ZmRzWaTF0BEhbn37yf3pSlaHP3oo1ibNzcwo+oxe/V+dh3LBSAkyMzo3tImqSa5vkMjZvy4h3ynhwPpeazZnU7Xs6p+azqoVStCunfDufIHUBQc780g9vnnqp5wLSVFSOhOURSyRo9FKVSf2QS1aUPkXXcanJX+Dp3IY8YPe7T4zm4tSCru0C1qhsjQIK6/oJEWz1ql35VPmbZKcz/Fk5Gp29y1jRQqobv8z+fh/KV4Xx6zmdiXJmMKCjI2KZ0pisKkRVtxutXnb2c1iCrTnVvUHAO7NMViVq+Cf9+fyfYjObrMG3JJV4LatAFAKSwk/+OPdZm3NpJCJXTlSU8n2/6sFkeOGE5w+/YGZlQ9Fv9xhPX7irtsmE080UfaJNVU9WPDuLJtPS2erVNbJZPJVKatkuODmdpdBlExZ/zOstvt/9H7pHa73Wy325uc+StFTZNtG4eSpTb6tDRuTNTIx89wRM1zwuHk9aUlbZIGdWlK64bRBmYkqqr0UvXvtxzjWFaBLvOG9bkOc/36AHjT0shfsECXeWub8vwKuN1ut39YvJ18ldjt9iC73X4XsAu4varzCf9SuGIlBQu+0uLYFyZgDg+8ZzavfLudnAJ1K/OGcWHc2V3aJNV0rRvGcEGzOAA8XoXP1h7UZV5TUBCRI4ZrsWPqdN22FqlNytMpYh0wFBhit9t/BuYC82w224nynMBut5uAbsAgoB8QD+QBf1YmYeGfvHl5ZI0Zq8Vh/foR2q2bcQlVk1U701i++ZgWj76uDaHBFgMzEnoZ0rU5v+9XFzws2HCIYZf/h8jQqj9bjbh5MLmvvIqSl4d7506cK38IyF0DqlN5lqdfYrfb+wATgMuBy4C37Hb7LmADsAl1U8RMoAiIBeKA5sCFwPmou/yaABfwFjDeZrOl6f6/RhgmZ/KLeFJSADDHxREz7hmDM9JfntPN5K+3anGv9g3pnJxgYEZCTxe1SKBpQgQH0vPId3r4akOKLvuImWNiCB88iLz3ZgBqWyUpVBVTrqe/NpttIXAOcC3q1h0eoBVwMzARmA7MQ916/iPgNeAR4FIgEtgHPAU0s9lsD0mRCixFGzeSN+N9LY4ZZ8NSp46BGVWPqd/v4ni2+jA8NjyIh66WNkmBxGw2MbjUys1Pfz2A2+PVZe7IEcPBol55O3/5haLNW85whCit3E1ibTabAnwLfGu32+OB7qi79nYCGgAJQAiQgXqFtQNYBfxis9mk2VWAUlwuMkeOUvdLAEIuv4yw/v0Mzkp/Szcd4fN1Jc8t/ndNa126bQv/ck37hkxdsZvMvCJScwr5fssxrj636p1GrI0bE3ZtLwoWLgLUq6r4N16r8ry1RaW6mdtstgxgfvEfUYs53p2Ke5u6As4UFkbsC4HVJik7v4hXl+zg2z+PaGNdWiTQ45wGBmYlqktIkIUBnRozfaX6Ives1fvpcU4DXf5NR95zt1aoChYuxDN2DJaG8u+oPCr14ofdbpeOmwL33n3kvPKqFkc9/hjWJoHx1oGiKHy/5RiD3lxVpkg1TYjgyevbBlQxFmX179iEEKv6o3Hn0Vx+35+hy7zB7dsT3KWzGrjdON5///QHCE1l31B8zm63n7Db7dfpmo2oMRRFIXPUaHA6AQg695wyy3BrsvRcJ2Pm/sGTn/1JZl6RNv7fdvWZPqIzdYs7bovAFBsRTK/zkrR49mp9dgCGsm2V8j6ZhTc3V7e5A1llNzK8EHV13xlfNrDb7f2BbGC1zWbLr+T5hJ/Jn/spRWvWqIHFQuyLkzFZa/a+mIqi8PXGFF5bugNHoVsbrxsdwqjebbi0VaKB2QlfGnxRUxZsOISiqK8k7Etz0LxuZJXnDb3qSqzJybj37EHJzSV/ztyA7IOpt8peUSWj7jP1Vzm+thWwFLinkucSfsaTmkr2+JJO0JF330Vwu3YGZlR1KRn5PPTRBp7/akuZItW3QyPm3N9VilQt0yQhosx/8zl6tVUym8sUJsd7M1Dc7tMcIaDyhaoukGOz2bS1m3a7fZfdbl9ziq+dj/oOVbdKnkv4meynbSjZ2QBYmjYh6tH/GZxR5Xm8CnPX7GfI26v5bW/JO+yN4sN46/YLGdOnrS4vfYqap3RbpW//PMIJh1OXecP798Nc/PqGJyWFgsWLdZk3kFW2UDn4523DSNSl6n+3D/Xqq2b/yi0AKFj2HQVff63FsS+8gDkszMCMKm9fqoO7Z6zl1SU7KCzehtxsUn9AfXJvVzo0D7x3wUT5tW8SS5ukGABcHoX563RqqxQWRsRtt2qx492p0lbpDCpbqA4BEXa7PanUWCyA3W6PKP2FNputCMhCvQoTNZg3N5fsJ57U4vCbbiT0sksNzKhyXG4v7/+wh1vfXc3mw9naeHJiJNNHdOahq1tJWySByWQq05li/m+HKCzy6DJ3xG23Qqi6eNq16S+Kfv1Vl3kDVWUL1bfFf98NYLfbL0V92RegdekvtNvtViCGyi/cEH4iZ9JkPEePAmCuU4fop582OKOK25aSzR3T1jBt5W5cHvW3WKvFxJ3dk5l590W0bRRrcIbCn1zeOpEGseodg+x8F4v/SNFlXktCAuH9B2ixY+o0XeYNVJUtVFOBQuAJu93+BWqjWgW179+Df/vabsXnSa3kuYQfcK7fQN7MD7U45tlxWOLjDMyoYgpdHt5YtoPh039l93GHNt4mKYYP776I4d1aEGSV/aREWVaLmUFdStoqzVlzAI9Xn9t0pRdVFH63HNfu3brMG4gq25nioN1uHwp8DPQtHt4B3AZssNvtWajFrC7wJmoRW1f1dIURlKIiskaVapN0RXfCrr/e4KzK7/f9GUz4aguHM0rejggJMnPPFS25qdTurkKcSu8Lknjvh93kFro5nJHPLztSufzsemc+8AyCWiQT+t+rKPxuOQCOae8RN/mFKs8biCr9K6TNZvsCaIm67PwBoKvNZtsEvAw8BGwGVgJnFR/yTtVSFUbJfett3Dt2AmAKDyd24oQa0Zkhr9DNpEVbue+D38oUqQ7N45l1X1cGX9xMipQ4o4gQK30vbKzFeu0ADJTZATh/3jw86em6zR1IqvTcyGazHQGm/W1stN1uTwceBhoCR4GnbDbbiqqcSxjDtWsXua+/ocXRo0dhbdTIwIzKZ9XONCYt2kpqTsnW3xEhVh66uhV9LkiqEYVW+I8bOzdhzpr9uD0Kfx7MYvPhLNrp8DwzuHNngtqfi+vPTeB0kvfhR0Q/9mjVEw4w1XJT3mazvWiz2RoBYTabLclms31QHecR1UvxeskaNRqK1DZCQeefR8Qdtxub1Blk5RVhm7+Jx2b9XqZIXdqqLnMe6Mr1HRpJkRIVlhgdSo92JQ1kdXsB2GQq21Zp5ocoBQW6zB1IqvXpsc1m0+cNOWGI/FmzKVr3mxpYrcRNnozJ4p/LthVF4bu/jjLozV9YuumoNh4XEcz4G89l8uDzSZQefaIKBpd6AXjl1uMcydSnI1zYtb2wFN+l8GZkkD9PNqX4O1nmJE7Jc+wY2c9P0OLIe+8hqM3ZBmb071JzChk1ZyNPz9tEVr5LG+95bgPm3N+V/7bTZ5sGUbu1rB9Fp2T1JXCvAnPX6NOs1mS1lmno7Jg2HcWrz4aNgUIKlTilrKeeRinu7Gxp3pzoRx42OKN/UhSFBesPMfjNVfy8o2TT6MToUKYMuYBx/c+VzQ2FroaUuqpatDGFnALXv39xBYQPHoQpOhoA9969FC5frsu8gUIKlfiHgm+/pfDbJVocN3kSplD/um12OCOfBz5czwuLtpLnLGnq2a9jY+bc35WuZ0kjFKG/Tsl1SK6ndlEvKPKwYP0hXeY1R0YSMeRmLZYXgMuSQiXK8ObkkPXkU1ocPngQIRdfZGBGZXm8CrNX72fI26vYsK9kQ7tG8eG8fUdHRvVuQ0SoNEER1cNkMpVpVvvZ2oO43PrcposcNgyKt8op+nUtRX/8ocu8gUAKlSgjZ8JEvMfVJiLmunWJeerJMxzhO3uO53Lne2t5fekOnC71h4PZBLd0bcYn913MBc3iDc5Q1AY92jUgIUrtGJee62TZ5qNnOKJ8LA0bENanjxbLVVUJKVRC41y7lryPP9Hi2PHPYo41vvedy+3lvZW7uW3qGramlDSRbVEvkhl3duGBHq0IDfLP1Ygi8ARZzdzYqYkWz169X7fu55F336V9XPD1YtyH9Lm1WNNJoRIAKE4nWaPGaHHof68itPe1Bmak2nI4i9unruG9H/bgLm4iG2QxcdcVLZh590WcXbwNgxC+1PfCRoQVd9jfc9zBuj0nznBE+QS3a0vIJZeogdeL470Zusxb00mhEgDkvvEm7uKmmKbISGInGNsmqbDIw+tLd3Dne2vZk1rSRLZdoxg+uudihl2ejNUi/3yFMWLCg+l9fskuR/q2VSq5qsqfMxdvdvZpvrp2kO90gWvHDnLffEuLo8eOxtKwwWmOqF4b9p1gyNurmL16PycbVYcGWfhfz9ZMHd6Z5omRhuUmxEmDujTlZKvItXtOsOtYri7zhnTrhrWV2iJVycsjb9ZsXeatyaRQ1XKK10vWyNHgUt8HCe7QgYhbbz3DUdXDUehi4sIt3D9zPSmZJW1kOv6nDrPvv5iBF0mnc+E/kuLD6Vaqi/qcNft1mVdtq1RyVeWYMQOluI1ZbSWFqpbL++gjijZsUIOgIGJfnITJ7Pt/Fj/vSGXwm6v4asNhbSwy1MqT17fl9Vs70DAu3Oc5CXEmN5faAXjZX0dJK9VfsirC+/bFnJgIgPfYcQoWLtJl3ppKClUt5k45Qs7ESVoc9cD9BLVq5dMcMvOKePrzPxk5eyNpuSWtIS9vncic+7ty3QXSRFb4r3aNYjm3iboy1u1R+HztQV3mNYWEEFmqAbRj6jTdVhbWRFKoailFUch+8kkUh7pQwdqiBVEPPuDT8y/ddIRBb/7Cd5uPaeNxEcFMuKk9Lww6j7rSRFbUAKXbKn25/hD5pTqlVEXE0FswhYUB4Nq6FefPv+gyb00khaqWKvx6sbazKKDe8gsJ8cm5vV6FKd9swzb/L7JLNZHt1b4hcx/oyhVt68tVlKgxLmmVSKN49dZ0bqGbRRtTdJnXHBdH+MCbtNgxrfa+ACyFqhbyZmWR9fQzWhx+yy2EdOrks/PPWXOAeetKXmSsHxPKK7dcwDP9ziEmXJrIiprFYjYx6KKmWjx3zQHcHp3aKt05Aop/aXOu/AHX9u26zFvTSKGqhbKfn4A3Te02bq6XSMyTY3127pSMfKat3KXFV7Spx6z7u3JRS2kiK2qu3uclERMeBMDRrAJ+3J6qy7zWZs0IvaanFjumTddl3ppGClUt41y9hvzZc7Q49vnnMBdvL1DdFEVh0tdbtT59LetH8eyAc4kIkSayomYLDbbQ78LGWjxrlZ5tlUp2AM7/4ks8x4/rMm9NIoWqFlEKCsgcNVqLQ6/pSdg11/js/Es2HdVazZhNMLZPW+kuIQLGgM5NCLKot+m2pmTz58EsXeYNubADwR06qIHLheODmbrMW5PIT4laJOe11/Hs2weAKSqK2OfG++zcmXlFvLqk5P76TZ2b0kb69IkAUicyhJ7tG2rxHF3bKpVcVeV9/DHe/Hzd5q4JpFDVEq6t23C8864Wxzz5BJb69X12/leXbNdW+NWPDeWuK1r47NxC+MrNFzXTPv5pRyoHT+TpMm/o1T2wNFMXbChZ2eRMfEGXeWsKKVS1gOLxkDlyJLjV9zuCO3civNRuotXt193pLN1UsmfP6N5tCJfnUiIANU+M5OKWCQAoiroCUA8mi4Wo++7T4rz3P6hVtwClUNUCeR/MxPXHn2oQHEzsZN+1Scp3unlh0RYt7nFOA1nhJwLakFJtlRZvTCErT58+feE3Dyb02pKtd7KfepqcV1+rFR0rpFAFOPfhw+RMmqzFUQ89SFAL3912m7ZyN8ey1P5n0WFBPNLTty2ahPC1C5rFc1aDKACcbi9f/KbP5ocmk4m4V6YQdP552ljuiy+RbRuH4tXnvS1/JYUqgCmKQtbYJ1CKH7xaW51F1P33neEo/WxNyeazX0tufTzSsxXxkb7pfiGEUUwmU5m2Sp+vO4jT5dFlbnNEBAlz55RsrgjkzXifzIcfQXG5TnNkzSaFKoAVfPUVzhUr1cBkInbyZEzBvun84PZ4mbhwi7afVKfkOlxTakWUEIHsyrb1SSzuVZmZV8SSUs9oq8ocGUmdj2aWuQ1Y8MWXnBg2HG9BwWmOrLmkUAUoT0Ym2c+M0+KI224l5MIOPjv/7NX7tY3kQoLMjO7dRvr3iVrDajEzsEsTLZ6zZj9er37PkkwhIcS/8xYRQ2/RxpwrVnJi0M14MzN1O4+/kEIVoHKefRbvCfXlWkuDBkSPGX2GI/Rz6EQeM37Yo8V3dmtBUrzsJyVql+s7NCI8xALA/rQ81uxO13V+k8VCzMQJRD3ysDZWtH49aQNuxHNUvys4fyCFKgAV/vQz+Z/P0+KYCc9jjoryybkVRWHSoq043erD3bMaRJVp2ClEbREZGsT1FzTS4tk6vgB8kslkInrk48Q8a9fG3Nt3kNa3H+69+3Q/n1GkUAUYb0EBWWPGaHFY796E9fivz86/+I8jrN+XAahdpZ/o007aJIlaa2CXpljM6i3vDfsy2H4kp1rOEzl8GHFvvA5W9f1Ez+HDpPW9gaLNm6vlfL4mP0ECTO7Lr+A5oO4yaoqJIWa8/QxH6OeEw8nrS0vaJA3q0pTWDX3T8FYIf1Q/Nowr29bT4uq4qjopvN8N1PngfUyh6iIO74kTpPe/EefqNdV2Tl+RQhVAijZvxjG1ZHO1mKefwpKY6LPzv/LtdnIK1O4XSXFh3Nld2iQJcXOpperfbznGsazqW5kXekV36sydgylG7aOpOByk3zKUgiVLqu2cviCFKkAobjdZj48Cj/q+RvBFFxE+aKDPzr9qZxrLS20pP+q6NoQGW3x2fiH8VeuGMVzQLA4Aj1fhs7UHq/V8IR0vpO78zzHXK/4l1ekk4867yZszt1rPW52kUAUIx3szcP31lxqEhBA3eZLPloPnOd1M/nqrFvdq35DOyQk+ObcQNcGQrs21jxdsOISjsHpfzg06+2zqfrUAS7Nm6oDXS9bjI8l96+0a2XJJClUAcO3eTe5LU7Q4+pGHsf6n+WmO0Ne73+/ieLbaJik2PIiHrpY2SUKUdlGLBJomRACQ7/Tw1YaUaj+ntXFj6i74gqB27bSxnAkTyRn/XI0rVlKoariCZctI7zcApfiNdOvZrYm89x6fnX/zoSzmrSu5lfG/a1oTG+Gb7hdC1BRms6nMs6pPfz2A21P9/fksdeuS8PmnBF/URRtzTJ1G1v8eRSneTaEmkEJVQ3nS08m49z4y7hiuvdhLSAhxU17CFMIqE9wAABUJSURBVBTkkxxcbrVN0slfzrq0SKDHOQ18cm4hapqe5zYgrviXuNScQr7fcuwMR+jDHB1NwicfE9rzam0s//N5ZIy4U/sF199JoaphFEUhf/4XHL+8OwULF2nj5rp1Sfh0DsHt2/ssl49X7WNPqgOA0CALo6RNkhD/KiTIwoBOjbV49uoDPrsFZwoNJX7qu4QPHqSNFX63nPQht+DNzvZJDlUhhaoGcaekcOLW28h86GGUrCxtPPzGAdRb+T0hHTv6LJcD6Xl88GNJm6S7r2hBw7gwn51fiJqof8cmhFjVH7s7jubw+/4Mn53bZLUS++JkIkvtoFC0dh3pA27Ck5rqszwqQwpVDaB4vTg+/IjU7leWdEMHLI0aUWfWx8S9+grmuDif5eP1KrywcAsuj/rbYJukaG7qIm2ShDiT2Ihgep2XpMWzV+uzA3B5mUwmYp4YS/TTT2pjrq1bSbuhH+4Dvs2lIqRQ+TnXnr2kD7iR7CeeRMnLUwdNJiKG3UHiiuWEduvm85wW/n6YjQfUDs0Ws4mxfdpqbWKEEKc3+KKmnLxDvmpnGvvSHD7PIeqee4h9eQpY1HcdPfsPkNa3H66t23yeS3lIofJTittN7tvvkNqjB0Vr12nj1uRkEr6cT+z4ZzFHRPg8r/RcJ29+t1OLh1zcjJb1pU2SEOXVJCGCS1uVdIyZU41tlU4nYuBNxL83DULVzUy9qamk9R+Ac+1aQ/I5HSlUfsi1ZStpvfuQ8/wEKHSqgxYLkQ8+QOKyJT59FvV3U77ZhqNQXdbaKD6cYd2SDctFiJqq9FL1b/88wgmH05A8wnr0IGHWJ5iKd1dQcnJIv3kIBd8tNySffyOFyo8oTic5k18ktde1JV0mgKB27aj7zWJixozWGk4a4aftqazcelyLx/ZpQ2iQtEkSoqLaN4mlTZLaj8/lUZi/rnrbKp1OSJcuJMz7HHPduupAoZOM4SPKbBVkNClUfsL523pSe/Qk97XX4eSLeCEhRD8xlrpfLyS4XVtD83MUunixVJuk685PokPzOgZmJETNZTKZGNK1mRbP/+0QhUUew/IJbteWugu+wNKkeFdij4fMR/5Hbqkm10aSQmUwb14eWc/YSL+hH+7du7Xx4E4dSVy2lKj77/PZC7yn8/byXaTlqrcn4iKCeaDHWQZnJETNdnnrRBrEqq90ZOe7WPxH9bdVOh1rs2bUXfAF1rNba2M5z44ne+ILhrdckkJloMKffiL1yv+SN+N9TrZ3MEVEEPP8cyTMn0dQC/94/vPnwUy++O2QFj/aqzUx4dImSYiqsFrMDCr1WsfcXw/g8RpbECz16lF33ucEl3oO7njzLbJGjUbxGHfFJ4XKAN6sLDIffYwTg4fgOVRSAEK6dyNxxXIib78Nk9k//tMUFbdJOqnrWXW5qm19AzMSInD0viCJqFB1V95DJ/L5ZYfxL96aY2OpM2cWIVdeqY3lz55Dxj33ohQWGpOTIWetxQq+/Zbj3a8k/9PPtDFTbCxxr71KnY8/wtqokYHZ/dOHP+9lf5r6/lZ4sIVRvc+WNklC6CQixErfC0u3VdpvXDKlmMPCqDNjOmEDBmhjhd98S/rQ2/Dm5vo+H5+fsZbypKZy4q57yBhxF95S7UrCrutNvR9WED6gv98VgH2pDj78ea8W33NlS+rFSJskIfR0Y+cmWC3q9/6fB7PYfDjrDEf4hikoiLhXphBx5whtrGj1atJvHIgnPd2nuUih8pHCFSsoXLxYi82JicTPmE78u+9gObks1I94vQoTFm7BXdwmqW2jGPp3amJwVkIEnsToUHq0K9l1wKgXgE/FZDYTY3uG6DGjtTHXX3+R/YzNp3lIofKR8IEDCenaVf148CDqrfyesJ49Dc7q3325/hB/HVJ/s7OYTTwhbZKEqDaDS70AvHLrcY5k5huXzN+YTCaiHnyA2MmTwGzGmpxMzPhnfZqD1adnq8VMJhOxL07CfeAgoZddanQ6p5WaXchby0vaJN16SXOS60UZmJEQga1l/Sg6Jddh3Z4TeBWYu+YAj/Y62+i0yogYcjPmugkEtW2LpY5v36GUKyofsjZt6vdFSlEUXvpmG/lOdSlq04QIbr/sPwZnJUTgG1LqqmrRxhRyClzGJfMvwnr0wJqUdOYv1JkUKlHGym3H+Wl7yWKPMde1IUTaJAlR7Tol1yG5XiQABUUeFqw/dIYjag8pVEKTW+BiyuKSNv99OzTi/+3deXhU9b3H8Xc2EkiIIYEQWQIISASKYVeLAi0oiKDWXUFkUS7Ya7F91OJFf/66iFq9lCtKkSpUsCptLYutuK+oQSKLBDFsAVkCyhrInkz/mGEYuIISyJyTM5/X88wTzpmZzPc5k+d8OOf8zvfXtXWqgxWJRI6oqKhjmtXOz9lKRWW1cwW5iIJKgqa/mc+eQ+UANG4Yz50D1SZJJJwu7Xw2jRv6p934tqiMN9bsdLgid1BQCQCfF+xlYe624PIvL8+iYX3newyKRJK42GiuC7kN5K8fFzjeZ88NFFRCWUUVj4S0SeqblU7/85o6WJFI5LqqRwvq1/NfF9646xDLNu5xuCLnKaiE2R9sYuse/30bifGx/GqI2iSJOOWsBvW4ouvRkXVuaavkJAVVhNuwq4i5H20OLk8Y0J70ZOcmZxQRuPGCVhy5vz5n4x7WF4a/v56bKKgiWFW1jymL8oJTC3TJTOHqkAaZIuKM5qkN6Bdy+v3FTwocq8UNFFQR7B/LtpK37QAAcTFRTBraiWi1SRJxhZtDZgB+44udfHPQmSk23EBBFaEK95cw4+31weWRF59Dm/QkBysSkVCdW6TQJTMFgMoqH3/L2epwRc5RUEUgn8/HH/71JSXl/jZJrZskcuvFapMk4jahbZX+ufxrissqnSvGQQqqCPRWXiFL878JLk8a1ol6sfpTEHGbPh3SaZHaAICi0koWr9jucEXO0N4pwhwoLud//70uuHxNz5acn9nIwYpE5ERioqO46cJWweWXP91CZVXktVVSUEWYJ9/IZ99hf5ukJsnxTBigNkkibjYkuzlnNfB3idmxr4T3Q5pGRwoFVQRZvmkPr4acOrhnSEcSEzQlmYibJdSL4Wcht428sDTy2iopqCJEaUUVjyw+2iapf8emXJKV7mBFIvJDXds7k7gY/60ja7cfICfC2iopqCLEs+9tZNveEgCSEmL5lctmDxWRE0tLimfw+c2Cyw/9YzU79pU4WFF4KagiQP7Og8f0C/v5wHODUwmISN1we/92pCbVA2B/cQUTZi9jy7eHHa4qPBRUHnd8m6SurRoxrFsLh6sSkVPVJDmBR27IJjZwCrDwQCnjns1h3Y4DDldW+xRUHjf/0y18ueMgAPVio/n1MLVJEqmrumQ24vGbu5EQ558GxH9k9RnLN3n7mpWCysN27Ctm5jsbgsujLjmHVo0THaxIRE7XBe0aM31kD5Lr+0fsFpdXcfe8XN5ZW+hwZbVHQeVRPp+Px15dS2mFv01S2/Qkhv+4jcNViciZ0LllCn8a3Zsmyf5rzRVVPibPX8WC5V87XFntUFB51Otf7OTTDf7TAVFRMOnKTsSpTZKIZ5yTnsQzY3qTmeZvsVTtg0cWr+UvH2zy3H1W2nN50P7D5fzxtaNtkq7rlUnnFikOViQiteHslPrMHNObrGbJwXUz3l7PtNe/orraO2GloPKgaa9/xf7iCgCanpXAuJ+2d7giEaktjRLr8dRtPenRJjW47qVPtvDbBWs80xdQQeUxORu+5bVVO4LL917RkcR4tUkS8bLE+FieuKUb/c472m3mtVU7uO+llZQGpvOpyxRUHlJSXsmjr64NLg/onMGPz23iYEUiEi7xcTH8/vpsrux+9D7JpfnfcNfc5RSVVDhY2elTUHnIrHc3BtuqJNeP5e7BWQ5XJCLhFBMdxa+HdmRkyESoq7fu579mL+PbojIHKzs9CiqPWLfjAC99UhBcvuuyLNKS1CZJJNJERUUxfkB7fnFZh+C6jbsOccezOXy9p262XFJQeUBlVTUPL8rjyCCfHm1SGZLd7ORvEhFPu+mi1jx4dWdiAp1oduwrYdxzy8jfedDhyk6dgqqOK62o4ncL1pC/swiA+Nho7hvakagotUkSiXSXZzfn0RuziQ/cQ7n3UDnjZ3/G5wV7Ha7s1Cio6rDPC/Yy/OmPWbJ6Z3DdmH5taZmmNkki4tenQzrTbu1BUmCS1MNllUycm8sHdWimYAVVHXS4tJJHF69lwuzP2La3OLh+aNfm3KI2SSJynOxWjZgxqhdpgWlCyiurmfTyymNm/HYzBVUdszT/G256ain/DOnplRgfy6Rhnbj/yk7B89EiIqHaZzTkmTG9aZFaH/BPAfS7BWuY99Fmhyv7froTtI7Yf7icqUvW8XrIaT6Aizs04Z4rOpKenOBQZSJSVzRPbcDM0b2ZOC+X9YX+69rT38xnX3E5Px94rmuvbSuoXM7n8/HWmkKe+PeXwbZI4G+b8svLsxjQKcO1f1wi4j5pDeOZMaon9/x1BSu27APghaUFHCyu4L6hHYmNcd+JNgWVi+0+WMofXl3Lh199c8z6QV3OZuKgLFIS6zlUmYjUZUkJcUwd0Z0H/rYquH9ZvGI7B0sq+M21XYgPTMzoFu6LTsHn87Fg+dfcNH3pMSGVnpzAE7d046FruiikROS0JMTFMOWG7GPuuXx/3W4mzsvlUKm7Wi7piMpltu0tZsqiPHI3H3ufw896tuTOAeeSmKCvTETOjNiYaCZf1ZmUBvV44eMCAFYU7GPC7M+YOqK7a7rbaK/nElXVPl7+dAsz31lPWcXR1vwt0xpw/7BOdG2depJ3i4jUTFRUFP99WQdSEuvx1Jv5AOQXFjHu2WX8363dadaogcMVejiorLWtgZONu3zZGHNjeKo5uY27ivj9wjzWbj8QXBcdBTdf1Jqx/duR4LLzxSLiPSP6tCGlQRxTAu3Ytu0t5o5nl/HHEd1p17Sho7V5NqhCrAIWfMf6NeEu5HgVldX85cNNzPlwE5VVR2fjbNc0if+5sjPnNT/LwepEJNIM7daC5PpxPPD31ZRXVvNtURnjn1vG47d04/zMRo7VFQlBtdIY85DTRRwvb9t+Hl6Yx8bdh4Lr4mKiGN23LSP6tHHlEFER8b6+5zVl6vDu3PPi5xSXVVFUWsldzy/n4euzHZvfTnvDMCstr2LaknXc/uecY0LqRy1TeH78RYzq21YhJSKO6t4mladv60WjwOjisopq7n1xxTGzh4dTJBxRNbPWjgPSgD3AJ8aY1U4Ukrt5Dw8vzGN7YHJD8A8RHT+gPdf2ylT7IxFxjaxmycwc04tfPJ/Lzv0lVFX7sK98wcHiCm64sFVYa4mEoBoYeARZa98DRhpjtp7oTdba24DbvuOp7JoUsTB3G1MW5R2zruc5aUwa1tEVo2pERI6XmZbIM2N6MXFubvAM0NQl6ygqrWBs/3Zhq8PL55iKgd8C3YFGgUdf4F2gH/C2tfZk82G0Drz++EeNRjj06dCE5PpxADRMiGXyVZ1dM/RTROREmiQnMGN0L37UMgXwj0huG+ZRgK4+orLWFgCncoz5gjFmOIAxZjfw4HHPf2CtvRT4COgNjAWmneB3FQDvf8f6dmlpac0zMjJOoSxIS4rn7sFZvPflLu4Z0pHGDd1xI52IyPdJrh/Hk7f24P75K7kkK53+HZuG9fOjfD7f97/KIdbat4Hmp/CWRcaYe3/A7x0LzAJeMcZcU4PSarTRfD6fGsiKSJ1VXe0j+vSupdfoza4+ojLG/LSWfvWRBnphnQpXISUiddlphlTNP9eRT3XeBYGfmxytQkREvpdng8pa29ta+/9ajFtrfwLcHVicF96qRETkVLn61N9pehToFBiKvi2wrgvwk8C/HzDGfOxEYSIi8sN5OajmAlcDPYHBQBywC5gPTDfGfOhgbSIi8gO5etSfi2mjiYicuhqNxvDsNSoREfEGBZWIiLial69Ruc6SJUsoLCx0ugwRkdOSkZHBoEGDwvZ5CqqaqdF51pycnHVAhzNci4hIWG3ZsuWrQYMGZYXr8xRU4ZUU+HkAWOlkIR6Xjb95sLZz7dE2jkxHvvek73vhmaSgCq8N+HsXrjTG9HO4Fs8K3DvXF23nWqNtHJlCvvcN4fxcDaYQERFXU1CJiIirKahERMTVFFQiIuJqGkwRXnOA9/DPHiy1Zw7azrVtDtrGkWgODnzv6vUnIiKuplN/IiLiagoqERFxNQWViIi4mgZThIG19odcCGxkjNlf68V4jLV2LDALWGKMGXyC1/wLuBy40xjzdDjrq+tC/nZ9QHtjzMYTvO5doF9gcZQxZk7tVyfh4Ib9l4IqvOxJnisNWxUeYoz5s7V2KDDMWnunMeap0OettePxh9RrCqkaq8S/rxgD3H/8k9ba9vjb6hx5nXiTY/sv/VGFkTHmIadr8KjbgQuBx6y1bxljvgKw1p4LPA7sAUY7WF9dtwvYCYyy1j5ojKk87vmx+GcUeBW4KtzFSXg4uf/SNSqp84wxu/GHVQNgnrU21lobC8wLrLvDGKOJwE7PLCADuCJ0pbU2DhgJfAzkOVCXRAAFlXiCMWYh8BzQA3gw8OgJzDHGvOJkbR7xInAY/9FTqGFAU/xBJlIrFFTiJROBzfivo9yP/+75u5wsyCuMMUXAS8Aga22LkKduBw4C8x0pTCKCgko8I7Az/Q0QE3iMD6yTM2MW/u06GsBa2woYCLxgjCl2sjDxNgWVeIa1tj5wX8iq65yqxYuMMTnAF8Boa200/tOA0ei0n9QyBZV4yWNAFjAN//ToowND1+XMmQW0AgYBo4BcY8wKZ0sSr1NQiSdYay8F7sT/P/77gBFAGTDLWtvYydo8Zi5QAswEmgPPOFuORAIFldR51tpUYDZQAQw3xpQZY9YAD+AfkfYnJ+vzkkD3gb8DLfCPAnzR2YokEiioxAtmAM2AycaY1SHrnwA+BK6x1g53pDJvmgxcDVymwSoSDupMIXWatXYEcD3wAf5gCjLGVFtrRwKrgSette8ZY7Y5UKanGGO2AludrkMih46opM6y1mYCT+K/j+dWY0z18a8xxmwG7gZSgOestVHhrVJETpdm+BUREVfTEZWIiLiagkpERFxNQSUiIq6moBIREVdTUImIiKspqERExNUUVCIi4moKKhERcTUFlYiIuJqCSkREXO0/7H8J6OicIZQAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] @@ -1265,7 +1273,7 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 29, "metadata": {}, "outputs": [], "source": [ @@ -1289,7 +1297,7 @@ " \n", " def one_over_chi(U):\n", " \n", - " chi_rpa_wk = get_chiRPA_spin_dependent(p.copy(U=U), chi0_wk=chi0_wk)\n", + " chi_rpa_wk = get_chiRPA_spin_dependent(p.alter(U=U), chi0_wk=chi0_wk)\n", " chi = chi_contraction(chi_rpa_wk, op1, op2)\n", " \n", " # -- If any value is below zero we are already in an ordered phase\n", @@ -1318,7 +1326,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 30, "metadata": {}, "outputs": [], "source": [ @@ -1332,8 +1340,8 @@ "xi = 0.1\n", "\n", "Ts = [1000, 750, 500]\n", - "hubbard_models_doped = parameter_scan(hubbard_spin_dependent.copy(mu=xi), T=Ts)\n", - "hubbard_models_zeeman = parameter_scan(hubbard_spin_dependent.copy(zeeman=xi), T=Ts)\n", + "hubbard_models_doped = parameter_scan(hubbard_spin_dependent.alter(mu=xi), T=Ts)\n", + "hubbard_models_zeeman = parameter_scan(hubbard_spin_dependent.alter(zeeman=xi), T=Ts)\n", "\n", "U_spin_cs = []\n", "U_charge_cs = []\n", @@ -1345,7 +1353,7 @@ " U_spin_c = get_phase_transition(hubbard_model_zeeman, S_z, S_z, 0, 10)\n", " U_charge_c = get_phase_transition(hubbard_model_doped, n, n, -10, 0)\n", " U_sx_c = get_phase_transition(hubbard_model_zeeman, S_x, S_x)\n", - " U_sc_c = get_sc_phase_transistion(hubbard_model_doped.copy(spin=False), guess=-U_sx_c) \n", + " U_sc_c = get_sc_phase_transistion(hubbard_model_doped.alter(spin=False), guess=-U_sx_c) \n", "\n", " U_spin_cs.append(U_spin_c)\n", " U_charge_cs.append(U_charge_c)\n", @@ -1355,9 +1363,30 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 31, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5,1,'Hubbard with $\\\\mathrm{Zeeman}=\\\\xi$')" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "fig = plt.figure(figsize=(11,7))\n", "\n", @@ -1416,24 +1445,52 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 32, "metadata": {}, "outputs": [], "source": [ - "_, delta_1 = get_lambda_delta(hubbard.copy(mu=xi, U=U_sc_cs[0]))" + "_, delta_1 = get_lambda_delta(hubbard.alter(mu=xi, U=U_sc_cs[0]))" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 33, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "delta_plot = delta_1[Idx(0), : ].data.reshape(hubbard.nk, hubbard.nk).real\n", "\n", "plt.imshow(delta_plot, vmin=0.9*np.mean(delta_plot), vmax=1.1*np.mean(delta_plot))\n", "plt.colorbar()" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/python/triqs_tprf/ParameterCollection.py b/python/triqs_tprf/ParameterCollection.py index 5a37efed9..22dffd7c8 100644 --- a/python/triqs_tprf/ParameterCollection.py +++ b/python/triqs_tprf/ParameterCollection.py @@ -79,14 +79,21 @@ def keys(self): def dict(self): return self.__dict__ - def update(self, **kwargs): - self.__dict__.update(kwargs) + def alter(self, **kwargs): + """Change or add attributes + + Returns + ------- + p : ``ParameterCollection`` + """ + p = self.copy() + p.__dict__.update(kwargs) + return p - def copy(self, **kwargs): - """Shallow copy that allows for changing/adding attributes + def copy(self): + """Shallow copy """ p = ParameterCollection(**self.dict()) - p.update(**kwargs) return p def __getitem__(self, key): @@ -290,6 +297,6 @@ def parameter_scan(p, **kwargs): ps = [] for parameter_value in itertools.product(*parameter_values): - ps.append(p.copy(**dict(parameter_value))) + ps.append(p.alter(**dict(parameter_value))) return ParameterCollections(ps) diff --git a/test/python/eliashberg/eigenvalue_solver.py b/test/python/eliashberg/eigenvalue_solver.py index 446a4836d..df07472ee 100644 --- a/test/python/eliashberg/eigenvalue_solver.py +++ b/test/python/eliashberg/eigenvalue_solver.py @@ -103,7 +103,7 @@ def run_solve_eliashberg(p): Es_pm, eigen_modes_pm = run_solve_eliashberg(p) - Es_iram, eigen_modes_iram = run_solve_eliashberg(p.copy(solver='IRAM')) + Es_iram, eigen_modes_iram = run_solve_eliashberg(p.alter(solver='IRAM')) print(Es_pm[0], Es_iram[0]) diff --git a/test/python/eliashberg/product_summation_vs_fft.py b/test/python/eliashberg/product_summation_vs_fft.py index ec9c10156..84172b30a 100644 --- a/test/python/eliashberg/product_summation_vs_fft.py +++ b/test/python/eliashberg/product_summation_vs_fft.py @@ -208,7 +208,7 @@ def compare_next_delta(p): print('The summation and FFT implementation of the eliashberg product' ' both yield the same result.') - deltas_with_fit = compare_next_delta(p.copy(fit_const=True)) + deltas_with_fit = compare_next_delta(p.alter(fit_const=True)) diff = compare_deltas(deltas[2:], deltas_with_fit[2:]) From 2fcc3656d7736d78558c88f74d0fd8e863b81365 Mon Sep 17 00:00:00 2001 From: Stefan Date: Tue, 14 May 2019 12:05:30 +0200 Subject: [PATCH 025/121] [doc] add parameter_scan to refs --- doc/reference/python_reference.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/doc/reference/python_reference.rst b/doc/reference/python_reference.rst index 285834cef..645f8d407 100644 --- a/doc/reference/python_reference.rst +++ b/doc/reference/python_reference.rst @@ -118,4 +118,4 @@ Parameter collections :members: .. autoclass:: triqs_tprf.ParameterCollection.ParameterCollections :members: - +.. autofunction:: triqs_tprf.ParameterCollection.parameter_scan From fc49e7459e6728ba874af726f29bb007d2370154 Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 15 May 2019 18:40:16 +0200 Subject: [PATCH 026/121] [doc] add eliashberg tutorial --- .../PHT_Hubbard_Model.ipynb | 618 ++++++++-- doc/documentation.rst | 4 +- ...tion on the attractive Hubbard model.ipynb | 861 +++++++++++++ .../plots/SPHT_hubbard_phase_diagram.svg | 1082 +++++++++++++++++ 4 files changed, 2495 insertions(+), 70 deletions(-) create mode 100644 doc/user_guide/Linearized Eliashberg equation on the attractive Hubbard model.ipynb create mode 100644 doc/user_guide/plots/SPHT_hubbard_phase_diagram.svg diff --git a/benchmark/eliashberg/particle_hole_transformation/PHT_Hubbard_Model.ipynb b/benchmark/eliashberg/particle_hole_transformation/PHT_Hubbard_Model.ipynb index f0f374a0b..28ccfa21f 100644 --- a/benchmark/eliashberg/particle_hole_transformation/PHT_Hubbard_Model.ipynb +++ b/benchmark/eliashberg/particle_hole_transformation/PHT_Hubbard_Model.ipynb @@ -68,7 +68,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -77,7 +77,7 @@ "T = 1000\n", "U = 1.0\n", "mu = 0.0\n", - "nk = 8\n", + "nk = 32\n", "norb = 1\n", "nw = 50\n", "spin = False\n", @@ -86,7 +86,7 @@ "zeeman = 0.0" ] }, - "execution_count": 3, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" } @@ -107,7 +107,7 @@ " zeeman=0.0, # Strength of zeeman term\n", " \n", " # -- Technical parameter\n", - " nk=8, # Number of points in one dimension considered in the Brillouin zone.\n", + " nk=32, # Number of points in one dimension considered in the Brillouin zone.\n", " nw=50, # Number of Matsubara points in positive dimension.\n", " )\n", "hubbard" @@ -126,14 +126,14 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "Starting run with 1 MPI threads at : 2019-05-14 10:35:41.957241\n" + "Starting run with 1 MPI threads at : 2019-05-14 14:36:57.601312\n" ] } ], @@ -147,7 +147,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ @@ -160,7 +160,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -169,13 +169,13 @@ "Text(0.5,0,'DOS')" ] }, - "execution_count": 6, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -193,12 +193,12 @@ "\n", "# -- Bandstructure\n", "ax_bs = plt.subplot(gs[0])\n", - "ax_bs.bsplot(e_k, path)\n", + "ax_bs.bsplot(e_k[0,0], path)\n", "ax_bs.set_ylabel('$\\epsilon(\\mathbf{k})$', rotation=0, ha='right')\n", "\n", "# -- Density of states\n", "ax_dos = plt.subplot(gs[1])\n", - "ax_dos.dosplot(e_k)\n", + "ax_dos.dosplot(e_k[0,0])\n", "ax_dos.set_xlabel('DOS')" ] }, @@ -221,7 +221,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 9, "metadata": {}, "outputs": [ { @@ -235,11 +235,11 @@ "Two-Particle Response Function tool-box \n", "\n", "beta = 11.6045250062\n", - "nk = 64\n", + "nk = 1024\n", "nw = 100\n", "norb = 1\n", "\n", - "Approx. Memory Utilization: 0.00 GB\n", + "Approx. Memory Utilization: 0.01 GB\n", "\n", "--> fourier_wk_to_wr\n", "--> fourier_wr_to_tr\n", @@ -293,7 +293,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 10, "metadata": {}, "outputs": [], "source": [ @@ -318,7 +318,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 11, "metadata": {}, "outputs": [ { @@ -327,13 +327,13 @@ "Text(0.55,0.18,'$\\\\chi^{(c)}$')" ] }, - "execution_count": 9, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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0CySxTZtw2tspOP64gf1GSM6phkREJI/F0wJJ331IoFuzzSBG2hh+P8EzzgAgsnYtAO333Ufbb27FM2UyVT/5MYbXm7zeP+9QfEuWEHrk0a5j8+cTWbuOxi99ifoPXEr73fdQfv2XKfvSF3u8L/TIo3hnzsS/YsWAyyi5pRoSEZE8ll5D0n9/C++0oY+0CRxxBADRtWuJbtpE4+e+AD4fVbf8BO/kyT2uL37ve2j92c8pu+YLGB4PJZd/hJLLPzKgd3Xcex9F77q4R82JjF2qIRERyWOpgaS/5hdIH2kz2LlI/MuXARB54QUOfuQKnPZ2yr54TbJJprvid78LYjFCf79/UO8JP/kUsd27KPngZYO6T3JLNSQiInlssH1IfKlNNoMc+uubNQtPZSXx7TsACJ6zmtI+Fs4zgkEqvn8j9sHBrZtjt7dRedNNfU7yJmOPAomISB4bdKfWlEASe6Pvicky8S9dSvipp/DOnUvljd/r9/rgSasG/Y7OkToyvqjJRkQkj6UN+60eQA3JvK5htLHNmwc8FwlA5MUXCf/nPwAUX/JePGW9L+Qn+UeBREQkjw22hsQzeTJGhdsU4rS0DLhja/xgAwev+ChEIgBE128cQmllIlMgERHJU048nja5maeiot97DMPAv3Bhcj+2sf9g4dg2DVddRXz3bgoSQ3+jr74yhBLLRKZAIiKSp+ymJkg0uRjl5Rh+/4Du8y9alNyObuo/kLR870bCjz+Bf/kyqn/+U4yKcmKbt2B3dAyt4DIhKZCIiOSptOaaQaz54ksJJLENfQeS0COP0vKDmzEqKqj62U8xgkEChx8B8TjRtesGX2iZsBRIRETyVNocJP2s9JsqvYZkU6/XxXbu5OAnrgag6uYf4Js1y71/mTtBWujBBwdVXpnYRn3Yr2VZTwInAItN09w82u8fjyzL6t6N/TTTNB8b4L0e4DVgJjDPNM19I1w8ERmnBjtLayffotQ+JJtwbBvDk/7vWycc5uDlV+A0NlL6yasJnnF68lzBqpW0/uQWWm/5KZGXXiL45jP6nI9E8sOoBhLLst4GrATumAhhxLKsqcAXgXOBGUAT8Bxwk2ma/8xl2TqZpmlblvUt4FbgeuCq3JZIRMYKu35wI2w6eaurMSrKcRqbcEIh7Pp6vDU1adc0Xm8SfeVVClatovRzn007FzzlFMq+fB1tt99O5Pk1+JceNrwfRCaEUWuySfxL/ZuAA3xjtN6bLZZlLQPWAlcDhwJhYBJuOHnYsqxrc1i87u4AtgGXW5Z1SK4LIyJjw2CH/KbyTp6S3I7v29/jfOV3vs2M3TuZdOfve9SeAJR+9EqmPvUkM7ZvpeKrNwzq3TIxjWYfkrOBw4AnTdNcP4rvHXGWZRUCfwaqgReBw03TLAcqge8BBvAty7LGxHSBpmnGgP8F/KiGREQShhdIuhbDs/f3DCQigzWageTDic8/jOI7s+UKYA7QCpxnmuY6ANM0m03T/Bxwb+K6b+WofJn8PvF5iWVZAxvbJyITWnyQs7Sm8qQEkvh+dU2T4RtUHxLLsu4A/gt4A/df3N80TdPpdk0V8Apun4qfmKb5ccuyqoHzcJtr7url2S8CK4BvmKb55W7nVgJPAnuBOaZpRgZT7ix4b+Lzd6ZpZlpd6n+AdwBHWZa12DTNDdksjGVZHwF+3u3w503T/G7njmmamyzLehlYjtus9KdslklExr7URes8lYOsIZma0mSzV4FEhm+wNSQzcKv9FwBfBz6W4ZqfJ67bAHwucey0xH2vm6Z5oJdnd36xz+h+wjTNp3CbRqYCOW0GsSyrFDg6sdvbmLVncDu4ApzeyzUjVZ6LgZ92O/yF1DCS4qnE55hoShKR3FKTjYwlgwokpmmeittv4qHEoXeknrcs64O4NSgR4D2maXZOw7cy8bmmj8fXJj57BJKEpxOfg1/6cWQtwe0jApBxVh/TNG2gc7agpdkqiGVZbwFuI/2/4xdM0/yfXm55PvF5UrbKJCLjR+rCet5BBpL0JhsFEhm+QQ/7NU2z0bKsb+L+K3t553HLsuYBP0jsXm+a5osptx2X+Oxr8YJea0gSOte57nOUiGVZNwBmX9f0dbtpmjf0c820lO3aXq/qOjetj2uGzLKsk4G7cWueOl3TRxgBeDnxudSyrFLTNFuyUTYRGR+GOg8JgHdKSiDJMMpGZLCGOg/JC7j9QWosy5oGHABuB0qAx4DuzQWdX8p1fTyzvxqSgsRnf2VuBYbaoNk6gGuKU7b7WoihPfFZMsSy9OUY3DlFClOOXWua5nf6ua/z998ApgAKJCJ5ygmHcVoTf+V5vRjl5YO6P3XYr5psZCQMKZCYptliWdZWYB6wDLdJ5gSgEXh/oski1aTEZwO966whKbcsq9g0zbZu59+U+Oyzg2ii70Sm/hMjxej/kqz7b9Kbaa41TfO/B3Bf6u//JGDcT04nIkPTvf+IYQzurzbPlPQmG8dxBv0MkVTDGfbbWf1/BfClxPaVpmnuzHBtZ+1GX6NjUps/0mpJLMuaA7w5sXvfIMs50lJrUQp7vQqKMlw/UlL/uz07wDACEErZ7qvsIjLBpfYfGWxzDYCnuBijOFFhHIngNDaOVNEkT41EIDkf8AK3maZ5Zy/Xdkbxij6elzp8tnuzzY9wa3OeME3zucEWdISlBqfpfVzXeW5PFssCcHxiaviBSP1bp77Xq0RkwosPY4RNJ++U1NlaNfRXhmc4a9m8nLK9nb5nAK3DHbLbVwyvw61BCZASSCzLugJ33owQ8PH+CmVZ1ufoGm48WN/tZbhsqg24/WcM3Jlne6y9nZgmv3M5zNeGWJa+3Ae8PWX/Wsuy9pmmeVM/96X+/vfVn0dEJri0JptBzkGSvG/KZNi6FXCbbfyLF49I2SQ/DaeGJPXL7TLTNJv7uLbzS7vXETKJCdY6axNmAFiW9Sbg5sSxy03TXDuAcpXgdtgcyq9+O6AmRqZ0Dp89s5fLjgc6e4hlY5G9m4Afdjt2o2VZ7+nnvrmJzybcSeZEJE/ZDV2BxDvIWVqT96XORaKRNjJMQ6ohsSxrNvD9lEMHe7s24Snc+UmO6ee63bhTsk+3LGsJ7hTsAdy5NW4bSNkSw3ZvGMi1w/A74FjgvZZlfdU0ze7NMp01NGtM0+xRgzJCPgXMomsuGAO41bKsg6ZpPtDLPccmPp/K0PFYRPLIUFf6TaW5SGQkDbqGJNEc8VvS+4Ms7+XyTk8mPo+0LMvbx3Wd/TPeBDwCTMadG6SvuTVy4WfADqAU+KtlWUvBncXVsqzvABckrvtS9xstyzrVsiwn8evUoRYgESjeAzybctgP3G1Z1vG93NYZSP411PeKyMQwnFlaO6X3IVEgkeEZSpPNF4BTcEePdM7Y2l8geR7YijuHx6l9XNfZsfVY3D4nXxvARGWjLjED7dtxO4YeBayzLKsJd9jz53H7mHzRNM2Hen/KiJXjPGBLyuFi4G+WZaU15lqWFcSdwr/X9YREJH+MSCBJmz5enVpleAYVSCzLOgr4amL3arqG4PYZSBL9Q36d2H1XH5d2BhIH+Jxpml8ZTPlGk2maLwOH4/Zx2Yo7tLke+Btwpmma3+7l1s5J4toZgQ6vibWBziG9k2o18JBlWTNTjp2LW6PzmGmaqQFGRPLQcIf9gppsZGQNuA+JZVlFwB0kmgVM0/yNZVmd68r0V0MC8BvcKd0vsCzrKtM0w90vSDTNjLXmmV6ZprkX+GTi10Cdkvi8xTTNAf0fbJpmn7MNmab5OlDTz2Penfj8xUDeKSITW7w+ZaXf6uohPSN9+njVkMjwDKaG5HvAYtxajCsSxzrXpqmxLGtWXzebplmL2/eiCrhskOWcSE7BnXJ+1IKXZVnzcZuYXgN6mytGRPJI6iibkehDYu9zZ2sVGaoBBRLLss4FrsRtSvmAaZoHARJDfbcnLrsh0U+hL1/D7XtyjWVZw5kDZVyyLKsGN9T9zDTN0fznxBdxJ6+7TqNrRMRxnG5NNkMLJEZZGQTdibidjo6utXFEhqDfQGJZ1hTgV4nd75mm2X1ejc5+JB8Emi3L+k1vz0o0Ubwf+F9gZm/XTVSmaR4wTdMwTfPTo/XOxKioLcDnTdO8d7TeKyJjl9PWBhF3JQ8jGMRTOLSVJAzDSFtkTyNtZDgGUkvxa9zhty8D12U4fy3uHBgX4I6M2dXXw0zT/BPwp8EVU4YqUSPyzVyXQ0TGjpEYYdPJO3ky8TfecJ+7fz/Mnzes50n+6jeQmKb51n7Ohxh8x04REckRewQ6tCbvTxtpo46tMnTDmTpeRETGoZEY8tspfaSNmmxk6BRIRETyzEg32SSfq6G/MgwKJCIieSY+koFk2rTkdry2to8rRfqmQCIikmfSakgqh9lkM6trwGRsV59jGkT6pEAiIpJnUgOJd5idWr2zZie342/sHNazJL8pkIiI5JkR7UMydQr43AGbdn09dnv7sJ4n+UuBREQkz4xkIDG8Xrwzpif342q2kSFSIBERyTMjOewXwJfabLNTgUSGRoFERCTPpE2MNswaEujWsXWn+pHI0CiQiIjkEScex25sTO4Pd5QNgHdmVyCJK5DIECmQiIjkEbupCRwHAKO8HMPvH/YzfbNmJbdjarKRIVIgERHJIyM5B0kn7+yuQBLf+caIPFPyjwKJiEgeGckRNp18c+Ykt2Nbt+EkamBEBkOBREQkj6R2aPVWj0wg8dTUYFSUA+C0tmoKeRkSBRIRkTySPuR3ZAKJYRj4Fy1K7sc2bhqR50p+USAREckj2WiyAfAvXJjcjm7cOGLPlfyhQCIikkeyFUh8aTUkCiQyeAokIiJ5JD7Cs7R2Sm2yiW5Sk40MngKJiEgesQ+mztI6vJV+U/kWdTXZxDa9jmPbI/ZsyQ8KJCIieSRbTTbe6mo81W7AcTo6iG3dOmLPlvygQCIikkdSR9l4RzCQAASOPiq5HX7q6RF9tkx8CiQiInkkvYZk5PqQABSsXJncViCRwVIgERHJE044jNPa6u54vRhlZSP6/IKVJya3I08/rX4kMigKJCIieaJ7/xHDM7JfAb7Fi5P9SOyGBqKvrR/R58vEpkAiIpIn7CwN+e1kGEZaLUnbbbeP+Dtk4lIgERHJE/EsjbBJVXTxRcnt9t//nujrr2flPTLxKJCIiOSJtCabyuwEkoJTTqFg1Sp3Jx6n9ac/y8p7ZOJRIBERyRN2XV1yO1s1JIZhUPrpTyb3NdpGBkqBREQkT8R3705u+2ZMz9p7AkcfjVFY6L5z505iKe8V6Y0CiYhInojt6goG3hkzsvYew+8ncPTRyf3Is89l7V0ycSiQiIjkiXhtSiCZmb1AAhA4/rjkdliBRAZAgUREJE/EU2tIZs7M6rsKjj8+uR159tmsvksmBgUSEZE84IRC2AcOuDteL94pU7L6Pv9RR4LXC0Bs82bszhliRXqhQCIikgfitXuS296pUzF8vqy+z1NYiG/ePHfHcYiu35DV98n4p0AiIpIHYrt2Jbez3X+kk/+wpcnt6Guvjco7ZfxSIBERyQOxrVuS277Zs0flnf6lqYFE69pI3xRIRETyQGzDxuS2b/GiUXmnf+mS5LZqSKQ/CiQiInkgurErkPgXjVIgOeyw5HZs/XqceHxU3ivjkwKJiMgE5zgO0Y2bkvv+RYtH5b3emho8NTVuGTo6iG3bPirvlfFJgUREZIKz9+7FaWoCwCgtxTNt6qi923/E4cntyJo1o/ZeGX8USEREJrjuzTWGYYzauwuOPTa5HXlOM7ZK7xRIREQmuNTmGt8o9R/plDqFfOS5/4zqu2V8USAREZngYqk1JKM0wqZTYPlyCATccmzdSrxztliRbhRIREQmuFyMsOlkBIMEVixP7quWRHqjQCIiMoE5tk0stclmlGtIAAIpC+2FHnlk1N8v44MCiYjIBBbfuROnowMAT3U13urqUS9D4VlnJbc7HngAJxIZ9TLI2KdAIiIygaU214x2h9ZO/iNX4J3hrp/jNDYRfvKpnJRDxjYFEhGRCSy1uWa0O7R2MgyDwvPOTe63/9//5aQcMrYpkIiITGC57NCaqvBt5yW3O+69j8jadTkri4xNCiQiIhNYdEPum2zAHf5bcPpp7o7jcPDDHyFsEj3UAAAgAElEQVTy0ks5K4+MPQokIiITlBONEtuyJbnvX7ggh6WB8q9cD14v4Ha2PXDBhQolkqRAIiIyQcW2b4fEiBbvtGl4ystzWh7/ggWUf/UG8PncA+EwjV/8klYBFkCBRERkwoqlNtfkqENrdyWXXkrNfX+CggIAoq+8Svtdd+W4VDIWKJCIiExQY6VDa3eBFSsoverjyf2OP/8lh6WRsUKBRERkgsrlonr9Kbr4ouR2+NlncUKhHJZGxgIFEhGRCSptUb1FC3NYkp58M2bgmzfP3QmFCWuNm7ynQCIiMgE5oRCxbdvcHcPAtyC3I2wyKTjl5OR2+IknclgSGQsUSEREJqDo5i1g2wB458zGU1SU4xL1VHDSScltLbonCiQiIhNQbIx2aE1VsPJECLqjbWIbNxFdvz7HJZJcUiAREZmAxuoIm1Se4mIKzzwzud/+p3tzWBrJNQUSEZEJKHVRvbEyB0kmhRecn9zu+NO9OIlmJsk/CiQiIhNQZO2rye2xWkMCEDz1VIyKCgDitbV0/OWvOS6R5IoCiYjIBBOv3YO9dx8ARlHRmBxh08kIBCi+5H3J/Zbv3YgTi+WwRJIrCiQiIhNM5MUXk9v+5csxEgvajVWlV16BUVYGQGzLFpqu/4rWt8lDCiQiIhNMaiAJHHVkDksyMJ6KCko/emVyv+23t1G7cBEHr/qEVgPOIwokIiITTPipp5LbgSNX5LAkA1fysY8SPGd114FQmI4/3cuB8/+L2K5duSuYjBoFEhGRCSS2axfRVxIdWv1+Ck48MbcFGiDD56Pqxz+i+EMfwlNT03UiEqH9rrtzVzAZNQokIiITSOj+B5LbBatW4ikvz/o7v3zXy3zv74Ob1OwXj27m6t8+n3bMKCig4qs3MPXFNZR+9jPJ4+1334PjOCNSVhm7FEhERCaQjvvvT24XvuUtWX/f63ubeXz9Pt63cu6g7rvo+Nms3dnImm31Pc4ZhkHpR6/EKC0FIL59O9EXXuxxnUwsCiQiIhNEfP9+Ip2r5no8BM86s+8bRsAf/r2D4+ZNYkp54aDuKy8KcMqSKdz5zBsZzxuFhRS+tStQtd5663CKKeOAAomIyAQRevAhSDRtBI4/Du+kSVl9X0ckxiOv7ePNh0/tcc5xHO5bs4vLfvZvTvn6w5z17Uf41G1r2N8cSl5z+mFTeGrTARrbIhmfX/y+93a96977iO3YMfI/hIwZCiQiIhNEWnPNOedk/X2v7myiIxJn2ayKHue+fu9abrx/PSfMn8R/v+tIPn/uErweg6JA15woy2dXErcdXth+MOPzA0ceScGqVe6ObdN8401Z+TlkbPDlugAiIjJ8dmMj4aeeTu4HV6/u4+qRsX53E0UBLzOqitKO/99/dvLQq3u45bLjODwlrJx5+LS068oK/UwtD7JuVxOnH9azlgWg9OpPEH7ySQA67r6bjre+hcJRaIqS0adAIiIyAYQe/gckplz3H7kC34zpWX9nXWuY8qJA2jHHcbj1ia287aiZaWGkN+VFAepaw72eD5z4JgrPPZeOv7pr3DR8/CoiH/ogRCLE9+2j9GMfw3/Y0uH9IDImKJCIiEwAo91cAxCJ2QR86S3/2w60sb85xKlLpwzoGQGfh3C092niDcOg4tvfJPz8f7D37sNpb6f1hz/qKsOzzzHl6ScxAoFenyHjg/qQiIiMc3ZbG6HHH0/uD6W55p03/4vTvvEPPvjzZ3h2c12P8/ubQpzznUd50w0P8sSG/YDb5NISiqZdV9fi1nZMKikY0HtbQtEetSzdeSormfS7O/DOndvjXHzPHtrvvW9A75KxTYFERGScC/3zEQi5QcC3eBH+eYcO6v647XD4zAomlwV5bXcTX/zjS7SHu1bcjcVtrrvrZRraIrxv5SGcvHgyAHMmFdPYFqEj0nXtpFI3iGw90Nrve23bYV9TiNnVxf1e61+0iMn3/42y679M0TsvTDvXestPcWx7QD+rjF0KJCIi41zHX/6a3B7KZGhej4F5wRHc8bETmTelhPZwnPW1TcnzNz2wkVd3NnLk3EquPGNB8viyWRXYDmzc05I8NmdSMYumlXHTAxv485pdrNl2kL+8sIsb7nmlx3u3HWilIxJnxZz++5oAeMrKKL3yCipv+j7T1r2KUeR2po1t2kT7H+4c9M8tY4sCiYjIOGa3tRF65J/J/cLzzh3ys3xeDysXuOvIdIaMh1/dw93PvcGk0gK+fuFyvB4jef3sScXMn1LC05sOJI95PQbfefcKjpxTyc8eeZ3P3L6G25/azrwppT3e9/TrdUytCLJ0xuCnt/dUVFDykQ8n95u/+S3idT2bmmT8UKdWEZFxLPTww+nNNQsXDut5i6eXAbBxTzPb9rfyzT+vw+sx+Po7l1Nd2rNfyNuPnsnvnt7BlWcswJMIK1PKC/nqhcv7fdfDr+7hvCNnYBhGv9dmUvKJq2i/5/+I79qF3dBA/WUfYtIffoen2G0CchxnyM+W0acaEhGRcSytuea884b9vMXT3dqKdbsaufbOl+iIxPnYmxewYk5lxuvfdtRM4rbDY+v3Deo9z2+tZ29TBxcdP2fIZfUUFlLx39+CROiIvvAC+09/Mwev+Ch7lq1g33EnEFm7dsjPl9GlQCIiMk7F6+oIPfpYcn8kAsn0ykLKi/zsOtjBjro2TlkymfeuPKTX6wv8Xq4//3Di9uBW422PxPnK+UdQWugfVnmDp55KuXVDcj++axcdf/0rdn098dpaDl5xJXZr/x1sJfcUSERExqmWm38EYbe5xr/siEGPrunNgkR/j5lVRVz/jsP7vf7YQ6s584hp/V6X6uTFk1m1aPKQytddyYc+SMV3/wejvGdflPj2HTR9+foReY9kl/qQiIiMQ7GdO2m77bbkfumnPz0iz123q5GX32gA4PxjZlISHF4Nxmgpfve7CJ59NuHHH8M+UEd0/Xra/3gXAO133U3BqadQ9I535LiU0hcFEhGRcajlezdCxF0lN3DMMQTPfPOwn9nUHuG6P75MNO42v2zZN76aOrxVlRSdf35y34nbdNxzDwCNn/08nrJygqeflqviST/UZCMiMs5EN2yg/e57kvtlX7p22KNJbNvhK3e/wt6mECsXukN/N+xpHtYzc63iG1/DO2c2AE4oRP0l76fufZdQ/+GPsPe4E2j41KexW1r6eYqMFgUSEZFxpvk7/wOOW4tRcPrpFBx//LCf+cvHNvPslnqWTC/jmxctp6zQx466NkKR3teZGes8paVMuuN2vDNnJo+FH32M0P0PEN+9m/a77ubAuW8jvmdPDkspnRRIRETGkfDzawg9+FByv/zaa4b9zKdfP8BvnthKWaGfb1y0ggK/l4XTyojbDpv2ju9aEt8hh1Bz7/8RPPusjOdjmzdTd8n7sZuaMp6X0aNAIiIyTjiOQ/O3vpXcLzz/HfgPWzqsZ9Y2dHDDPa8CcMMFRzC9shCAxdPcCdIeTyykN555p02j+te/YvI/HqLixu9S/vWvUfLRK8HndqOMrd/Agbe9g8gr7vT2jm3jxMdvzdB4pU6tIiLjRPixx4g886y74/NR9rnPDut5kZjNl/74Es0dUS47+VBOTPQdAXco7+1PbeeOp7bz2u4mVi2s6XM+kvHAv2QJ/iVLuvYXL6bhk58C3JqSA+e8Fe/MmdgtLTjNzQSOP47ST1xF8NRTc1Ti/KIaEhGRccCxbZq/9d/J/eL3vBvf3LnDeuaNf1/Phtpmjjm0io+cNj/t3PHzJ3HVmQuZWVXIqzsb2d8cGta7xqKiC/+Lyh/djBEMJo/Fd+3CaWoCxyHyzLPUX/IB2v7whxyWMn8YjjO42fVE8oFlWY8Bp8yZM4dLL700x6URgbbb76DxmmsBMIJBpjz9JN4pU3JcqokhumkTLd+/iY6//R16aaopvPBCSq/+BL5DD8FpbMRu78BbVYlRWDjKpR0XhjTkS002IiJjXOSFF2m8/ivJ/eIPf0hhZAT5Fy6k6pafYLe1Ed+1C6OgAAyDg5dfSTSxFk7H3XfTcffdUFCQnB3XKCqi9JNXU/Lxj2kRvxGgJhsRkTEsvm8f9R/5SHISNN+SxZRe/Ykcl2pi8hQX41+0CN/cufjmzGHSXXdS+I63p1+UCCMATns7zd/6NvXvv5To66+nXeZ0dIxGkScUBRIRkTHKCYep//Dl2HvdlXSNigqqf/VLPMXFOS5ZfvCUlVH14x9R/bvbCZ51JkZREUBanxOA8COPsP/U09l36ukcePv57Fl+JLXzF7J35UmEHnssByUfn9RkIyIyBjmOQ+N1Xyb6wgvuAY+Hqlt+gm/OnFF5v207vPxGA2WFfuYlFtvLV8FTTiF4yik4joPT2opRXAzxOE1f+zptv/5NcpK6WLdakvj27dS/9xKCZ59F8SXvw798BYbXQ3TtOuK1tQSOPWbYHZMnEgUSkRHm2DY4DobXm+uiyDjW9r+/pf33XaM7yq//MsGTTxqVd6/ZdpAfPrSRDbXupGgXHjebq85cSDCQ33+mDcPAKE2EM4+Hiq9aFP3XBbTc9ANCjz4G0WjG+0IPPpQ2mV2Sz0fRxRdTcvmH8c/vGuXkxGLu+3y5+4p2QqEeNUHZplE2IhkMZ5RN+7330vKDH1L2hc8RXL1and1k0ML//jd173oPJL6YCi+4gMqbb8r6n6VtB1r58cObeHLjgR7nZlcXcc15Szn6kOqslmG8sltaiG3ditPSinfObIyCAprMG+j4818GdL939mx8s2Zht7cTW78eJxajYOWJFJ5zDsGzz8I7eXLyWicSAZ8PwzPyvS7s1laav/VtIs/9h5q//QUjEBjKY4b0B1WBRCSDoQYSJxpl36mnEd++AwD/kSsov/ZaClatzEo5ZeIJPfooBy+/Eqe9HQD/8mXU3HN3VoeXNrRF+Pkjm/nzC7uI213fCR4D7G5fEUfNreSDp8zjqLlVeDwK2/2Jvrae9rvuIvTEE8R37gLHwTN5Mk5bG/aBnsEvI8PAt2ghnvJy7Lp6Ylu3gt+Pf8ECCs99KwUrV7qLCBoG8V27iG3fAdEovsWL8R+2tEeQdWIxnPZ2PGVlXceiUTr++leav/0d4rt2AVD62c9Q9plPD+XH1rBfkVyLrl+PXVfftf/iS9Rd/C4KTj6JsmuvIbB8eQ5LJ2Nd251/pPEL1yRrRjyTJlH1i19kNYxs2dfCp29/IW3iM8OAc5ZN5/LT5/OfrfV8//4NtCcW2XthewMvbH+e6pIAJy+ewkXHz+aQySVZK99451+6hHLzK5R3O+44DpGn/03rr39N+LHHcUJ9TDznOMQ2bEw/FokQXbeO6Lp1fb7fM3UqgcMPx1NVidPeQWzrVqKbN0MkgveQQ/DPm4cTChF55RWc5vR1i6LrN+A4zqjV8qqGRCSD4TTZxA8epPVHP6b11v9NGyIIEDjheLyTaiDgB48Xw2OA14sRCOCpqcE7ebL7OWWyuz1lSlaqZWVscRyH1pt/6K7im+CdMYPqO27Dv2BB1t77wvaDfOH3L9IaiiWPHXNIFZ84exGLpnX963lvYwe/fnwLf3upNq0GBSDg8/Cp1Ys5/5iZap4cIicUIrp5C3Z9HUYwiG/2bBzbJvTAg3Tc/wCRZ58F2x618hgVFVR87asUnv+Oof43VZONyEgZiZlaY7trabnpJtr/cOeQ/zLxVFYSOOF4Ck44gcAJJ+BfukQBZYJx4nGarvsybbfdnjzmX7qU6tv+F+/UqVl77z/X7eWGe14hGne/A4oKvJjnH8HJiyf3+iW0+2A7dzy9nUdf20dDWyTt3JsPn8rn37qE8qIh9TmQPtiNjcTeeAOntQ2jrBTfvHkQjRJ6+B+EHnuc6Nq1xPe7iyB6q6vxLZgPtk346X/jtLYO+D3e6dMpeve7KLnsUjyVlcMpsgKJyEgZyanjo5u30PI/36Xjr38ddrmM8nIKTnwTRRdcQPDNZwy1w5mMEfG6Oho/93lCD/8jeaxg5UqqfvnztPb9kXbnv3dw04MbOkerUl0S4PvvO5qF0wb2zrjt8NKOBr5//3o27+v6wisr9POeE+dy3pEzqC4tyEbRZRCcWIzYxk3Etm3DbmnBCBbgnTED/6JFGAUFRNauw647gBEocDvVzjt0pGq5FEhERko21rKJbdtGbMtW7LZWiMbc5c0dG+I2TkcH8QMHsPfvJ75/P/F9+4nX1rqLfPXCU1VF4QXnU/yui9NWMJWxz7Ft2u/8I01f/zpOY9d/48Lz30Hljd/LWtCM2w4/eXgTdzy9PXlszqRivv++o5leOfh+KqFonJvu38C9a3b1ODe7uoh5U0o5/5hZHHtolZpz8osCichIGQuL6zmOQ2zTJsL/fobIM88QfubZXnvl+5cvo+iiiyh6x9vxVFSMckllMKKvv07jNdcSefa5tOMlV15B2XVfylqTXENbhBvueYVnt3R1uj5iVgXffc+Rw25meWLDfm56YAO1DZmnSz/mkCo+f+5S5kzSDLN5QoFEZKSMhUDSneM4xDZvpuNP99L+x7uI79nT86KCAgrPWU3RxRdRsGqV+puMIXZHB60/+jEtP/5J2gRa3tmzqfjm1wmedlrW3v3qzkau++PLaSNpTl48ma9euIygf2QmO4vGbP6xbi9/fmEXr7zR2KPzq8eAMw6bylnLpnH4zAoqivyqNZm4FEhERspYDCSpnHic8L/+Rfudf6TjgQeTC6+l8s6YQdFF76Toonfimz07B6UUcNejabvjd7T88EfYiY6HAPh8lFx5BaWf+iSeLA3rdRyHPz7zBjc/tDEtIHzgpEO5/PT5eLM0j0h7OMb2ujb+8sJu7luzs8dcJuAGlJlVRRw3bxLvXTmXaRXZG9oso06BRGSkjPVAkspuaKD93vtov/OPRF99NeM1gRNPpPhdFxM8ZzWexAJhkl1OOEz7XXfT8oObidfWpp3zH3UUld/5dlb7/rSGonzzvnU88tq+5LGyQh/mBctYubAma+/tbuOeZn700Cb+s7W+12sCPg9vXTGDt66YzpIZ5VkLSjJqFEhERsp4CiSpouteo+3OO+n4vz9hNzT0OG8UFRFcfTaFb3sbBatWZu1f5vnMbm2l/Q930nLLT7H37k0755k6lbLPfJqid78ra81pjuPwwCt7+OFDGznY2lVztnRGGV9/54ohdV4dCZv2NPPgq3t4cftBtu5vIxSNZ7yuwO9hWkUhRQEfRQVels+u5KLjZ2s48fiiQCIyUsZrIOnkhMOEHv4HbXfeSfixxzPPgxIIEDjmGIInraLg5JPwH3GEFgQconh9PaGHHqbj/gcIP/lkjwnxPJMmUfqJqyh+33uzumDZln0tfPdv63lxR3oYvfC4WVx99mICvrHTpygUjfPi9oP84tHNvLa7uc9rg34vpx82hRMX1DBvSglBv5dIzMbvNZhWUai+KGOPAonISBnvgSRVfM8e2u++h/a77ia2ZUuv1xkV5RScuJLgySdRcNIqLYvej9jOne5Mmg88QOS5/2QMfZ6aGkquuJziD7w/q01lbeEYv3psC3c+syOtr0hNaQGffstiTl+avQnWhstxHF7c0cDfX6rlmc111LWE+78pxYKppVx43GxOXTJZtShjhwKJyEiZSIGkk+M4RNeto+Pe+wj98xFimzb1eb139mwKTlpFwQkn4F+0yJ00aZSXIx9LHMchtnEjHfc/QOiBB4muXdvrtf6lSyl677spvvjirK5D09wR5e7n3uCPz+ygsT1l5I7H4OIT5vChU+dRXDC+lixrao+wvzlMKBpn2/5W7nx2B1v2DWy20TmTiplWUYjfa9DcEaUk6GfVwhpOXjKZ6hJN1DaKFEhERspEDCTdxffuJfyvJwn960nC//pX+giQTDwevLNn41+4AN/ChfgXLsS3cAG++fMnXF8UJxQiumkTsY2biG7ZQmzLVqLr1hLf8UbmGwyDwLHHEFy9msLVZ+ObMyer5atrCfP7f2/nT8/vpD2c3hfjyLmVfO4tS5g3pTSrZRgtjuPw2u4mntp0gFd2NlLb0EHcdvB5DPY2hXoML87EMGD+lFIOnVxCZXEAA2gNxZhcHmTx9DIWTyujpix/w3YWKJCIjJR8CCSpkpOwPfEvQk/8i8gzz+C0tw/4fu/MmfgWzMc3bx7eadPwVFbiqazAU1HhbldX46msHJNt/fGDDcRee43I2rVE171G9LV1xF7fDPHMnS6T/H4KVq2kcPVqgmefhbcmuyNXHMdhQ20z963Zxd9friUSS28imloR5MozFnD2EdPG5O9zNjS1R/j7S7X8c91e1tc2Dyic9Ka6JMCiaWVUlxTg8xp4PQZ+r4e5NSUcPrOcuTUlGv0zcAokIiMl3wJJd04kQuTFFwn/60l3ifNNm9zagWH8fWEUFeGdNRPfrNl4Z83EO2OGO0W6YSR+ARjudZNr8NZMxjO5Bk9VVbKzrWPbOOEwTns7TkcHTiiEEQhgFBe7fTSCQYjFiO/bR7y21v21dy/xvfuwDxzAbmnFaWvFaW3Dbm3FaWnBru99OGqmnyF4+ukEzzmb4OmnZ3W9mU4HmkM88Moe/v7SbrYdaOtx/pCaYt5/0qGcefhUfN6x02l1tHVEYuyoa6OuJUzMdij0e9l+oI3H1u/j5TcaMs6FMhhej0FZoZ/SoNsEFrMdAj4PC6aUsmhaGdMqCykN+gn6PYSiNqFonPIiP/Mml1AS9I/ATziuKJCIjJThBJLH1+8jbjscOrmEmVVFE+ZLwunoILplK7HXNxHb9DrR1193F+7asaP/2oTh8HgwSkshHMYJhfq9FscZVnDq5D3kEPxLFuObNw//vHnu59Ilo9KP5mBrmKdfr+Mfa/fy3Ja6jF+mS2eUc+nJh7JqYQ0e/cu9T22hGBv2NFPb0E5zRxTHgcKAlzfq29hQ28ymvS10RLL3Z3hyWZCKYj+liWDSGooRicWZUh5kdnUxUysKKSnwURz0JWthDNwQVFVSwKTSAooLfHgM9492WzhGgd9LSYFvxP/bt4VibNnfwpZ9rbxpwSSmDm3CuiEVanz1dhIZB37zxFY21LrDGP1eg9mTijmkpoRDa0qYXB7EY4BhGHgM8Ho8yephr8fA5/EQ8HkoCngpDHgpCvgoL/KPiVBjFBYSOPwwAocflnbciUTchQM3byG2ZQvxunrsxkbsxkacxkbshgbi+/bhtPX81/2A2Hafiwx2v3bQCgrwL1qI//DD8R+2FP9hh+FfsgRPScngnzVEjuOwZX8rT248wJMb97Nud1PGTBX0ezlt6RTOO2oGR84Zm01gY1Fx0MfRh1Rx9CFVGc/HbYed9W28vq+F9nCcWNwmZju0hWNsrG1m7a5G6lt7zoY8UPubQ2nT9nfadqCNZzYPvIauO4/hrrBcVOCjMODF7/Vg4P79YhjgMQx8XoNCv5eg30vccYjFHeK2+/PF4w4x20n+vC2hKHsbu8ppXnAE54ziDLoKJCIjyLYdtqdUq0fjDlv2tQ54lEAmhgEVRQGqSwJMKi2gusT9NaU8yMzqImZVFTGlvDBn7dtGIIB/0SL8ixb1eo3jODiNjcR27iS+c5f7uWePW7PSWaOR+GW3tmLvP+CufnzgQI8J3oxgEKOw0B29UlAAkQhOezt2e7s7/4dh4KmpwTt9Gt7p0/FOm4Z3yhS8kydjlJfhKS7BKCnGKC7BU1KMp7oawz+6Veq27bCjvo1X32jkxR0NrNl2MOMXVqej5lbylhUzOG3plHE3amY88HoM5taUMLem9xAajsZpCcVoCUUxAJ/XQ2N7hE17Wnh9bzMH2yK0hmKEonEK/V4K/F72NXWwva6NWDw7LRG2A43t0bQRViNp894WWJ6VR2ekP9nSK8uyZgJfBVYD1cAe4F7AMk2z5zSgmZ9xZuL+FcCRQCXwlGmaq/q4p6//e581TfOEbtc/BpzST1F+bZrmhwZS5uGIxGzeccxMtu1vZeuBVg40D25OhUwcx12ptaEtwuZego3PazC9opCZVUVdv6rdz+kVhTmvYTEMA6OykkBlJSxbNqh7nUgEu7XVDSLBYJ8znDqxGDjOqAeMvjiOw57GDl7b3cz63U28VtvExtpm2vtoIvAYsGx2JasW1nD6YVNzNruqdClIhIxJpV3Dh2dWFXH4zL5X147GbPY2ddAaitEcimJgUBL04fMY7G7o4I26Nupbw7SGY7SHY24uT9wbidkcbA1zoCVMOBpPNt0VBtyJ4drCsRH/Ob0eg7mTipk3pZQlM8pH/Pl9USCRjCzLmgc8DUwG7gM2AMcBnwRWW5a10jTNgdQ1fhx4OxACNuMGkoHYAdya4fiuDMduBR7r5TmfAKqA+wf43mEJBrx8avXi5H5LR5RtB1rZur+VbQdaaemI4QC242DbDvHEr5idqEaNO4RjNh2RGB2ROK3hGE0D+NdPLO7wRn07b9T3HBnjMWByeZDpFYXMqCxiWmUhMyq7tquKA2O66t8IBPBWZa5q73GtL3d/pcVth31NIXYdbGf3wXZ2HWxny/4W1tc2D+i/YXGBjxPmT2LVohpOXDBJk3xNEH6fh1nVxRnPLZw2vE7R0ZhNSyhKeyROezhGzHbc2kjcf8jYjtsc0x6JE4rG8RoGPq8Hn8fA63WbiH1eA5/HPV7g8zCjsgh/jmb0VSCR3vwEN4xcbZrmDzsPWpZ1I/Bp4BvAlQN4zn8D1+EGmlnAtgG+f7tpmjcM5ELTNG/NdNyyrEWACezDDVWjrrTQz7LZlSybPdAc1lMsbnOwLUJ9S5j61jB1Le6vPY0d7Ep88fXVvm07sLcxxN7GEC9s71mxFfB5mFTqdpyrKS2gpjTo7pe5+5NKg9SUFlCkpgJicZvazt/3evf3fndDR+KzfVBV81UlAZZML+fIOZUcObeSRdPKcl6TJeOL3+ehqqSAgcX1sU9/w0gPlmUdCpwFbAd+3O20CVwOXGJZ1mdN0+yzp6Jpmv9Oee4Il3FxwbIAAAiCSURBVLRflyc+f2OaZnYaWUeBz+thclmQyX1M3NQejrG7oZ2dKV+Uuw66+3Ut4T4HnURiNrUNHdQ2dPRZjoDPQ3GBj5Kgj5ICHyVBf8p253E/JYVdx4oL3GGS7rZvTH3hxuLu0MyOSJzmjmiiLT5CY1uEpvYoDe0RmtojNLRFOdgW5mCruz+U4aOlQR+Lp5ezdEYZS2aUs2R6GZPLgmO6ZkpktCmQSCanJz4fMk0zbdiCaZotlmU9hRtYTgD+maUyVFiW9UFgKtAErDFN85mB3mxZVgB4P25z7C+yU8Sxo6jAx4KpZSyY2rMKOByNs7cpRG2D+6/5PQ0d7G5od0NIo9u2PRCRmE0k5vZlGarCgDdteGNyRADgSUxEFfB58Hs7t70EfO4xr8dwm7kSzV224zaTOI6THLXkSYwuiNsOHYmw0ZGoru7+OZxJtHpTVRJI68czq7qIRdPKmFVVpPAh0g8FEsmkc7hEb4udvI4bSBaSvUCyHPhV6gHLsl4GLjFN89UB3P9fwCTgYdM0t/Z2kWVZlwKXZji1YsAlHeMK/F7mTCpmzqTM7dht4Rj1LW7HubqWEAea3Sahzv3OJqJwbAhDarvpDAgHBrmA2lgypTzIjMrCtM7Ds6qKmF5ZpBEwIsOg/3skk86u1b1N/tB5vO/u5UN3I3APbiAKAYuBa4ALgUcsy1phmubufp7R2Vzz836um0v/I3QmtOICtzlldi+BBdyRIuGYTVti2GNrOJbYjtEaitIW7tyOJbajtIVitHbbHkvzMHo9BkG/lwK/h7JCPxVFAcqL/FQWBSgvClBR5Kei2P2sLC6gqiRAVXFgTDU7iUwkCiQyFJ11z1n5ejFN87PdDj0PvNOyrLtxaz4+h9uxNiPLshbghoyBdGbdDjye4fj86urqGVOnjt1l20eTYbhf3kG/l+rSoa2aattOYuRQlNZQDNtxkkMcHQfitk007hCN20RjNpFun7G4g8fTOaGckdh291NHFTiOO7IoGPBS6PdSGHAnjSr0ewkG3J+h0O/N2UgCEclMgUQy6awB6W0Qelm360bLT3EDycn9XHc5bmjqtzNrYoTOrb2cHkP/nh//PB6D4qDbf2TK6E5vICLjgP6JIJlsTHwu7OX8gsRnb31MsuVA4rPXtoVEZ9YPkCedWUVEJgoFEsnk0cTnWZZlpf0ZsSyrFFgJdAADHvUyQjpnaO21kypwPlAD/KOvzqwiIjK2KJBID6ZpbgEewu3w+fFupy3cGorfps5BYlnWYsuyFjNMlmUdZVlWjxoQy7KW4U7GBnB7H4/o7Mz6s+GWRURERo/6kEhvPoY7dfzNlmWdAawHjgdOw22qua7b9esTn2mTLViWtQr4cGK3c+WqBZZl3dp5jWmal6bccjVwgWVZjwA7gTDuKJvVgBe3Geb3mQpsWdb8RPn2AX8e2I8pIiJjgQKJZGSa5hbLso6ha3G9t+Aurncz7uJ6Bwf4qPm4fTpSTe527NKU7XtxO80uw52gLQjU465F8wvTNPsKGh9hgJ1ZRURkbDGcsTQxgMjYov85REQGb0jTEqsPiYiIiOScAomIiIjknPqQiGTBAw88wN69e3NdDBGRIZs6dSqrV68etfcpkIj0bsjLsz777LMb6FqkUERk3NmxY8fG1atXD3s6h4FSIBHJjs4hzk3AS//f3t2EWlGHcRz/arYoWlQEhUqujJYtatHOTWWRUkStNLk3DeRC1EoQ8/FpKbYI6fWEHcgwIoKgqEXQpSBoEYnVIjAMCXqBIIpeJPG2mGMcLlhSZ85zZ873A2dxZwbuj/8c5vzOzP/MVAbpsZtoHm/gGLfHMZ5N5/f7Ff+24SRZSKR2nATWAccjYlNxll7KzEWahyg6xi1xjGfT2H4/Oc3/66RWSZJUzkIiSZLKWUgkSVI5C4kkSSrnpFapHUNgEfi6NEW/DXGM2zbEMZ5FQwr2u8+ykSRJ5bxkI0mSyllIJElSOQuJJEkq56RWaUIy82ImZF0VET+1HqZnMnMnMADejYg7L7DN28BdwEJEPDPNfF039t5dAjZGxFcX2O59YNPoz7mIGLafTtOwEo5fFhJp8vIf1v0xtRQ9EhEvZuYWYGtmLkTE0+PrM3M3TRl5xzLyn52l+Ux4CNi7fGVmbqS5nfj57dRPZccv31TShEXEgeoMPbULuBU4mJnvRcSXAJl5A3AI+BGYL8zXdd8D3wJzmbk/Is4uW7+T5gnYbwH3TDucpqPy+OUcEkmdEBE/0JSSy4GjmbkmM9cAR0fLHo6I7yoz9sAAuA64e3xhZl4K7AA+Ar4oyKUZYCGR1BkR8SZwBLgZ2D963QIMI+KNymw9cQz4leZsyLitwLU0hUVqhYVEUtc8Cpyimeewl+Zuko9UBuqLiPgFeBXYnJnrx1btAn4GXisJpplgIZHUKaMPzSeAS0av3aNlmowBzbjOA2TmBuA24JWI+K0ymPrNQiKpUzLzMmDP2KL7q7L0UUR8DHwGzGfmaprLN6vxco1aZiGR1DUHgRuBp4DjNB+cW2oj9c4A2ABsBuaATyLi09pI6jsLiaTOyMzbgQWab/B7gO3AGWCQmddUZuuZl4HfgeeBdcALtXE0CywkkjohM68GXgL+BLZFxJmI+Bx4nOYXIM9V5uuT0d04XwfW0/zq5lhtIs0CC4mkrngWWAvsi4gTY8ufBD4E7svMbSXJ+mkfcC9wh5OGNQ3eqVXSipeZ24EHgA9oCsjfIuJcZu4ATgCHM3MxIr4piNkrEXEaOF2dQ7PDMySSVrTMvB44THMfjAcj4tzybSLiFPAYcCVwJDNXTTelpP9r1dLSxTzgT5IkqT2eIZEkSeUsJJIkqZyFRJIklbOQSJKkchYSSZJUzkIiSZLKWUgkSVI5C4kkSSpnIZEkSeUsJJIkqdxfD8jYZ57Aoj8AAAAASUVORK5CYII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" ] @@ -371,7 +371,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ @@ -411,7 +411,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ @@ -433,7 +433,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 14, "metadata": {}, "outputs": [ { @@ -442,13 +442,13 @@ "Text(0.625,0.3,'AFM')" ] }, - "execution_count": 12, + "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -575,7 +575,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 15, "metadata": {}, "outputs": [], "source": [ @@ -595,7 +595,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 16, "metadata": {}, "outputs": [ { @@ -604,13 +604,13 @@ "Text(0.125,0.3,'AFM')" ] }, - "execution_count": 14, + "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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aYIllzX618StfZeMXv6QEL5IniedfoHnOCaRWrHA7olEaP3MpNUccEW5gJUrJXSQPIsG81fGZMzP7Nn//B6y/6rP4qVSIkYmUv/bHHqP5xJNINze7HVVVjLj6aqqz1n+QXEruInkSqa1lxDWfo2q//TL7ttzxC9ZecBF+e3uIkYmUr7Z/3suaT8zFD9Z08OrqaLr+Oqr22TvkyEqbkrtIHnlVVTRecTnVhx2W2df25z+z5uxzSAerU4lI/2z5/e9Zc86n8NvaAPCammiyNxKfNi3kyEqfkrtInnnRKA0XXkDN0Udn9rU/8CBrTj2N9Pr1IUYmUj5afvoz1l30aUgmAYiMHcvIhQuITZwYbmBlQsldpAC8SIT6s86k7uSTM/sSTz7J6hNPIvXuuyFGJlL6Nn3nu6z/3DUQdEiN7rSTG5Wyww4hR1Y+lNxFCsTzPOpOOpH6s8/K7Eu+9DKrZ88h+eab4QUmUqJ832fDF7/Exi9/JbMvNmkSTQss0TGjQ4ys/Ci5ixRY7dFH03DxxRBxH7fUsuWsnj2HjldeCTkykdLhp1Ks/+zVbP7e9zP74jNmMMLcQGTEiBAjK09K7iJFUHPYoTReeSXE4wCk31nF6jknknjqqZAjEwmf397OugsvZsvtd2T2Ve27LyOuvYZIbW2IkZUvJXeRIqnez31ZeTU1APjr19N8yidoX/RwyJGJhCe9ZQtrzj6H1j/9KbOv+tBDabzyCryqqhAjK29K7iJFVDVzJiNuNHiNjQD4LS00f/IMWu++O+TIRIovvX49a049jfYHHszsq/noUTRcdCFeNBpiZOVPyV2kyOJBB6HI6KCDUCLB2vPm0/KrX4cbmEgRpd59l9UnnkTiyScz++pOPon6s8/Giyg1DZX+giIhiO28M00LFxAZP97tSKdZf9nlbP7h/4UbmEgRJN96y40aeenlzL76s86i7qSTtLJbnii5i4Qkuv32jFywgOiECZl9G8yNbPzGN7XgjFSsjn/9i9XHzya1bLnbEYnQcPFF1H7s6N4fKAOi5C4SosiokTTZG4lNnZrZt+mb32LDDQY/nQ4xMpH8Szz9NKtnn0D6nVVuRyxG45VXUJM1XbPkh5K7SMgi9fU0Xfd54ntvXQij5f/9iHWfuRy/oyPEyETyp/3hxTSffCp+MAWzV1PDiGuvpTproSXJHyV3kRLg1dQw4rOfperAAzP7Wn/7W9bOm59ZNEOkXLX+7W80f/IM/JYWALyGBkbccANVs2b28UgZLCV3kRLhxWM0XnopNUcckdnX9vd/0Hz6GaSD5S5Fys2WX/+GtefNh2DZ48ioUTQtWEB8yuSQI6tsSu4iJcSLRqifdx61xx2X2Zd45BGaTzmV1Nq1IUYmMnCbf/h/rPvMZZBKARAZN46mLywktsvOIUdW+ZTcRUqM53nUnz6XurmnZfZ1PPMszbNPILXy7RAjE+kf3/fZ+I1vssHcmNkXnTCBkQsXEt1++/ACG0aU3EVKVN3xx9Mwfx4E436Tr77qxga//kbIkYn0zE+n2XCDYdM3v5XZF5s6laYbDZFRI0OMbHhRchcpYTVHHEHjZy6FYCrO1H/+w+o5J9DxwoshRyayLT+ZZN1lV9Dy/36U2Rd/z3touu7zRBoaQoxs+FFyFylx1QcdxIirr4ZgEY306tWsPvEk2h9/POTIRLby29pYe948Wn/zm8y+qgMPYMTVV2cWS5LiUXIXKQNV++xN0/XX4dXVAeBv3MiaU0+j7b77Qo5MBNKbN9P8yTNp+/s/MvuqP/RBGi/9DF48FmJkw5eSu0iZiE+bRpO9Ea+pCXAlpTVnf4otv/9DyJHJcJZau5bmk08hsXhxZl/tscfSMH8+XlQpJiz6y4uUkdjEiYxcuIDI2LFuR0cH6y66mJaf/TzcwGRYSq18m+Y5J9LxzLOZfXWnnUb9J0/XAjAhU32JSJmJ7rADTQsXsHHhF0itWAG+z/qrP0dy2TL8lha23HkXfksLXn09dXNm0zB/HrGJE8MOW8pcctkyNt9y69b/r9pafM+DYNY5PI/6886l9sgjww1UAJXcRcpSdMwYmhZYYpMmZfZt/v4PaPnpz/A3bwbfx9+8mZbb7+DdIz5M271qm5fBa7v3Pt494sO03H7H1v+vLVu2JvZIhMZLL1ViLyFK7iJlKjJiBCNuuJ7YlClbd3ZdKjaZxG9tZe28+SSXLStqfFIZksuWuTUOWlshmez+oGiU2KTdixuY9ErJXaSMRerqiE7Ytc/j/I4ONt/6wyJEJJVm8y239r06YTrNlj/9uTgBSb8ouYuUucTDi/s+KJlky52/LXwwUnG23HlXzyX2TqkUiQcfLE5A0i9K7iJlrr9LwvqbWwociVSizmVa+zxOSxOXFCV3kTLX39m/vIb6Akcilcir79//jWahKy1K7iJlruqQQzJzz/coFqNuzgnFCUgqSt2c2RDrY9R0NErVoYcWJyDpFyV3kTJX9/Fj+vzy9eJxGuadW6SIpJI0zJ+HF4/3flAsRt0xHytOQNIvSu4iZS46fjwjrrgcqqu3LcFHIni1tYy+9RZNZCODEps4kZHfubn7O6NRqK5mxBWXEx0/vriBSa80Q51IBajaZx9Gff0mtvzpz7Tfey8EQ5ci48cz9te/VGKXIYnU1m7dCKaV9WpqqDr0UOqO+ZgSewlSchepENHx42k891PUHXcs6y68CAB/3TqiO+4YcmRS7tqzhlvWHPURGs45J8RopD9ULS9SYaJjxxIZNw4Av7WVxNNPhxyRlLv2hx/O/B6fOTPESKS/lNxFKlB85ozM7+2LHu7lSJHepTdsoOPZ59yG5xGfPj3cgKRflNxFKlBVVukqu9QlMlDtS5ZAOg1AbPfdiTQ0hByR9IeSu0gFyq46TTy5lHRra4jRSDnLbm/PrhGS0qbkLlKBIiNHEt1lF7fR0UHi8cfDDUjKltrby5OSu0iFUru7DFVq9WqSL7/iNqJR4tOmhRuQ9JuSu0iFis+alfld7e4yGO2Lt1bJx/bYQ/PHlxEld5EKFZ8+PTPhSMezz5HesCHkiKTcqL29fCm5i1SoSH09sd13dxvptOv1LDIA7YsWZX6vUnt7WVFyF6lg8ZwhcYt7OVIkV/Ktt0gtf9NtVFURm7JHuAHJgCi5i1Sw+CyNd5fByW5vj++5J15cs5WXEyV3kQoWnzo1s1Jc8uVXSK1eHXJEUi6yR1iovb38KLmLVDCvpobYHlurU7NLYyI98X0/d3x71sgLKQ9K7iIVrmqW2t1lYJKvvUZ61bsAeHV1xCbuFnJEMlBK7iIVLqdTXVbvZ5GeZP+fxGdMx4sqVZQbvWMiFS42eQpUVwOQWv4mybfeCjkiKXU549tVJV+WlNxFKpwXj+VMG6p2d+mNn07n9pTX+PaypOQuMgzkDInTPPPSi44XXsBf72Yz9JqaiO68c8gRyWAouYsMA1Uzc+eZ930/xGiklGX3kq+aORMvmMJYyouSu8gwEJ04Ea++HoD0qndJvvZayBFJqcptb1eVfLlSchcZBrxoxC0kE1CveemOn0iQWPJoZlvt7eVLyV1kmMhdAlad6mRbiWeewd+yBYDI2LFEx40LOSIZLCV3kWEiZ7z74sX46XSI0Ugpyp1yVqX2clYyKwFYa+8HDuuy+3BjzP3Fj6Z71tr1QFP2PmOMeptIWYjuvBNeUxP+hg346zfQ8cILVGkMs2TJnXJWyb2c9Su5W2uXARMAa4y5MV/H9mAj0Br8nhjE47vGczhwb7D5PmPMY/14zCjgHaAKuMAY84PgrlVAGxAFthtqbCLF5HkeVTNnZr7A2x9+WMldMtKtrSSeXJrZ1vrt5a1kSu5ZLjXG3JbH890PLMddcJwB9JncgVNxib0d+GXnTmPMVABr7UTgjTzGKFIU8VmzspL7YhrPPz/kiKRUJB5/AhKuPBXdaScio0aFHJEMRcW3uRtjfOAnweap1tp4Px52RnD7B2PMusJEJlJ82e2oiSWP4ieGXDkmFSKnSl6l9rJX8ck90JncxwBH93agtXYKcECw+eNCBiVSbNFx2xMZOxYAf8sWEs88E3JEUiq0xGtlKcVq+T5ZayPAXFwJe29cJ7dm4CHgm8aYR7OPN8a8aq19GDg4eMzvezl9Z6l9FfC3PIcuErr4rFm03+u6obQvepjq/fYLOSIJW3rjRjqeedZteF7OnAhSnsqu5G6tbcQl3Z8AR+BK463ADsDJwGJr7cXdPLSzFH5M0GGuu3N7wOnB5s+NMcl8xi5SCnKGxD2seeYF2pcsgWBoZHTiRCKNDSFHJENVdsmdrUn9WeBjQL0xpgkYBVwLJIFvW2sP7vK4X+F6ulcBp/Rw7kOBiVnPI1JxqmbOyPyeeHIp6dbWXo6W4aB90dZJjTSCojKUVXK31h4BHA8sw42B/4sxphXAGLPeGPNl4Hrc67om+7HGmA3A74LNM+he5/6njTFqjJSKFBk1autKX4mE6yUtw1r7YnWmqzRlldyBM4Pb24wxa3s45vbg9nBrbbTLfZ1V8wdaaydn32GtrQVO7HKcSEVS1bx0SjU3k3zpZbcRjRKfNi3cgCQvyq1D3UHB7WXW2gv6OLYO1x7/bta+fwArgR2BTwIm677jgRG4av3bEalg8Zkzabv7bkDJfbjLXmcgNmUKXm1NiNFIvpRbyX2H4LYJGNfLT6e67AcbY1LAz4LNTwYd6Dp1VsnfbYzJviAQqTjxGdMhWKe745lnSW/cGHJEEpacJV5VJV8x+ltybwtua/txbGdCLUQvnc6LkeOMMX8Y5Dl+DHwW2A14P/CQtXY8cGTW/SIVLdLQQGy33Ui+/jqk07QveZTaDx/Z9wOl4mTX3GjK2crR35L7muB2h94OstZWA6O7PCafVgW3gx6EaYx5EejsQfTJ4HYubr74dcAfBx2dSBnJaXdfpKr54Si5YgWpZcvcRlUVsT2mhBqP5E9/k/tTwe1BvR4F++OSZPZj8umR4PaEIZ6ns3R+srW2hq1V8r8wxrQP8dwiZSF71a/s3tIyfOQs8TptGl68P7NzSznob3L/bXA7yVp7XC/HXR7cvkFhkvttwe2+1tqehrMBmZXdenIHbsW5JuA6YK9gv6rkZdiIT5sGUXctnnzpZVLNzSFHJMWm9vbK1a/kboy5D9fTHOBn1tr51trMuubW2qnW2p/hepwDXGeMSec3VDDG3A3cGWz+P+tkmgqstaOstcdZa38PfLOX86wB/hxsdo6Hf6XrtLUilcyrqSE2ZWs1bPYXvVQ+3/dpf3hRZlvrt1eWgQyFOw03J/tBwA+A71tr1+NmfKsPjvGB640xhRxKdgbuouR44AbgBmvtBsDDDWXrdFsf5/kxMJutFzgqtcuwE581k+TLboxz+8OLqTvu2JAjkmJJvvY66XdcNyavro7YbruFHJHkU7+HwhljmoHDcJ3Q/ozr3NY5AfErwP8C7zXGfDHfQXaJo8UYMxs4BleKX4HrxV8FvIobo34icGEfp/oLsDr4Pc3WIXIiw0aVJrMZtnJWgZs+HS/adc4vKWcDmsQmWEjlZ5RAIjTG/JmtVeuDeXwHsH3+IhIpP7EpU6CqChIJUsuWkVyxgthOO4UdlhRBTmc6tbdXnHKbxEZE8siLx4nvuWdmW0Pihgc/naZ9cVZnOrW3V5xSnH72R9baHwW/H26MuT/MYLIFfQya+jxQpIzEZ86g4xm3TlL7w4upP+XkkCOSQut48SX89esB8EaMILrLLiFHJPlWSsl9LVsnqemUCCOQXqxi62x9IhUhdxGZRfi+j+d5vTxCyl37oqxe8jNn6v2uQCWT3I0xc8KOoS/GmKlhxyCSb7Hddserq8PfsoX0O6tIvvY68cmTwg5LCih72GOVquQrktrcRYY5LxpxC8kE1Gu+svkdHSQe3TqlhzrTVSYldxHRPPPDSOLpZ/BbWgCIbLcdkXHj+niElCMldxHJTe6LF+On8z7BpJSInPHts9TeXqmU3EWE6C674DW5gSD++vV0vPhSyBFJoWg++eFByV1E8DyP+MwZme3s3tRSOfzWVhJPPpnZVnKvXEruIgJ0nYpWi8hUovYnnoR2t6p1dKediI4eHXJEUihK7iICQHzWrMzviUcfxe/oCDEaKYSc9va/uETGAAAgAElEQVSsmhqpPEruIgJAZPvtiYwdC4Df0kLi6WdCjkjyTfPJDx9K7iICdNPurvHuFSW9cWNmmmE8j/gMldwrmZK7iGRkV82r3b2ytD/6GARDHKMTJxJpbAw5IikkJXcRycguzSWefBK/tTXEaCSfskdAVKm9veIpuYtIRnT0aKKd67m3t7ve1VIRcsa3Z9XQSGVScheRHLmrxKndvRKk1qwh+VIwMVE0SmzatHADkoJTcheRHPFZGu9eaRKLH8n8Hps8mUhtbYjRSDEouYtIjvj0GRDMN97xzDOkN20KOSIZqjYNgRt2lNxFJEeksYHoxIluI5WifcmjvR4vpa/rYjFS+ZTcRWQbVWp3rxjJFStJvfGG24jHiU+ZEm5AUhRK7iKyjZx2d63vXtZySu3TpuFVVYUYjRSLkruIbCM+bU+IRgFIvvQSqTVrQo5IBit3CJyq5IcLJXcR2YZXW0Ns8uTMdnZvaykfvu+TeFid6YYjJXcR6VZ2ImhT1XxZSr7+Bqm33wbAq60ltvvuIUckxaLkLiLdyh3vruRejnJK7dOn4wVNLVL5lNxFpFvxPfaAeByA1BtvkFyxMuSIZKDU3j58KbmLSLe8eJx41jSlKr2XFz+dzu0pP1PzyQ8nSu4i0iNNRVu+ki+9THrdOgC8ESOI7rJzyBFJMSm5i0iPskt7iYcfxvf9EKORgcgptc+YgRfR1/1wondbRHoU2303vGCRkdTbb5N8/Y2QI5L+yh7hUKUlXocdJXcR6ZEXjRKfPj2znVC7e1nwOzpILFmS2db49uFHyV1EehXPKvWp3b08dDz7HH5LCwCRMWOIjB8XckRSbEruItKreJdFZPx0OsRopD/aFy3K/B6fORMvWMJXhg8ldxHpVXSXnfFGjAAgvW4dyZdeDjki6Uvu+Ha1tw9HSu4i0isvEtmm9C6ly29ro/2JJzLb8ZkzQoxGwqLkLiJ9qtI882Uj8cST0N4OQHSHHYiOGRNyRBIGJXcR6VN2yT2xZAl+R0eI0Uhvcsa3q0p+2FJyF5E+RcaPI7LddgD4LS10PPtcyBFJT3La2zUEbtiKhR2ASDlof+wxNt30dQDie+1F0/XX9Xhs4oUX2Hij7fOc0QkTGPX1mzLbbffdz+bvfS+z3XjlFVS/7309Pj69cSNr582HVAqA6sMOo/Hii/p83sHwPI/4zJm0338/4HpjV/3XewvyXDJ46U2bSDz9dGY7PmN6L0fn13D/jJQaldxF+qH9/gcyv3c89xypNWv69TivsRGvqanbn0jQA73H53zggd7vX7Qo86VVDLmd6jTevRQlHn0s8z8RnTixz/+xfNJnpLSo5C7Sh/SmTSSWLoXqaqr324/2RYtof/Ah6mYf3+djR37ly0S3335Az+fV10M6TWLpU6Q3bSLS2Njtce0PPAhAZOxY0qtXD+g5BiMnuT/xBH5bG15NTcGfV/ovdxW44lXJ6zNSelRyF+lD59V/9b77UnPkEW5fHyWGIYnFqDrgAEilehx2lvzPf0i+/jqRsWOJT51auFiyRMeMJrrjjm6jvd31ypaS0p49n3wRk7s+I6VHyV2kD53VjdWHHEJszz2JbLcdqRUr6Pj3qwV7zprDDnPPHZQ8eozp0EOhiJOPabx76UqtXUvHiy+6jUiE2PQ9i/bc+oyUHiV3kV4k33qL5Ouv4zU2En/PXnieR/XBBwPQ/sD9BXve2PQ9iYwdS/LVV0muWJlzn59OZ6YXrTns0ILF0B2t7166EosfyfwemzyZSLCaX6HpM1KalNxFepG5+j/wQLyY66JSfcgh7r6HF+N3JAvyvJ7nbX2eB3NLJh3PP096zRpiU6YQ3WGHgjx/T+Izts52lnj6adKbNxf1+aVnYbW36zNSmtShTqQHfipN+0MPAVD9/vdn9scm7Ep0111JvfkmiSefoPqAA3o8x/rPXQOR7q+hR938bSJ1dT0+tuawQ2m9807aH3qIulNPySz+0VkNWR1USxZTpLGR6MSJpJYtg1SKxJJHqTniQ0WPQ7aV3d6eXcNSSPqMlC6V3EV60PHsM6TXrSMydiyxabkdcqoPcV9k2cN/uuNv2oS/YUO3P/h+r4+N7rgjsSlTSK9enWlL9dvaaH/0UYjFqD7ooCG8usFTu3vpSa18m+Trr7uNeJz4HnsU5Xn1GSldKrmL9KCts7rx4IO3WTKz+uD3s+X2O1zV9IaNRJq6H4876rvfGfAwn5znOexQkv/+N+0PPEDVjBnuS6u9nar37U+ksWHQ5x2KqlkzafvTnwC1u5eK9sVZs9JNnYpXVVWU59VnpHSp5C7SjXTLFhKPPw7kVjd2io7djti0aW4oTtba2flWfdDBEIuRWPIofnuiJKobY3vumalG7XjhBVJr14YWizg567cXqUpen5HSppK7SDcSixdDsDjK+iuv7PXYtgceoPZjRxckjkhjA1XvfS+Jxx6j9e676Xj+ebzGRqr22acgz9evmGpriU2eTPJf/wJcL+3aYz4WWjzDne/7ocwnr89IaVPJXaQbbQOYgCP1xhskl79ZsFiqD3VDebbccQf4PtUHHZTplRyW3CFxancPU2rZMlIr3VAwr7aW2KRJRXlefUZK2/B+9SLdSL39DslXXgFg5E1fIzJ2bI/Hbv6f75B48knaH7if2BlnFCSeqve+F6+xEX/TJqA0qhvjM2fS+ts7gdxe2lJ82X//2PQ98aLRgj+nPiOlT8ldpIu2YOKN6IQJxCZO7PXYqgMPJPHkk7Q9tIi6uafjRfNfGebFY9SfdaYbflZdQ3zK5Lw/x0DF99gD4nHo6CD5+uukVr5NdMfhOZ44bNk1J8WaclafkdKn5C6Sxfd92h8Mxu32spRkp6p9/wuiUfz16+l45mmq3luYZVBrDj0UDi2dmba8qiri06bR8Zxb17198WLqTjwh5KiGHz+dpj1rZrpitLfrM1Ie1OYukqXjhRcyq0dVHdD3F1ekvj7zhdrWx3jeShOfuXW2ukL2hpaeJV9+hXSwtKrX2Eh0110L/pz6jJQHJXeRLJ0TbkR32IHYLrv06zHVwRdc4oknSLe0FCy2UtN1fXe/jwlHJP9yp5ydgdfDTG95fU59RsqCpw+kFJq19n7gsAkTJnDWWWcN+PHJFStJLV+e77BkiPxUirVnn4Pf2grAuEUPEtttt5CjGl7WnHU2bf+4B4D6886l9sMfDjki2UY8TvV++w7lDINa004ldxEZFC8azVlWVL3mi8tPJmlf8mhmu2rWrBCjkVKj5C4ig1aleeZD0/Hsc5mhX5ExY4iMHx9yRFJKlNxFZNDiWaXF9sWP4KfTIUYzvGzT3u4NqvZWKpSSu4gMWnSXXfAaGwFIr1lD8uVXQo5o+Mhd4lVV8pJLyV1EBs2LRHKHxKlqvij8tjban3g8sx2fMaOXo2U4UnIXkSHJqZpXci+KxNKnoK0dgMgOOxDdbruQI5JSo+QuIkOS06luyaP4yWSI0QwP2ZMGFWvKWSkvSu4iMiSR8eOJjBkDgL9pEx3PPhdyRJUvZ4nXIq3fLuVFyV1EhsTzvC6z1alqvpDSmzeTePrpzHZ8utrbZVtK7iIyZDnru2sym4JKPPoYBE0f0QkTiDSNCDkiKUVK7iIyZNm9tdufeBy/rS3EaCpb7vh2VclL95TcRWTIotttR2SHYD33tnbXm1sKIru9vUrt7dIDJXcRyYucXvNaArYgUmvX0fHCC24jEiG25569P0CGLSV3EcmLnHb3rNKl5E/ikUcgWMkzNmkSkbq6kCOSUqXkLiJ5kd1rO/H006Q3bw4xmsqk9nbpLyV3EcmLSNMIohMmuI1kksRjj/f+ABkwjW+X/lJyF5G8iavdvWBSb79N8tVX3UY8TnyPqeEGJCVNyV1E8qZK7e4F0774kczv8T32wKuuCjEaKXVK7iKSN7E994SI+1rpeOEFUmvXhRxR5chpb1eVvPRByV1E8iZSV0ds0iS34fuud7cMme/7ueu3z9T67dI7JXcRySvNM59/qeXLSa1YAYBXU0Ns0u4hRySlTsldRPIqd313tbvnQ/bfMbbnnnixWIjRSDlQcheRvIrvsQfE4wAkX32V1NtvhxxR+ctZv32WquSlb0ruIpJXXnWVS/CB7F7eMnC+7+eOb9fkNdIPSu4ikne5VfNqdx+K5CuvkF6zBgCvsZHohF1DjkjKgZK7iORd7mQ2D+MH86HLwOX0kp8xAy+ir23pm/5LRCTvYpN2x6upASC1YgWp5ctDjqh8aT55GQwldxHJOy8WIzZ9emZbveYHx08maX9kSWZbyV36S8ldRApC67sPXcdzz+Fv2gRAZPRoojvuEHJEUi6U3EWkIHIns1msdvdB6NpL3vO8EKORcqLkLiIFEZ2wK15jIwDpNWtIvvJKyBGVH7W3y2ApuYtIQXiRCPEZMzLb2b2+pW9+ezuJxx7PbCu5y0AouYtIwWie+cFLLF2K39YGQGT8eKJjtws5IiknSu4iUjA5yf2RJfjJZIjRlJfs9vYqldplgJTcRaRgojvuQGT0aAD8TZvoeO65kCMqHzmT12j9dhkgJXcRKRjP87bpNS99S7e0kHjqqcx2dt8Fkf5QcheRglK7+8AlHnsMgiaM6K67EmlqCjkiKTdK7iJSUNnJPfHY4/jt7SFGUx5UJS9DpeQuIgUVHbsdkfHjAfDb2kgsXRpyRKVPS7zKUCm5i0jBVandvd/S69bR8fzzbsPziO85vfcHiHRDyV1ECi67almT2fSu/ZElEEzVG5s8mUh9XcgRSTlScheRgsvu7Z146inSLS0hRlPacqecVS95GRwldxEpuEhTE9Fdd3UbyaTrDS7dUnu75IOSu4gURU7VvNrdu5VatYrkv//tNmIx4lOnhhuQlC0ldxEpipzx7mp371ZOqX3qVLzq6hCjkXKm5C4iRRHfczoE65F3PP886XXrQo6o9Ki9XfJFyV1EiiJSX0ds8mS34fu0L1kSbkAlSO3tki9K7iJSNNmlUVXN50ouX07qrbfcRnX11gshkUFQcheRotEiMj3LKbVPn44Xi4UYjZQ7JXcRKZr41GkQJK3kv/9NatWqkCMqHWpvl3xScheRovGqq3KGd6n07vi+n/O3qJo1K8RopBIouYtIUeW0u2sJWACS//oX6dWrAfDq64lOmBByRFLulNxFpKjU7r6t3F7yM/Ai+mqWodF/kIgUVWzyZAgmZ0m99RbJ5ctDjih87YsWZX6Pq0pe8kDJXUSKyovFiE/fuozpcC+9+6mUWwkuoPHtkg9K7iJSdGp336rj+efxN24EIDJqFNEddww5IqkESu4iUnTZvcHbH16MH6xfPhxlT+YTnzkTL5iiV2QolNxFpOiiEybg1dcDkF69muS//hVyROHJGd8+S1Xykh9K7iJSdF4k0qVqfni2u/uJBIlHt65tr/Z2yRcldxEJRXav8Oze4sNJYulS/LY2ACLjxhEdOzbkiKRSKLmLSChyxrs/sgQ/lQoxmnBoFTgpFCV3EQlFdMcdiYwaBYC/cSMdzz8fckTFl93eXqX2dskjLTtUBNbaE4HDgL2B9wCNwM+NMacP8DxfBfYF9gC2A1qB5cDvgO8YY9b08DgPOAM4G9gLqAXeAR4HrjPG/Cvr2GVAX3Nf3mCMWTiQ2EW68jyP+MyZtD/0EOB6jVe95z0hR1U86S1bSCx9KrMdn6HFYiR/lNyL4zpcUt8M/AeYNsjzXAYsBf4BvAvUAwcANwLzrLUHGGPeyn6AtbYG+DVwDPAKcDuwCdgROAR3oZDdVfm/gZHdPLcHXAPEgb8OMn6RHNFdd8n8vvFLX2bTzf9D3ZzZNMyfR2zixPACK6DksmVsvuVWWn79a+jocDvr6zNt7yL5oOReHJfhkvqruBL8fYM8zwhjzDbfANbaLwLX4pLvhV3u/gYusX8ZV0pPd3lsPHvbGPPf3T2xtfYjuMT+lDHmiUHGL5KReOoptvz6Nzn7/M2babn9Drb8+jeMvvUWaj54eEjRFUbbvfexdt58/I4OSCa33rFlC+uuvIoRV1xO1T77hBegVAy1uReBMeY+Y8y/jTFDmqmju8Qe+FVwOyV7p7V2EnA+rvr9810Te3DOjn4+/bzg9pZ+Hi/So9Q777DxG9+ERGLbO5NJ/NZW1s6bT3LZsqLHVijJZctcYm9tzU3sAL4P7e1s/MY3Sb3zTjgBSkVRyb0yfDy4fbbL/k/gLuB+DIyw1n4c2AVYA9xrjHm1Pye31o4LnmMzrlpfZEi2/PFP2ya4Lvy2NppP+QTxaYNtxSotHS+/3HfVezLJlj/9mcZzP1WcoKRiKbmXIWvtlUAD0ITrYPd+XGL/SpdD9wtum4DXgDFZ9/nW2u8Dlxhj+hqDdA6uSv42Y8ymXuI6Czirm7v27uP8vfKq4ngN9UM5hZSYxKKHoK+hb75P6j//IfWf/xQnqFKQSpF46CG8z1wSdiSSJ14s3vdBBaDkXp6uBMZlbd8NnGWMWd3luO2D2wXAPcHjlgH746rXLwRW4zrkdSvoaX9usHlrH3FNxPUpyKvo2LGa3KPC+K3qPNYTv7WVqr32CjsMKXNK7mXIGDMeMtXlB+FK7E9Za48xxizNOjQa3L4NzDbGtAbb9wbD85YCl1trv2SM6abxE4AjgN2Bpf3oSLcMeKCb/ZPHjBmz0/jx4/t6aTJMePX1+Js3931cbS2jvvfdIkRUeGsvuBD60SNetVSSD0ruZcwYswq4y1q7FDec7SdA9kwY64Lbu7MSe+djn7HWvgFMAvYEnunhaTo70vVVascYcxtwWw93D99lv2QbdXNm03L7Hb23u8di1J18MrUfPrJ4gRVQ/ckn9e81zzmheEFJxVJv+QpgjFkOvAjMsNZul3XXK8Ht+h4e2pn8a7u701q7PXAc6kgnedYwfx5evPe2SC8ep2Heub0eU06G42uW8Ci5V44dg9vsXkr/DG63mdfSWlvN1qFzy3o459m4jnR39NaRTmSgYhMnMvrWW/BqayHWpQIxFsOrrWX0rbdU1EQ2w/E1S3iU3EuMtTZurZ0WjFHP3j/NWrtNo7W1NhJMYrM9sNgYsy7r7r8CrwMfsdZ2rdu8HteL/gFjzDYDa7t0pNPYdsm7mg8ezvb3/J36uXPxGhvA8/AaG6ifO5ft7/l7xU1gA8PzNUs4PN9XU2ihWWuPB44PNscDH8El3YeCfc3GmCuDYycCbwDLjTETs87xGeAm4EHcsLY1uB7zh+E6vL0DfMgY82KX534/8HegCrgLNxf9fsChuJ7y78+eWz7rcR/C9bBfaoz5r6G8/oD+0UREBs4bzIPUoa449gbO7LJv9+AHXMK9so9z3IPr1HYwbp76kUALriPdT4GbjTFruz7IGLPIWrsvYIDDg8etCs610BjT0yDifnekExGR0qKSuxSL/tFERAZuUCV3tbmLiIhUGCV3ERGRCqM2dyl5d999N+9opSwRKWPjx4/nqKOOKtrzKblLsQyq3Qjg0UcffRmYmsdYRESKavny5a8cddRRRVviUMldykFDcLsBeDrMQMrE3rg5DMrp71WOMQ9Vub7mco07LJ1/r4a+DswnJXcpB68COwFPG2M+EHIsJc9aez9u/oOy+XuVY8xDVa6vuVzjDkvW3+vVYj6vOtSJiIhUGCV3ERGRCqPkLiIiUmGU3EVERCqMOtRJObgNuJ+el6aVXLdRfn+v2yi/mIfqNsrzNd9GecYdltsI4e+lueVFREQqjKrlRUREKoySu4iISIVRchcREakwSu4iIiIVRsldRESkwii5S8Ww1sastR+w1taHHUu5stbuaq39tbX21GB70Kv5iXSy1h4YdgzDjZK7lD1r7Uhr7deABPB9YFzIIZUda+17rLV3AW8AxwC7ARhjSmasbPA+HxP8Hg07nkKx1saD27L/frbWnmetXQb8yVq7X9jxlBJr7eHW2hestWcH23m9kNYkNlK2rLUTgBuBM4BNwI+BPwOrQgyrrFhrDwG+AByCm2Tja8BfKKGlPK21o4ErgGuC7XHGmNXWWq+ULj6GKrhwuRK4B/eelCVrbQy4CrgcGA3cB/wCeDPMuEqFtfYE4AZgFrAciEP+L6SV3KXsWGu3B74BzMUl8u/hkvpjxpi1YcZWLoIv4O8C5wGvA58FFgNLjTFtYcbWKSi5HoKL7aPAOmAUcAlwPa7mMRVagHlird0LlwznBruqrbX/Y4zZUC4XMEGpswr4Ku5iuwb4G/AbYJExZnmI4ZUEa+05uP/bCcAS4DLgn8BLhXg+JXcpR+8FPgS8A8wH7jPGbO7uwHL5ciym4G+StNa+Eex63Bjz9az7o8aYUkia2wEX4hL7t4E/AX8FLrXWftEY01bu76+1dn/gJtxFzN9wFy/vA+YAPwI8oORfnzHGt9bW4i682nHv213GmPXZx5X7+zUYQTPLr4DjcEn9OuApY8yLhXxeJXcpG1lfDItxH5aLgFZjzGZrbRUwGVeam4Ar0T9tjEmGFnDp6kwYtwGfAE4OShVp4FBgurV2Fq4kdg/wV2PM6hDibMGVbO4wxvwOwFr7S1wJ9wLgW5R/6X0PYCxwpTHmm0EzyQPA6dbanxtjEqWYEK21EWNMOms7ZoxZb639Hi6xx4PtKDAeqMZV0b9rrX3bGNMRTuTFFfydOqy19wMfB940xvw86/6a4CK1yhiTyOdza255KUvW2qOAn+AS/ReAo4ETgGm4NqwNwCPANcaYZ8KKM0zW2hG4znE+8DauejQZ3BcxxqSttdfi/n4/wFXPXws0AZuBxuBUjwDnG2OeK3aisdbWAa1ANKhtOAD3nr9jjNmxWHHkW+ff0VrbAEw0xjwf7K/FXdAcAJxsjPlNCdWkAJk+D6uytiOAZ4xJBf1g3sD9z5yLex1zgb1wNTHrgEXAtcaYF4oefJFlvc/b4Wpm9sFdzKWAo4D/wtVEAvwd+JUx5o1uTzZASu5SVrI+LGNwnb/Oxn2Z7Ab8A9cZbBfgwODnUeAsY8wrIYVcdNba8bi2vbNwbZ8pXC3dX4AvG2MettZWG2ParbW7475Udgc6gFuCH4CpwOnA8cDdxpiji/pCemCt/T2uFHSOMea2Ukt+Q2Wt/QTwc+CPxpjjwo6nk7X2eFzCHo+7eF4BmM5kFJTek0HtyknAs7ik/iJwNy6pHQRMAp7CfS6LfsFYbFnfWVfh+iTcjrvIuQDYAjQDO+M+o/8CzjDGPDbUv0vZD7WQ4aXzn90YswaXlN7A9cLdyxjzEWPMt40xV+K+/B/GtV+eZK2tCSvmYrHWRoIe13fjEvLPgEtxHXfuxdVufBUgSOyeMeZ14LfA74ADjDGXGGNeCH7uBM4B1gNHdY5VDmvse9bwt+8Gt1cDlGpiH8Lf6ffAC7i/+UeCc4U29M9ae6i19gFc57gpQC2wN+7C76dBbQpAZ4xfDG5TwEnGmJnGmCuNMWfi+hL8GleCvaRYr6GQ+vE+d97/K+DfwGm4i5/PABOB9+P6EN2Ga6b5Cgy997ySu4TKWruLtfYya+1Z1trDssb49viBybrvIdwH4WJjzPNBcvOCKue1uF70adwHJzoMJmTZF/g/XKeszwGfNcZ8xxjzXdyX6n+Ag7ImFOnsc/M9XIn+qeDv5wEE7YDrcXMHgGv2GJTBvM9ddSZxY8zfgQeBqdbaY4PzxEvh/bXWHmGtvdhaexhZ8y0M8HVuwV3AxIFPBvtCuYCx1n4Y9/7vgOvRf4IxZgbwAVyyOgjXO77zgjFijHkW+BJwtTHmt8F5Ov/XXsBdYLYBH7HW7lqOpfaBvM9B85cXjBj4BfBDYP/gs7nWGLPSGPMQriS/CviAtfbgns7XX0ruEgpr7U7W2v/DtfMuBP4fbjzs3dba3Xv7wGeV3lcCP+lsuzPGpIP7Oh/7F1y118FAdTl+iQxQB+61H2WM+akxZgNkOu1sxJXQAXYF6OzUZIxZbox5PPjdz/o7dd6uDG6TA60qHMr73MP5OkuH3wtur+18LWG+v9baOdbaV3Dtql/Dvca/WWvnBfENNLZf4WqkPp71RV/U0nvQ32E+rpnrfGPMtzr7BuCq2r+Dm19it6CZLNsXjDH3dG509vUIOuGtxCX5CK6TXdkYwvvcmaS/D3zdGJMz5j+4kG7HJX5wNW9DKr0ruUtYFuCq9b6P67F9FO4L7XDgh9bafftzkuADkdHlSncyrmrwWaCtFEp2hRIk3aeAY4GXrbWZmoqgN26UrSWMXofgBB2kMskf+Fhw+8wgvmzy8j53yirB/gbXbrt/5zmstcdaa8/vJtEUVFB6+z6uE+JluNf5TVw/hh9Ya+cM9JxBzdMtuE6Npwf7Utba3YJOeMVoHkni2v5nG2Pu7XzO4H8thZsRMg5UGWPWBPvTQazbzJWQdXESw03gkqKMJrYZyvuc9Xd5xxjzr24O6Rx50Pl9tmao8apDnRSdtXY2rhT5C2PMaVn7RwM34z40vwI+bYxp7k9p0W47NKcB90GcC9xojFlQgJdSFrI69DyB67G8n+nH0DZr7Y644YbX4KoTT8/+G/fj8YV4nz0gZtzwotNxIyaewCX604B64GBjzCP9jXMorLXVwP24ZHWMMeb+rPvOwtVU/Bs4zxjzYD/P2fl+jcddmKaB83FV45cDDxhjzi1GRzRrbV3QTNBdfAfhmkd+ZIw5r4fHd14opoPtKK7JaCGu6eEyID2Q/6swFOJ9Dh7b9XvrEVw/oWONMX8aSswquUvR2K1zZe8W3P4p2O9Z19N2LW7muSW4NuLONt4+SyhZXx7jrLUfxbU9z8V13vlG3l5EGQq+iGfghtz8safEHvRZiFtr97LWXoT78r0SN3Tp5s62w76er8Dvsx8k9pG4cfhtuL4G5+E6DR5UrMQeGI/rZPZPY8z9wd+ws33557jmgynAGdbacdB3iTur2ekd4I/A9riplb8b/L48+7jB6s972TWxd3EYLof8rZfHp4P/m5rgYuBruFTJiKUAAA1LSURBVJEcDwLfMMYkSz2xB/L+PkPO99Z0a+1tuMR+81ATO2gSGymirA/xlOC2s+opYrZONvMcrt3pQOAT1to7jDEbeyulWDc2+FO4tvUdcFfXjbhJTr5ijGnJ/6spLGvtLsCJuCEzbwCLg6Q22NJaZwL9Q3D+nOFjwRfRYbiLogZcj+gtuBLWTZ3NH/157kK9z1lxdk5i81+4BP+/wFeN6/lfbKNw7cbjIPPa03br5CW343pDH4372/+hn7UTh+GaMD4S7G4GPmeM+X6PD+wHa+0RuLkgngNewc3yOKCZ44KLxRpcR9U1uKmfu3uukbgLr4/iPpcH4iaY+gNwnTFm2VBeS5Hl7X22W6fqHY0bKngwcCSwP66m6wedx6nNXcpCVptbZ5vTxyC3J3Dw5f9P3Pj0/XD/9L0yxrQC03HD3+px1fE7GWOu6E/1cykpQAe0iHWz952M+0J/BLbtfR2c901cW/YfgHnGmHHGmC907dfQj+csyPucFeduuETxXWCcMWZ+SIkdXCn6P0C9tXY6ZL6UOy9wnsBNmTseOLSzvbwPs3DNFp/FJfWTjTGThpLYC9DhbwrwQVyH1tasUmy2FuAU3IX3gbj/vf2NMcdndcwrF/l+nw/H9X35Da5poho41RhzkjHmZdBQOCkjWV/ui3CddfYP2nW7VmGtwlVH1gL7BFfHmX90a+1Ua+3J1tpRWY/5PG54zoHGmOvKLalnyXcHtDRuTPJ04GcmmIM/qH7f31p7dNaxr+H6J5xrjLljsC+gwO8zwH8DtSVy8ZYAngd2wpWIM1/KwZd/Ajed7CrcsLG67Adba+uC9tzs4WLrce/50caYvY0xvxlKgPns8Jf1/p0U3N4FW3vDW2vHdL4e4zpkfhXXyfMAY8xpxpgnhvJaQpS39zl43Au4+QC+DhxpjHmvMebX+QxYyV3C8A5ujPosuimxBSXFl3DtqTvB1i+VoKrvR7gOXh/Mesw6Y8wTpoznkg86oJ0N/Na4yWT+aNyY7gtxs1odBlxh3VSWA+ktPR/3t7zTWltlrX0/bvGKO3DrbO/eeWAfbawDlff3OXjcpoHWJhRK0OSzCBgJHB50Fuz63jyBm/73AFwJjeCY9wLP4JqPss/5ZlBjcvdQ4wsSyldwNVpXGGNuNsb83riJnj4dHPYla+2h/Tmf2TqV6inAi8aYRcHz7GytPRm4lWByoeD4V40xD5qs6WrLUT7f5+Ai9i3g28YYa4xZUoiYldylKLopsf0eV2I7wVo7OvjSiGQdtwzXLjUr6JTjB1fI64HHcVfReZmDOWyF7IBmrd0J13b/LG5o4FdxCfN6XGI9JJ9V2sP0fb4dF+PHcf0AMvMFBH0bmnHt2+BqUTq14KZiPd+6uQgKcWHan45gezCwjmD7B+f8obV2rLX2U7ikfjtwBG7seyXK1/vcOSyuoIvnKLlLwWR/SQQfgLi1dmRQhfUPXHvrMQTjeMnt4LkBNwTo5azzdN5+zhizlzFmaWFfQXEMsANaHNcBbYTpX+/1g3CdCxvZOh3tA8BUY8wxxpiHhxr/cH+fg45hd+ImBzo96AyJdfP3dzZRxHBf8p0LxESNW+/gNFy/gW3GhefJNh3BjJv/PRIkl9txF35H43pq96ett7Maf2fc6/5fXMewy4wxTcaYb/X4yDJW4u/zNjTOXQrOut7s7wFm43piX4/rBX48rnfoJuBQE6zeFrSxfgHXI/pMY8xPw4i7WIIvgJS19jJcCf07xpht5t221u4K/BL3RXqGMea3ffWotdZ+G1f9uhk3d/UXjDHvFuh1DNv32brV0H6MWzL3W8aYK7LuOwTXNv0G8CHjZgssVlyjcFXCG4BTjDEvZv/PBJ0tLa4q/Zu4PhebeznfTsCTuCF54EqqC4bSR6OclOr73B0ldymYoPrvSFxnsFNw01jeDZwWVLtirf0WrjT5Li4BvInr/HUirvfp6cW82g2TtXY/3GI3S4E5xpiVXb6Iq4ErcAnxS8ANJncCjKm45PoPY8y6YN903FCk7xSqnVrvs2Ot3R/XG70JdyH1RPD7XNyKaOcYY7odNlbAmOpxcz0cAJxr3GJAnfd1TkZzFK5/wxvA8dkXf9ZNQZvq/N+x1k4Mjo3h/v/uK9ZrKRWl+D53R9XyUkgp3BSanROhTDPGHG2MWW+3DpdagOtElsJV21pc79rv4D4kZf2FP0CF6Gj4ojHmGwXugKb3GTDGPIZb6OVu3HK738K9zg5czUTRv/AL0OHvLdxKb4cMx8QOpfk+d0cldykoa+3e/7+9+4uVoyzjOP49lCgWCGI0BUUlQFKxGCSgErxpNRq9MEWJaExpgsRIIl74F2NMnjw3/rtBhYQr1EYIcgNFNCpE4EoNYiwqFqOhR9HQmhYkBIQe4HjxvtOzbHf3nLazO6fT7ydpdt+d2dk33bS/fd955h1gT0Q8XtvHAc3a1IP7nUYp/lkH3FfP1/beiCnSqymXev2Ucr/rJ+rfWVO4cwGl0GxHRFw0eIw6Bb+pvm+m56n9npdkuePdOcAG4MBNeTrsz5mUNQXWUJZHvWdgW3NK6FbKrMvmiLirbltP+TEJsLYPP8DatNq+52GuUKepiogdcGBhk8UYsdRkDafd1NWy+m4w0JsCNODEOtIdLkD7HuXfaVNZ+7ICtHqcOcod3L4SZUGfmfN7XlIL1XayFIydioj5zLydckpnS2Y+EhGP1UKwZkZnZCFYZn6CUmlvsA9Zbd/zMEfumrrlir6OVX0rQPN7Xr2OpkIwtcNwl2bMAjR14WgpBFM7LKiTZs8CNM3c0VIIpnY4cpc6YAGaurLaC8HUDsNd6tAKCtD8ByrpkBnuUkcMb0nTYrhLktQzFtRJktQzhrskST1juEuS1DOGuyRJPWO4S5LUM4a7JEk9Y7hLktQzhrskST1juEuS1DOGuyRJPWO4S5LUM8d33QFJmobMPOjGGREx10VfRsnM7cDmoZc3RcT9HXRHPWO4S+q7vcCLbR0sM7cBW4GdEfHWFb7nM8ANwPPAaRHxX+BJYE/d5XU4k6oWGe6S+u4dETHf4vF+SAn3czPzooh4cAXv2Vof76zBTkRc2WzMzHngzS32Ucc4fylK0qG5H/hHfb51wn4AZOZ64J21uW1KfZJexnCXpEMQEYvAj2rz45m53Axo8wNgN/DLqXVMGuC0vKRODUxJfyAiDgq/zDwZeAqYA86IiH9PoQ/nAZ8HNgGnA88BD1NC/KaIWBh6yzbga5Rz5R8E7hpz3DlgS23eEhGtnfuXJnHkLqkzmflqls417xiz2/mUYN83pWC/BngIuBI4E3gBOAm4BLgRuDsz1w6+JyL+Dvy6NidNzW8E3lSfOyWvmTHcJXXp/Pq4OyL2jNnn7fXxobY/PDM3A9cD/wO+CqyLiJOAVwHvB/5KCejrRry9CesP1R8pozTB/4eI+FNb/ZaWY7hL6lIT3ONG7YP7tBrumbkG+G5tXhER34iI/wBExEJE3EOZcn8G+GRmnj50iNso0/evBC4fcfy1wGW16ahdM2W4S+pSM3KfFO7NPm2P3DdSTgnMR8Qdo3aIiF3Abyn1SRuHtj0F3Fmbo6bmPwycTJnmv7WVHksrZEGdpC5NHLnX0fV5tdl2uF9SH1+fmbsn7HdKfXzjiG3bgI8B787MsyLi0YFtTeD/vJkRkGbFkbukTtRLyJoV3saN3N8CnAAsAH9puQvNNPsrgHUT/pxQ91s7fADgbuDx+vyK5sU6hf/e2nRKXjPnyF1SV86lnK9+BvjbmH2aKfmdEbG/5c9vBjd3RMRHDucAEfFiZt4MfIkS7lk3bQHWAE8w5jI5aZocuUvqSjMl/+eIeGnMPhfXx9Yr5Vla131F68NP0IzMz87MZqq/GcX/eAo/SqRlGe6SutKMykdeAlen7S+tzWmE+2/q4/rM3HC4B4mIh4Hf1+bWzLwAeFttOyWvThjukrrSjNzPHrP9CywVsf1xCp//K+Cf9fl1tXhvpMw8dZljNSF+OfCp+vyRiHjgyLooHR7DXVJXmpH7hsz8dma+BiAzz8jMbwFfH9h3ITPf0OaH1yVlPwssAu+jrET3rrpkLJl5fGZemJnfBB6dcCgol7otAKcCn66vOWpXZwx3STNXg/q1lGD9BaUgbV9m7gceA75MWfq1cS9wddv9iIifAFcB+4H3UK5pfzYz91IWqHkQuBYYtwJdc5y9wM9q8zjgJeDmtvsrrZThLqkLzZT8LspU9veBfZTR7wPARyPiGuAW4Fngd8DIhWaOVET8AFgPfIdys5gXKNe27wPuA75IWXN+OYMj9Xsj4l/t9lRaOS+Fk9SFA6vORcTTlNHzVcM7RcSW4demISLmgc8d4TG2U25wI3XOkbukLkztZjCSHLlL6sa01osfZVdmWVsmIlbNyDoztwObu+6H+slwlzRTmXkicE5tTjPcx91CdrV4koP76II3asXc4uJi132QdAzJzIspC8g8DZwSEf4nJLXMcJckqWcsqJMkqWcMd0mSesZwlySpZwx3SZJ6xnCXJKlnDHdJknrGcJckqWf+D8qYQoP3Dy9SAAAAAElFTkSuQmCC\n", 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\n", 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" ] @@ -665,7 +665,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 17, "metadata": {}, "outputs": [], "source": [ @@ -679,7 +679,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 18, "metadata": {}, "outputs": [ { @@ -688,13 +688,13 @@ "Text(0.5,0,'DOS')" ] }, - "execution_count": 16, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -706,20 +706,20 @@ "source": [ "# -- Bandstructure\n", "ax_bs = plt.subplot(gs[0])\n", - "ax_bs.bsplot(e_k, path, color='grey', ls=\"dotted\", alpha=0.5)\n", - "ax_bs.bsplot(e_k_nn, path)\n", + "ax_bs.bsplot(e_k[0,0], path, color='grey', ls=\"dotted\", alpha=0.5)\n", + "ax_bs.bsplot(e_k_nn[0,0], path)\n", "ax_bs.set_ylabel('$\\epsilon(\\mathbf{k})$', rotation=0, ha='right')\n", "\n", "# -- Density of states\n", "ax_dos = plt.subplot(gs[1])\n", - "ax_dos.dosplot(e_k, color='grey', linestyle='dotted')\n", - "ax_dos.dosplot(e_k_nn)\n", + "ax_dos.dosplot(e_k[0,0], color='grey', linestyle='dotted')\n", + "ax_dos.dosplot(e_k_nn[0,0])\n", "ax_dos.set_xlabel('DOS')" ] }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 19, "metadata": {}, "outputs": [], "source": [ @@ -739,7 +739,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 20, "metadata": {}, "outputs": [ { @@ -748,13 +748,13 @@ "Text(0.08,0.1,'AFM')" ] }, - "execution_count": 18, + "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -856,7 +856,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 21, "metadata": {}, "outputs": [], "source": [ @@ -883,7 +883,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 22, "metadata": {}, "outputs": [], "source": [ @@ -906,7 +906,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 23, "metadata": {}, "outputs": [ { @@ -915,13 +915,13 @@ "Text(0.07,0.15,'CDW')" ] }, - "execution_count": 21, + "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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gcaLMUBEiIl12WsqaIWs/3MP2fdUephEREekd4vH4oQPSFy/C5/N5mChzVISISJcNGRBm0vAiAOJxWLVeixeKiIi0pe75F4hu2QKALxIhfNrpHifKHBUhItItUgeoP/j6dmobGj1MIyIikv2qVjQNSA+dMQdfJOxhmsxSESIi3WLy8CJK+uUDUF7TwFObdnmcSEREJHtFt2+n9oknk+1wHxmQnqAiRES6hd/vO2RsyKp1GqAuIiLSkupbb4NYDIC8KVMIDh/ucaLMUhEiIt1m1rjBBP3OgLp3tpfzzvaDHicSERHJPvG6OqpuvyPZ7mu9IKAiRES6Ub9wHieOGZRsa7peERGRw9U88gixPc66Wv6SEvKnn+hxosxTESIi3Sp1gPpTm3ZxoKrewzQiIiLZp2p5yrS8C+bjCwQ8TOMNFSEi0q1Gl/bjqJICAOqjMR7asN3jRCIiItmjftPb1K9f7zQCAcLz5nkbyCMqQkSk26X2hqxav5XGWNzDNCIiItmj6uamXpDQjBn4Bw70MI13VISISLc7cUwJhSGna3nH/hpe/nCPx4lERES8Fzt4kJpV9yXb4cV9b0B6gooQEel2+UE/M44uTbY1QF1ERASq776HeE0NAIFRowiOH+9xIu+oCBGRHnH6+FJ87vOXP9zDtn3VnuYRERHxUjwWo3JF061YkUWL8Pl8rRyR21SEiEiPKB0QZuLwIgDicbhv3VaPE4mIiHin7oUXaPz4YwB8BQWETj/N40TeUhEiIj1mTsoA9Qc3bKe2odHDNCIiIt6pWr4i+Tx0xhn4wmEP03hPRYiI9JhJw4so6RcCoLymgac27fI4kYiISOZFt2+n9smnku3wwoUepskOKkJEpMf4/T5On3DoAPV4XNP1iohI31J18y0QiwGQN2UKweFHepzIeypCRKRHzTy6lKDfGXj33o5y3tl+0ONEIiIimROvq6P6jjuT7b48LW8qFSEi0qP6hYOcOGZQsn3vqxqgLiIifUfNw48Q27sXAH9JCfknnuhxouygIkREetyciU0D1J96excHquo9TCMiIpI5qQPSwwsW4AsEPEyTPVSEiEiPGzW4H6MGFwJQH43xwOvbPE4kIiLS8+o3baL+tdecRiBAeN5cbwNlERUhIpIRs1Om6121fiuNMQ1QFxGR3HbItLwzZ+IfONDDNNlFRYiIZMQJowdRGHK6oHcdqGXtB7s9TiQiItJzYgcOUHPf/cm2BqQfSkWIiGREftDPzHGp0/VqgLqIiOSu6rvvIV5bC0Bg9GiCxxzjcaLsoiJERDLm9PFD8LnPX/5wD1v3VnmaR0REpCfEYzEqV9ycbEcWLcTn87VyRN+jIkREMmZw/xCTRxQl26vWqTdERERyT92aNTSWlQHgKyggdNpp3gbKQipCRCSjTk8ZoP7wxu3U1jd6mEZERKT7VaX0goTOPANfOOxhmuykIkREMmrS8CIG9w8BUF4T5clNOz1OJCIi0n2i27ZR+9TTyXZk4UIP02QvFSEiklF+n4/Txx86QD0e13S9IiKSG6puuRViMQDypk4lcOSRHifKTipCRCTjZo4rJS/gDNB7f2c5b2876HEiERGRrovX1lJ9+x3JtqblbZmKEBHJuMJQkBPHlCTbK1/91MM0IiIi3aPmoYeJ7dsHgH/wYPJPONHjRNlLRYiIeCJ1BfWn397F/qp6D9OIiIh0Xeq0vOGFC/AF9FG7JfrOiIgnRg0uZNTgQgAaGuM8+Po2jxOJiIh0Xv1bb9Hw+utOIxgkPHeut4GynIoQEfHMnJTekFXrt9IY0wB1ERHpnaqWr0g+D82cgb+oqJW9RUWIiHjmhNGDKAwFAdh1oJYXN+/2OJGIiEjHxfbvp/r++5Pt8KLFHqbpHVSEiIhn8oJ+Zo0bnGyvWqcB6iIi0vtU3X0P1NYBEBgzhuAx4zxOlP1UhIiIp04bPwSf+/zlD/fy6d4qT/OIiIh0RDwWo+rmpgHpkUUL8fl8rRwhoCJERDw2uH+IySOa7ptdtW6rh2lEREQ6pm71ahrLPgHAV1hI6LTTPE7UO6gIERHPzZ5wRPL5wxu2U1vf6GEaERGR9qta3tQLEjrjDHyhkIdpeg8VISLiuYnDBzC4v/NDu6I2yhNv7fQ4kYiISNuiW7dS+/TTyXZk0UIP0/QuKkJExHN+n4/TxzdN17ty3afE45quV0REslvVLbeC+/sqb9o0AsOGeZyo91ARIiJZYea4weQFnIF8m3dWsGnbQY8TiYiItCxeW0v17Xck2+FFizxM0/uoCBGRrFAYCjJ9bEmyvfJVTdcrIiLZq+bBh4jt3w+Av7SU/BNO8DhR76IiRESyxuyUFdSfeXsX+yrrPEwjIiLSssoVTSukhxcswBfQx+qO0HdLRLLGUSWFjB5cCEBDY5wHX9/ucSIREZHD1b/xBg0bNjqNYJDw3LneBuqFVISISFaZPbGpN+S+9VtpjGmAuoiIZJeqFSnT8s6cib9ogIdpeicVISKSVU4YNYh+oSAAuw7W8uLm3R4nEhERadK4bz/Vf/1rsh1erAHpnaEiRESySl7Qz6xjBifbGqAuIiLZpPruu6DWGbMYGDOG4LhxHifqnVSEiEjWOe2YIfjc569+tJdP91R5mkdERAQgHotRdfMtyXZk8SJ8Pl8rR0hLVISISNYp6R/i2JEDk+1V67Z6mEZERMRR99xqGj9xeuh9hYWETj3V40S9l4oQEclKqdP1PrRxOzX1UQ/TiIiIQOXypml5Q2eeiS8U8jBN76YiRESy0oQjB1Da3/nhXlkb5fE3d3qcSERE+rLop59S98wzyXZk4UIP0/R+KkJEJCv5fb5DekPuXbeVeFzT9YqIiDeqbr4F3N9DeccdR2DYUI8T9W4qQkQka804ejB57gq0H+yq4K2tBzxOJCIifVG8poaqO+5MtsOL1AvSVSpCRCRrFYSCnDR2ULK98lUNUBcRkcyrfvAh4gecP4T5S0vJP/4EjxP1fipCRCSrpd6S9cw7u9hbWedhGhER6YuqVjQNSA8vXIAvoI/QXaXvoIhktZElhYwpLQQg2hjngde2eZxIRET6kvqNG2nY+IbTyMsjPHeut4FyhIoQEcl6qb0h97+2jWhjzMM0IiLSl1StuDn5PDRzJv4BAzxMkzuCXgcQ6QnW2qXAsjZ2ixljAu7+o4GPW9n3LmPMl1q41teA7wKTgEZgA/AbY8xDHUstLTl+9CDuXbeVytoonx2s5cXNu5kz8QivY4mISI5r3Lef6gceSLbDixd5mCa3qAiRXLURsC28djowF3g0zWtvAPen2b4p3Ymstb8BfgRsA/4E5ANfAh601n7fGHNNB3NLGnkBP7PGlfLEW85aIf9+10bicYjkB1g87Ui+PGs0IwYVeJxSRERyQbSsjMobbqR61X3EKyuT2wMjRxI8+mgPk+UWFSGSk4wxG3EKkcNYa9e6T29M8/JGY8zP2nMNa+0snALkI+AkY8x+d/uvgdeA31hrHzLGlHUsvaRzxICmVWlj7nIh1fWNPPDaNh7ZuJ0rLzmOWeNKPUonIiK5oPaZZ9l3+TeJNzRANHrIa407d9KwcSP5xx/vUbrcojEh0qdYa48FZgDbgYe7eLpvuY+/TBQgAG7RcS0QAr7exWsIsLu8lrte+TTta9FYnNqGGFfctZFt+6oznExERHJFtKzMKUBqag4rQJwdopT/9v9o3LUr8+FykHpCpK/5pvv4F2NMY5rXj7TWfhMoAfYCa40xb7ZwrsT0GI+lee1R4KfuPqYLeQV4+u1dbQ5GjzbGueOlMv75nEkZSiUiIrmk8oYbnR6Q1kSjVD/0MP0v+4fMhMphKkKkz7DWRoCvADHgzy3stsD9Sj3uOeBrxphPU7YVAsOBSmPMzjTn+cB9PKaVPEuBpWleOq6lY/qqdVv2Jm/Bakk0FuexN3eqCBERkU6pXnVf+h6QVI2N1K9ZAypCuky3Y0lf8rfAQOBRY0zzpbergZ8DJwLF7tcc4FngDOBpt/BIKHIfD7ZwrcT2ga3kGe1eo/lXUSvH9Em1De2bkre6vo1fHiIiIi2IV1W1b7/a2h5O0jeoJ0T6ksvdxxuav2CM+Rz4z2ab11hrFwIvAKcAlwF/6OA1W/v7fRmwOs3241Ahcohwnr9dhUhBvn6kiYhI5/gKCw+ZDavF/cLhDKTJffqNLX2CtXYSMAtnKt1H2nucMSZqrf0zThEym6YiJNHT0VKx0FZPCcaY5cDyNFmfw+kREddJY0t4cfPuVm/JCvp9LJ46LHOhREQkpxRcdCFVt9/R+i1ZgQD5s2dnLlQO0+1Y0le0NSC9Nbvdx+TtWMaYKpwZtvpZa9N98h3nPm7u4LUkjXmThxIMtP7jKhjwcems0ZkJJCIiOaffNy+HYBt/nw8GKTjn7MwEynEqQiTnWWvDwN/jDEj/SydOMcN93NJs+zPu4+I0x5zVbB/pgtIBYS474wvkB/34fYe/7gN++cVpWrBQREQ6LTh6NKGWejkCAQiFGPCjHxIYOjSzwXKUihDpC76IM9D8kTQD0gGw1p5irc1Ps30u8AO3eWuzl693H39irS1OOWY08F2gDljWpeSSNHnEQK44bzKnHTOEcJ6f1FokDtS1MYWviIhIaxo//5y6NSlDNfPzwefDF4kQmj+f4t/8WgsVdiONCZG+IDEgPd0K6Qn/C0x2x2Nsc7dNpWktkJ8aY15KPcAY85K19v+AHwJvWmtXAvnAJcAg4PtaLb17lQ4Ic8nMUVwycxQAf31tK0+85SwatWz1Fs6ceAQ+X5quEhERkTZU3nAj1NYBEBw7lqL/+W/9TulB6gmRnGatnQicRtsD0m8BXgFOAv4R+A7OuI67gdnGmF+kO8gY8yOctT524RQ7XwXeBs41xlzTPe9CWjJ38lDyg86PsQ92VfD8+7vbOEJERORwjXv3UrXi5mQ7suQiFSA9zBePtzzdjLW2jeXBWrTaGHNGJ4+VLrDWzsAZo/CeMeZOr/NIxyVmxxo1ahRLly7tseu89vG+Hjt3Jq1a9ylPv/0ZABOOHMCyy2foF4eIiHTIwf/+HyqvuRaAwKhRDPzV/+Lz9/6/1edNnIC/uLjtHbuuw7942/ruftbCV2JN+9oWXs+NTze90wzAAF/yOohIJsybPIy8gPOz770d5az9cI/HiUREpDeJ7d9P1fIVyXbBkotyogDJdq2OCTHGpB3+n7KOwV3GmKXdH0tEpH2KCvKYdUwpq9/9HICbnvuImUcPVm+IiIi0S+VNy5KLFAaGDyf/lFM8TtQ3qMwTkV5vwbHDCLpz927adpB1W9QZKyIibYuVl1P556bZ+yNLlqgXJEMyNjuWtfZi4BvAdGAgzi1bLwF/MMasTrP/PwG/A/5qjLnAWvsN4NvABKAaeBa4whizxd1/FPATnPEQQ4Ay4I/AVcaYeLNzHwdsAA4aYwZaa+cD/wKcCISBd91jb2p+bLPzTAf+H06v0BFurjeAFcAKY0ys2f7Nr3sGzsxKJwOlwM+NMT9z9z0BuACYDxzlvqdyYCPOKtu3pWaz1g4E9qdc7vw0Y3qON8ZsbJ6jhfd2AXAf8IYx5rhmrx3AWRH8eDfTvwMLgWHAS83HA7nf328DM4HB7jHrgeuNMfenu75IRxQX5jNj3GBecAemL1v9ESd/ocTjVCIiku2qli0nXl4OgH/YMEKzZnmcqO/o8VLPWhux1t4P3IOzgFspUIPzof1C4Dlr7RVtnON6nEXmprmbhuBMg/qCtXaktXYq8CrOrEZFQB4wHvg9kHZWo5Rzfx14HFiA8/0I4RQjfwZWWGvT3tNhrf2Je82vACOBemAATkFyE/CAtTavleteBjwNnOtes/kiB68CP8X54H4EzvesBJiHM5PT7c2yxXDG41S47TpaHsvTXY4HXgcuc7NFU1+01vqttdcBTwIX4RQpNTjT1y4C7rPW3tDNmaSPWjhlGH73FqwNn+zn9TL1hoiISMtilZVU3PinZLvgogvxBdQLkimZ+E5fB5wPvI/zQbTQGFOEUyz8AKf34JfW2rNaOP4M4Gs4058OcL9OBj7B+VD7S+AOYBMwMeXcv3KP/xe3lySdAuBanL/4jzDGFON8QLbu63+P8xf8Q1hrv4ZT3JTj9GQMNsbJmCE1AAAgAElEQVT0d893Lk4vzNm0XAAVANfgLH6XuG4hhy5s96T7vkcCYfd9DcAptPbhDDy/LLGzMabcHcPzn+6mx4wxQ5t9vd1Cns66Cuffdboxpp8xpiA1E04R9W1gB04vWJH7PvrhTGW7B7jcWnvY91iko0r6hZhxdFPvx02rP/IwjYiIZLuqm28hfuAAAP4hQwiddprHifqWHr0dy1p7Ik1rKJxpjNmZeM0YUw783lpbDdyAcyvVo2lOUwT8kzHmTynb1llrvw88gFMo7MD5IFzjnrsS+Ff3NqATcIqgq9KcOw/nL/mXGGMaU3L9zL296f8BP7XW3miMibrvKQz82j3+ImPMMynvqQ54yFpb5p73+9baX7rnbH7dR40xX0s5th6nsEq0DyvKjDEVwJ+ttZ+57/07wJ+a75dBFcAiY8yBxAZjzIcA1tphwBU4RebC1ALIGFMN3OK+j8eBK6y117d265tIeyycMoyXP9xDLA7rt+zjzU/3M/WojExNKCIivUispobK65tuxii48AJ8Qa3hnUk93ROy1H28M7UAaeYOIA7MsNb2S/P6AZzxGc097R4H8PtEAZJmH4BjW8n4v4kCpJn/wbnFaSjOYncJZ+PcUrYxtQBJZYzZBLwJRIBTW7jur1vY3h6P49xaNbWF71mm/Cm1AGnmyzirhz/RUg+MMeYJYC8wAmesj0iXlA4Ic9LY1N6QLR6mERGRbFV9y63E9u4FwF9SQmjOGd4G6oN6uuRLjO75hrX20jb2DQBHApubbd/s9hIcwhhTba2twrm1Z1ML5/zMfWztT6HPpdtojNllrX0fmIjTm5LYL/GeJlhrd7Vy3sSA75FpXosDL7dyLNZaP84H+UtxxsIMxhk70txQ4MPWztWD1rbyWuL7tKCN71OR+zgSZ0IAkS5ZNHUYr3601/mf7MM9vLP9IJOGF7V5nIiI9A3x2loqrr8+2Y5ceAG+PPWCZFpPf8eHuY+JsRxtKUizraUeFIDGNvZJvN7SAPEaY8z+Fl4D2I5ThJSmbEu8p7D71ZZ076mqhZ4bIHnL1wM4g+UTanHGUCTe0xCc1SkL25Ghp+xu5bXE96mQ9mVM930S6bAjiiKcOGYQ690V4Zet/ohff/kEj1OJiEi2qLrzTmKfOWtL+YuLCZ95pseJ+qaeLkISt3t9zRhzcw9fqyekmxkr8Z6WGWO+0cnzprv9K9UPcAqQgzhTBz/Y/HY2a20FTi+QlyuytfY+Et8nY4z5r0yEEUlYNPXIZBHy/Pu72byznGOGtefvICIiksvidXVUXnNdsh05/3x8+fkeJuq7enpMSOJ2qEk9fJ3OirgD0FuS+Gt+6l/8M/Gevug+/psx5sY0BUghTgHSWYmpdFvryenq/SvZ/m8vOezI4gjHjWq6C3PZGo0NERERqL5nJY07nY9VvqIiwvPneZyo7+rpIiQxZuDCltbbyAJz0m201h6Bs9YIODNdJSTe03Rr7VE9lGmE+7ihhddb+z8msd5Ia9/vxGDykLV2cAv7nNTK8e2R+D4tcosmkYxaPPXI5PNn3/mMjz6raGVvERHJdfGGBiquuTbZjpx3Lr5QuuG2kgk9XYQk1r04Bvh+aztaa72aR/NfrbWBNNv/BWew/C7ghZTtD+LM6BQAftdacdWF93TQfZyS5pwh4GetHJuYDrjFHh5jzDaaVlc/P801huMswtgVt+HM4DUQ+HlrO3r4by85bGRJAVNGNv1vsFy9ISIifVr1qlU0bt0KgK9/fyILFnqcqG/r0TEhxphXrLU34SxU93tr7UjgKmPMVgBr7QCc6W+X4nyoX9KTedJoAI4D7rDW/sAYs91a2x9nTMYP3X1+nlgjBMAYU2Wt/QFwM87iiw9aa39qjNkAYK3Nx1lJ/EvAxaSfHastTwJHA1daa7cCTxpjYu7K8FcB43BWaE93E2NiOtzp1topxpi3WrjGPTgLQF5prf0EeBanF2U2zrotzVdw7xBjzFZr7c+B/wJ+4BYa/22M2QxgrS0ATgH+DqfYOqUr1xNJ56xpR/LWVqfj76m3d/EPZ3yB0aVezmotIiJeiEejVFx1TbIdOedsfJH2zC8kPSUT85F9B+fD8leAHwM/ttaW40xTO4Cm24buz0CW5qpxCo4/Axdbaw+4mRI9I7eQZo0SY8wt7ofq/8NZN+Rsa20NUIMzliJxfEtraLTl58B5wHDgMaDOWlsP9McpnC4F/kL6ImQ98AbOtL5vWmv3AFXua39jjHnHff4z4BycaZGfxJl9K4YzS9X7OD1BXV0I8Rc4Y1f+BafQXOpOq1yP831K9MRt7OJ1RNIaNbiQScOLeGf7QeJxWPH8x5iLDutgFBGRHFfz1wdoLCsDwFdYSHjxYm8DSY/fjoUxps4Y8/c4sz3dCWylaXrbMpy/yF+Ks/J5xhljlgGLgKfcTfXAa8A/4szqlXYVb2PMVTiDrq8F3sP5AN8fZxD7k8D/B0zuZKadwMk4hcZOnH+nSuBuYKYx5t5Wjo0Di91jP8X5sD/K/cpP2W8nMANYjjOI3O8+/sa99p7OZG+exRjzrzjjS5YBW9zrFOKscv8gcBkwv6vXEmnJWdOaxoY88dZOtu2r9jCNiIhkWryxkYqrrk62I2f/Df4CrQzgNV88nvYzdk6z1h6HM+j7oDGmtdmxRDLOWvscMGfUqFEsXbq0x67zmjuFbV9w9ePv895OZ7jUuScM5yfnH+txIhERyZTqvz7A/u98FwBfJELxddfi79c3bs3NmzgBf3FGht52eAKqHu8JERHx2uKU3pBHNu5gx/4W1woVEZEcEo/FqLjqqmQ7fNZZfaYAyXYqQkQk540b2p+jj+gPQGMszi0vfOxxIhERyYTaxx8n+t77TiMUInL233gbSJJUhIhIn5A6NuShDdv4/GCth2lERKSnxeNxKn7f1AsSWbwI/4ABHiaSVCpCRKRPGD+sP2NKnXUzGxrj3PKiekNERHJZ7VNP07Bpk9PIzydy7rneBpJDZGKK3qxjjNlIJwbQiEjv5fP5OGvakVz31AcAPPDaNr52+lgG99dquSIiuSYej1Pxhz8k2+EF8/EXFXmYSJpTT4iI9BmThhdxVIkzLWNdNMZt6g0REclJdatX07DBXYYsL4/Ieed5G0gOoyJERPqMRG9Iwn3rt7G/qt7DRCIi0t3i8TgVv0vpBZk7l8CgQR4mknRUhIhInzJl5ECGF0cAqG1o5I6XyrwNJCIi3ar+xZeoX7/eaQQCRC4439tAklavGRNirT1sVUVjTNaM67DWbgOGA6cbY17ohvMFgQa3OdIYs62r53TPOx1Y12zz08YYrVoufUKiN+TPz30EwMpXP+XvTh1NUUG+x8lERKQ7lP8+pRfkzDMJDB7sYRppSa8pQlLsARrTvWCtPQN41m2OMcaUtbDf/wD/6jZ/YYz5aTdnzGYNwGfu8wigueqkz5k2qphhAyPsPFBDdX0jd738CZfPHed1LBER6aK6V16hfu1ap+H3E7ngAm8DSYt6YxFyUkvFRXtYa38H/JPb/Ikx5spuSdX94oC7uk6yR6TLjDFvAEMBrLWXAX/qrnOL9BZ+n4/FU4exbM0WAO5+5VMunTma/pE8j5OJiEhXVKT0goTmzCZwxBAP00hremMR0inWWh9wHfAtd9MPjTG/8zBSq4wxjcAEr3OI5KoTRg/ikY07+Ky8lsraKPe88infOOMLXscSEZFOqn/tderWPO80fD4KLrzI20DSqj4xMN1a6wf+glOAxIHvZHMBIiI9z+/3sWjqsGT7zpfLqKqLephIRES6InUsSOi0UwkMG+phGmlLzveEuAO8VwBfBmLAZcaYZW0cMwb4EbAQGAFEgc3A3cA1xpjqdl57OfA14C5jzJda2e+nwH8B64wxJ6fkTjsw3Vr7C+AnwF+MMZdZa78OfBuYhDNeZj1wpTHm6fbkFOmrpo8t4ZE3drCnoo7ymij3vvopXz19rNexRESkg+rffJO6Z55xGj4fkYvUC5LtcronxFqbB9yJU4BEgb9vRwHyReBd4LtAYqRqCDgR+F/gJWttaTsj3O4+nmut7dfKfpc227/drLXLgJuA43GKrAHAXOAJa63mpBNpRcDvY9GUpt6Q218qo6ZevSEiIr1NxR+uSj7PnzGD4IgRHqaR9sjlIiQErAKW4PQoXGKMafVDvrV2Bk4hEAD+GzjKGFMAFACzcHoYpgHL25nhaZyZqAqAtAWBtXYaMBGngLirnedNWAJcAnwTKDLGDAC+ALyA8297jbU20MFzivQpJ3+hhEGFzvS8B6obuG99t8yGLSIiGdLwzrvUPvZ4sl2wZImHaaS9crkIuQM4B6gDLjTGrGrHMb/DuUXth8aYK4wxW8EZJG6MWQssBnYBf2OtPa6tk7mDy+92m19uYbdEL8izxpid7ciYaiDwdWPMjYlbxIwxW9xzNuDcSnZKB88p0qcEA34WpvSG3Prix9Q2pJ0FXEREstAhvSAnn0xw1FEeppH2yuUi5Hj3cYUx5uG2drbWjgdmAFXAjen2McbsBRKl9oJ25kj0viyw1pY0u6YP+FKz/TpiizHmsN4Td/zIa27z2E6cV6RPmTFuMAMLnOl591XW88Br6g0REekNGjZvpubhpo95BUs0FqS3yOWB6a/g9AJcbq19wxhzXRv7z3IfQ8An1tqW9kuM7RjZnhDGmJettR/h3Cb1ReD6ZtcchdNbc297ztfM+lZe2+4+FnfivCJ9Sl7Az4Ipw7jnlU8BuOXFj7lg+kjyg7n8dxoRkd6v4qqrIR4HIO/EEwiO1eQivUUu/4b9KvCY+/waa+0/tLF/4n6MIHBEK1+F7n4FHchyp/t4abPtifYjxpiDHThfQkUrr9W6j1p9TaQdZo0rpX/Y+bvM7vI6HtqwvY0jRETESw0fbaHmrw8k2wVLLvYwjXRULveE1AMXAg8B84AbrbW1xpjbWtg/UZAlp8ntRrfhTKl7urV2hDFmmztg/Ivu6525FUtEulF+0OkNWbVuKwA3P7+Fc48fTp56Q0REslLl1VdDLAZA3rRp5I072uNE0hE5/dvVGFMLnAc8j/NeV1hrWyqTP3Mfx3f3jFLGmHeBN4DUMSDzgCFAOU6hJCIeO+2YUvqFnL/N7DpYy6Nv7PA4kYiIpBP95BOqV92XbBdcrBmxepucLkIA3FmjzgZexpl693Zr7Xlpdl3rPg7AKRC6W6K3IzFLVuJWrPvcYklEPBbKCzBvctMKuyue30K0MeZhIhERSafi2uug0ZnJMG/yZPImTPA4kXRUzhchAMaYCpzpdV/HGSNxt7V2UbN9NtE00PtX1toWx3xYawustfkdjHEHEAeOd9cGudDdrluxRLLI7IlDKAw5naHb99fw5KZdHicSEZFU0e3bqb77nmQ78kWNBemN+kQRAuAO/F4AvIkzA9Z91tozm+32PZyxJNOANdbauYlbs6y1fmvtsdba/wQ+wrmVqiPX34qziCA4K5wX4dwC9nQn35KI9IBwXoAzJzX1hixb/RGNsbiHiUREJFXltddBQwMAwQkTyJs0yeNE0hl9pggBMMbswylE3gUiwIPW2lNTXn8FZxXyCuBEnAKh2lq7B2e2qbcACwzF6dXoqESvxwnu493ugoYikkXmTBhCOM/pDfl0bzXPvK3eEBGRbNC4cydVd9yZbBdcvASfz+dhIumsPlWEABhjPscZ8/EBznS7j1hrT055/SFgHHAlsAGn+BiIM4D8ReCnwARjTGfm77wHZyXzBN2KJZKFCkJBzpx0RLK9bM0WYuoNERHxXMUfb4D6egCC48aRN3Wqx4mks3zxeO/4xWqtTQQdY4wp8zJLrrDWXgb8CXjaGDPf6zzisNY+B8wZNWoUS5cu7bHrvPbxvh47dy6oqovy03veoC7qDEy/8pJpzE25TUtERDKr8fPP2TVzFtTWATDg3/6N/BNPaOOovi1v4gT8xRlZt7rD3VF9ridERKQ9CkNB5kxsGvq1bPUWessfbUREclHlDTcmC5DAmDHknXC8x4mkK3rjYoUfW2sBMMboJsAOstZOB9Z5nUOkN5g7eSjPvfs59dEYH+yq4Pn3dzN7QofmpBARkW7QuG8fVTffkmxrLEjv15t6Qj5L8yUd18Dh30fdlyOSRv9wHqeNL022l63+SL0hIiIeqLzxT8SrqwEIHHUU+dOne5xIuqrX9IQYY3QzdjcwxryBM7uXiLTD/MlDef69z2lojPPujnJe/nAPM8eVtn2giIh0i9j+/VQtW55sF1y8BJ+/N/0dXdLRv6CISCuKCvKZdUxT0XGTxoaIiGRU5U3LiFdWAhAYPpz8U07xOJF0BxUhIiJtWHDsMIJ+597jt7YeYL1mFhMRyYhYeTmVf/5Lsh1ZcpF6QXKE/hVFRNpQXJjPjHGDk+2bVn/kYRoRkb6jatly4uXlAPiHDSM0a5bHiaS7qAgREWmHhVOG4XdnYtlQtp8NZeoNERHpSbHKSipu/FOyXXDhhfgCAQ8TSXdSESIi0g4l/ULMOLok2b5p9RYP04iI5L6qm28hfuAAAP4hQwidfprHiaQ7qQgREWknpzfEeb5uy17e2nrA20AiIjkqVlPjLE7oKrjwAnzBXjOpq7SDihARkXYqHRBm+tjU3hCNDRER6QnVt95GbM8eAPwlJYTmnOFtIOl2KkJERDpg8dRhJNboXfvBHt7dftDTPCIiuSZeW0vFH/+YbEcuvABfnnpBco2KEBGRDjiiKMIJYwYl2+oNERHpXlV33knss88B8BcXEz7zTI8TSU9QESIi0kGLpw5LPn/+/d18sKvcwzQiIrkjXldH5TXXJduR88/Dl5/vYSLpKSpCREQ66MjiAo4bVZxsL9NMWSIi3aL6npU07twJgK+oiPD8+R4nkp6iIkREpBMWTz0y+fyZdz5jy+eVHqYREen94g0NVFxzbbIdOfdcfKGQh4mkJ6kIERHphJElBUwZOTDZXr5GY0NERLqietUqGrduBcDXvz+RhQs9TiQ9SUWIiEgnnTWtqTfkyU27+GRPlYdpRER6r3g0SsVV1yTbkXPOxhcJe5hIepqKEBGRTho1uJBJw4sAiMdhxRqNDRER6Yyavz5AY1kZAL7CQsKLF3sbSHqcihARkS5I7Q15/K2dbNtX7WEaEZHeJ97YSMVVVyfbkbP/Bn9BgYeJJBNUhIiIdMHYIf0YP2wAAI2xOCueV2+IiEhH1Dz8CNEPPwTAF4kQPussjxNJJqgIERHporOmNa0b8sjGHew8UONhGhGR3iMei1Hxhz8k2+HFi/H36+dhIskUFSEiIl00bugAjj6iP+D0htzywsceJxIR6R1qH3+c6HvvO41QiMg5Z3sbSDJGRYiISDdI7Q158PVtfF5e62EaEZHsF4/Hqfj9Vcl2ZNEi/AMGeJhIMklFiIhINxg/bABjSgsBaGiMc6t6Q0REWlX71NM0bNrkNPLziZx7jreBJKNUhIiIdAOfz3fITFl/fW0beyvqPEwkIpK94vH4oWNBFszHP3BgK0dIrlERIiLSTSYNL+KoEmdaybpojNteKvM2kIhIlqpbvZqGDRudRl4ekfPO8zaQZJyKEBGRbtK8N2TVuq3sr6r3MJGISPZpPhYkPHcugUGDPEwkXlARIiLSjaaMHMjw4ggAtQ2N3KHeEBGRQ9S/tJb6deucRiBA5ILzvQ0knlARIiLSjZr3hqx89VMOVqs3REQkofx3v08+D595JoHBgz1MI15RESIi0s2mjSpm2ECnN6S6vpG7X/7U40QiItmh7pVXqF+71mn4/UQuuMDbQOIZFSEiIt3M7/OxeGrTuiF3vfIJlbUNHiYSEckOFb9vmhErNHs2gSOGeJhGvKQiRESkB5wwehBDBoQBqKyNcvcr6g0Rkb6t/vUN1K153mn4fBRcdKG3gcRTKkJERHqA339ob8idaz+hqi7qYSIREW+Vp/aCnHYqgWHDWtlbcp2KEBGRHjJ9bAmD+4cAKK9p4N5X1RsiIn1T/ZtvUvf0007D5yNy0UXeBhLPqQgREekhAb+PRVOa/tJ3x9pPqKlXb4iI9D0Vf2haFyR/xgyCI0Z4mEaygYoQEZEedPIXSiguzAdgf1U9963f5nEiEZHManjnXWofezzZLliyxMM0ki1UhIiI9KBgwH9Ib8htL35MbUOjh4lERDLrkF6Qk08mOOooD9NItlARIiLSw2aMG8zAgjwA9lbW8+Dr6g0Rkb6hYfNmah5+ONkuWKKxIOJQESIi0sPyAn7mH9vUG3LzCx9TH415mEhEJDMqrroa4nEA8k44geDYsR4nkmyhIkREJANOPaaU/uEgALvL63h4w3aPE4mI9Kzolo+p+esDyXbBxRoLIk1UhIiIZEB+8NDekBUvbCHaqN4QEcldFVdfDTHn51zetGnkjRvncSLJJipCREQy5PTxpfQLOb0huw7U8ugbOzxOJCLSM6KffEL1vauSbc2IJc2pCBERyZBQXoB5k4cm2yueV2+IiOSmimuvg0ZnJsC8yZPJmzjB40SSbVSEiIhk0OyJQyjIDwCwbV8NT27a5XEiEZHuFd2+neq770m2IxoLImmoCBERyaBwXoC5Kb0hy9dsoTEW9zCRiEj3qrz2OmhoACA4YQJ5kyd7nEiykYoQEZEMmzNhCOE8pzfkkz1VPPOOekNEJDc07txJ1R13JtsFFy/B5/N5mEiylYoQEZEMKwgFOWPikGR72eotxNQbIiI5oOKPN0B9PQDBo48mb+pUjxNJtlIRIiLigTMnDSUUdH4Eb/m8ktXvfe5xIhGRrmncvZuq225Ntgsuvli9INIiFSEiIh7oFw4ye0Jqb8hHxOPqDRGR3qvyhhuhtg6AwJgx5J1wvMeJJJupCBER8ci8yUPJCzg/hjfvquCFzbs9TiQi0jmN+/ZRteLmZLtgicaCSOtUhIiIeKR/JI/TJ5Qm2+oNEZHeqvLGPxGvrgYgcNRR5J803eNEku1UhIiIeGj+5KEE/c5fC9/ZXs7LH+7xOJGISMfE9u+natnyZLtgyUX4/PqIKa3TfyEiIh4qKsjn1PFNvSE3rd6i3hAR6VUqb1pGvLISgMDw4eSfMsPjRNIbqAgREfHYgmOHJXtD3tp6gNc+3udxIhGR9omVl1P5l5uS7ciSi/AF9PFS2hb0OoBIT7HWlgGjWnj5M2PM0OYbrbWzgP8AZgBh4EPgJuBqY0xjC9c5B/gxcDwQAN4GrjPGrOjqe5C+obgwnxlHD04OTP/L6o+YPrbE41QiIm2rWrac+MGDAPiHDiU0a5bHiaS3UBEiue4g8Ps02yubb7DWng/cC9QCdwH7gHOB3wGnAl9Mc8z3gKuBvcCtQD1wMbDcWjvFGPPj7nkbkusWThnGSx/sIRaPs6FsP2f84knqGmJE8gMsnnYkX541mhGDCryOKSJCtKyMyhtupPreVcSrqpLbw/Pm4QsEPEwmvYlP9x5LrnJ7QjDGjG7HvgNwej2KgFONMevd7WHgGWAmcKkx5s6UY0YD7wFVwInGmDJ3ezGwDvgCMMsYs7aDuZ8D5owaNYqlS5d25NAO0S0/2efqJ97nvR3lh20P+n0EAz6uvOQ4Zo0rTXOkiEhm1D7zLPsu/ybxhgaIRg99MRRiwI9+SP7xWh8kW+RNnIC/uDgTl+rwfMy6aU/EcTFQCtyZKEAAjDG1OLdnAXy72THfAELANYkCxD1mP3Cl2/xWTwWW3LK7vJaPPqtI+1o0Fqe2IcYVd21k277qDCcTEXFEy8qcAqSm5vACBKCujvLf/h+Nu3ZlPpz0OrodS3JdyFr7FeAonB6LN4E1acZ3zHUfH0tzjjVANTDLWhsyxtS145hHm+0j0qqn395FY6z1nuloY5w7Xirjn8+ZlKFUIiJNKm+40ekBaU00SvVDD9P/sn/ITCjptVSESK4bCtzSbNvH1tqvG2NWp2wb7z5ubn4CY0zUWvsxMBkYC7zbjmN2WmurgBHW2gJjzGF/vrbWLgWWpsl8XMtvR3LVui17aaMGIRqL89ibO1WEiIgnqlfdl74HJFVjI/Vr1oCKEGmDbseSXLYMmIdTiBQCU4AbgNHAo9baaSn7FrmPB1s4V2L7wE4cU9TC66OBOWm+WtpfclhtQ6xd+1XXt/EBQESkh6QOQm91v9raHk4iuUA9IZKzjDG22aZNwLestZXAj4CfARe283SJAVcdmcmhrWPKgNVpth+HCpE+J5znb1chUpCvH9si4g1fYWFyUcJW9wuHM5BGejv9NpO+6HqcImR2yra2ei0GNNsv8Xywe8zeVo45fLojwBizHFjefHtidqwWckiOOmlsCS9u3t3qLVlBv4/FU4dlLpSISIrIRRdSfXPzO5ybCQTInz279X1E0O1Y0jd97j4Wpmx73308pvnO1togMAaIAlvaecww9/zb0o0HEWlu3uShBNtYZTgY8HHprNGZCSQi0kzeMePb3ikYpOCcs3s+jPR6KkKkL5rpPqYWFM+4j4vT7D8bKABeSpkZq61jzmq2j0irSgeEueyML5Af9ONvYbb17yw4RgsWiogn4jU1VF5/fdMGX7MfVIFAcp2QwNChmQ0nvZKKEMlJ1trJ1tpBabaPAq5xm7emvLQS2AN8yVo7PWX/MPALt/nHZqdbBtQB33MXLkwcUwxc4TavR6SdJo8YyBXnTea0Y4YQzvPjg0MKkqc37UILzIqIFyquv4HGbducRmEhoTPPxBeJgM+HLxIhNH8+xb/5tRYqlHbTiumSk6y1PwP+DXgW+BiowFnB/GwgDDwCXGiMqU855gKcYqQWuBPYB5yHMxXvSuBvjTGH/A9jrf0+cBXOmJC7gHqchQ9HAL81xvy4E9mfQyumi+uzgzX84v63ibk/q39+8VQWTNG4EBHJnOj27Xw++4zkrFeFl/8jkQULPE4l7aEV00Uy71ngPpyxHF8Gfogz2PsF4GvAOakFCIAx5n53nzXAEuD7QIN77JeaFyDuMaReHZYAACAASURBVFfjFCpvA18FLgd2AUs7U4CINHdEUYQzJw1Jtq964n1qNE2viGRQ+c9/kSxAAqNHE547z+NEkgvUEyKSZdQTIs3V1DdiV71JRa1TfCydPZZvzRvncSoR6Qvq1q5lz8V/m2wX/Zclb+JEDxNJR6gnREREOi2SH+D8E0ck27e/VMb2fZp0TUR6Vjwa5cBPTbIdOvVUFSDSbVSEiIj0AqccPZhRg51ZpeujMa56/P02jhAR6Zqq224n+u67TiMUouDvv+JtIMkpKkJERHoBv8/HF085Ktle/d7nvPLRHg8TiUgua9y3n/Jf/TrZLrjwQgIlJR4mklyjIkREpJcYU9qPU77Q9CHgd4++R7Qx5mEikf+/vfuOk6ss+z/+me0lm056SBBChwAJLUGY0Kv0JlKC/lCx+6iPjwo3lyhYqIpIFRQFRUFRSpCWofde0guE9LbZzfad+f1xn5lMNpvNbrI7Z2b2+3698prcM+fMXHMyOedcd5V8VXPNNSTWrgWgYMgQyk86MeSIJN8oCRERySEnTxhFWbE/dS9YsZ4HXv0k5IhEJN80f/gR6+/ZsJRW5YUXECkpCTEiyUdKQkREcki/ihKOHT8iVb59+hzWrG/qYA8Rkc5LJBKsvfxyiPtW1uK99qJk//1DjkrykZIQEZEcM2W3oQzpWwZAbUMLtzw1O+SIRCRfNDz8CE0vvewLBQVUTp1KJNLl2VdFtkhJiIhIjikqLOD0A0anyv9+cxEzFleHGJGI5IN4fT3VP70yVS479liKRo/qYA+RrackREQkB+05qj97juoHQCIB1z46Ay0+KyLbovbm39O6eDEAkaoqKs46M+SIJJ8pCRERyVGnH7A9hQW+m8R7n6zl8feWhByRiOSqlkWLqLn55lS58vPnUlBZGWJEku+UhIiI5Kghfcs4fPehqfLv/juLusaWECMSkVxV/dOfQUMjAIU77EDplMNDjkjynZIQEZEcduz4EfQtLwZgRU0jf3xuXsgRiUiuaXzhRRoeeSRV7nPxVCKFukWUnqVfmIhIDisrLuSUCRsGjt774gIWra4LMSIRySWJlhY/JW+g9LOHULzrriFGJL2FkhARkRy3/46DGDvY991ubk1w47QZIUckIrli/T1/pmXGTF8oLaXivC+EG5D0GkpCRERyXEEkwlkHbZ8qPzdzBS/PWRliRCKSC1pXr2bdNdekyhWnn0bhoIEhRiS9iZIQEZE8MGZwHw7aaXCqfP1jM2hpjYcYkYhku5pf/ZrEWr/GUMHQoZSfcELIEUlvoiRERCRPnDxhFGXFhQAsXLmev7/yccgRiUi2anr/A9b/5d5UufLCC4mUlIQYkfQ2SkJERPJE3/Jijhs/IlW+Y/pcVtU2hhiRiGSjRCJB9eWXQ9y3lhaPH0/JxAkhRyW9jZIQEZE8Et1tCEP7lgGwvrGFW56cHXJEIpJt6v/9H5peedUXCgupvOhCIpFIuEFJr6MkREQkjxQVFnD6ARsGqT/89qd8+Gl1iBGJSDaJ19Wx7sqfpcplxx1H0ahRHewh0jOUhIiI5Jk9RvVjr9H9AUgk4LpHPyIeT4QclYhkg9rf3UzrkiUARPr1o+KMM0KOSHorJSEiInnotP1HU1Tgu1e8v6iax99bEnJEIhK2lo8/pub3t6TKlZ8/l4LKihAjkt5MSYiISB4a0reMw/cYmirf9N+ZrG9sCTEiEQlb9ZU/g0Y/WUXRjjtSGo2GG5D0akpCRETy1DF7j6BfeTEAq2qbuPvZeSFHJCJhaXjueRoefSxVrpw6lUiBbgMlPPr1iYjkqbLiQk6ZuGHA6X0vLeDjVevDC0hEQpFobqbauVS59NBDKd5l5xAjElESIiKS1/b/zCB22K4SgJbWBDdOmxlyRCKSaev/dA8tM2cBECkro+K8z4cckYiSEBGRvBaJRDjzwDEkVwB4YdYKXpy9ItSYRCRzWletYt2116XK5aefRuHAgSFGJOIpCRERyXNjBldy8LjBqfINj82guSUeYkQikinrfvlrEtV+raCCYcMoP+GEkCMS8ZSEiIj0Ap/bbxRlxYUAfLyqjvtfWRhyRCLS05ref5+6e+9NlftcdCGR4uIQIxLZQEmIiEgvUFVezAn7jEiV74zNZVVNY4gRiUhPSiQSVP/kcr9iKVC8774U77dfyFGJbKAkRESklzhstyEM61cGQF1jKzc/OSvkiESkp9Q/9BBNr73mC4WFVF54IZFIpOOdRDJISYiISC9RWFDAGQdunyo/8vZiPli0NsSIRKQnxNevp/rKn6fK5ccfT9HIER3sIZJ5SkJERHqR3Ub0Y+/R/VPlax+dQTyeCDEiEeluNb+9ifjSpQBE+vWj/IzTQ45IZFNKQkREepnTDxhNUYHvlvHhp9U89u7ikCMSke7SsmABtbfelipXnnceBRUVIUYk0j4lISIivczgqjKO2HNYqvy7J2axvqElxIhEpLtU//RKaGoCoGinnSg97NCQIxJpn5IQEZFe6Oi9htO/wk/Vubq2iT88OzfkiERkWzXEYjQ8/t9UufLiqUQKdKsn2Um/TBGRXqisuJBTJo5Olf/28kIWrlwfYkQisi0Szc1UO0uVSw87jOJx40KMSKRjSkJERHqpiTsM5DND+gDQ0prghmkzQo5IRLbW+rv/SMvs2QBEysupPO/zIUck0jElISIivVQkEuGsA7cnuXLAS7NX8sKsFaHGJCJd17pyJeuuvS5VLj/jdAoGDAgxIpEtUxIiItKLjR5UyaSdt0uVr39sBk0t8RAjEpGuWvfLX5GoqQGgcPhwyo87PuSIRLZMSYiISC930n4jKS8uBGDR6jr+9vLCkCMSkc5qevdd6u77a6pcOfUiIsVFIUYk0jlKQkREermqsmJO2HdkqnxXbC4raxpDjEhEOiORSFD9k8sh4RccLd5vP0r23TfkqEQ6R0mIiIhw6K7bMax/GQB1Ta3c/MSskCMSkS2pf/CfNL3xhi8UFtLnogvDDUikC5SEiIgIhQUFnHnA9qnyo+8s5v1P1oYYkYh0JF5bS/XPf54ql594AoXDh4cYkUjXKAkREREAdh3Rj/Hb90+Vr330I+LxRIgRicjm1Pz2JuLLlgMQ6d+f8tNPDzkika5REiIiIimn7b89RQV+0t6PFq/jkbc/DTkiEWmrZf58am+7PVWu/MJ5FJSXhxiRSNcpCRERkZTBVaUcueewVPnmJ2dT29AcYkQi0la1/RSamgAoGjeO0s9+NuSIRLpOSYiIiGzk6L2G07+iGIA165u4c/rckCMSkaSGZ56h4YknU+XKi6cSKdDtnOQe/WpFRGQjpcWFnDpxdKp8/ysfs2BFbYgRiQhAoqmJamepcumUKRTvtFOIEYlsPSUhIiKyiQk7DGTHoX0AaI0nuGHaDBIJDVIXCVPtXXfTMte3TEbKy6n8/LkhRySy9ZSEiIjIJiKRCGceMIaIH6POy3NW8fysFeEGJdKLta5YQc31N6TKFWeeSUH//h3sIZLdisIOQERy3/uL1vL6vNXMX1HLuvpm4vEEfcqKGDmwgr1G9Wf/HQdRVlwIwCNvfcqj7yzeaP+igghlJYUMqChh1KAK9hjZj723709hO/2cf3z/26yta+arR4xjz9GbXoDnL6/lmkc/AuDkCaM4eq9N582vb2rhB/e9RTwBl5+6J0P7aVaZ9oweVMHknbfj+Zk++bhx2gwO3HEwJUWqvxLJtHW/+CWJmhoACkeMoOzYY0OOKDck4nHWXPo14qtWEenbl4G33kKkqP3b39WXfo34io4rW6q+/z1KDzgAgKYPPmDdFRu6x/W/4XqKRo5sd794XR2r/98lqQkF+lx6KWVTolvxjfKHkhAR2Wo19c3cOX0us5f5C+OwfmXsNqIvRQUFrKlrYubidXywqJqH3/qUH5y0O4P6lKb2HVxVyo5DfHefeCJBfVMrS6sbeGn2Sl6avZL+FcV8YfIO7Day30afOW5YFa/NW82spTXtJiGzl9Zs9Pf2kpA5y2qJJ6BfebESkC04ad+RvDF/NfVNrSxaXc9fX1rABZ/9TNhhifQqTW+/Td1f/5YqV150EZFi3cJ1RvM77xJftQqAxLp1NL3xBqUHHtjhPsXjx2+2lalw8ODN7tf4zHSKvnBeu681vfhiKgERT79gEdkqdY0tXPvoR6yoaWSH7So59+CxjBxYsdE2Dc2tPDdjOdPeXUJdYyuD+mx4bcchfdq9mV1WXc8jby3mjQWr+d2Ts/h/U3Zi/PYDUq+PG9aX1+atZvbSde3GNXtZDQURGN6/nLnLamiNJygM1r1IbRMkKuOGVW3t1+81+pQVc+K+I/n7Kx8DcNez8zh2/AiG9C0LOTKR3iERj7P2Mpcql0yYQMm++4QYUW5peOZpAAoGDiS+ejUNTz+zxSSk/NRTKNljj05/RsHQoSRqa2l89lkqzj2XSOGmrcUNz0yHggIKx4yhdf78Ln2HfKU2dRHZKve/spAVNY2MGVzJt47ZdZMEBKCsuJCj9hrO/560O33LO1fnMbRfORdHd+TwPYaSSMA9z82nrrEl9XoycVi0uo76ptaN9o3HE8xbXsOogRXsObo/jS1xPl61fpPPSCYwOw/v2+nv25t9dpchjOjvW4zqm1q5+YlZIUck0nvUP/AgzW++6QtFRVReeGG4AeWQeE0tTa+/AZEIVd/+NhQU0Pz227SuXt2tnxMpKaF00iTia9bQ/O67m7zeungxLbNm+RaWAQPaeYfeSUmIiHTZinUNvD7fn8TPPXgMxVsYIzCkbxn9Kkq69BmnTBhFv4pi6ptbeXH2hj66Q/qWMaCyhHgC5i6r2Wifj1etp6E5zk7DqthpqE9W0rtngW+dWbS6DlBLSGcVFkQ448DtU+Vp7y7hnY/XhBiRSO8Qr62l+qqrU+XyE0+kcPiwDvaQdI3PPQvNzRTvvjvFu+1K8fjxEI/TGHu22z+rdMoUABqmT9/ktYZn/HO9fQxIW0pCRKTL3l+0lkQCRgwoZ/Sgyh75jMKCAvYbOxCAGYs37nqVTDBmtUkwUt2shlbxmSF9KIhENklC5iyrIZ6A/hXF6lLUBbsM78s+YzbU4F336Axa45qyV6Qn1dz4G+LLlwNQMGAAFaedFnJEuSV5818a3Pwnk4DGZ57p9s8qHrcThaNG0fTaa8TXb2iBT8TjND77LJE+fSiZOLHbPzeXKQkRkS77eJVvSRgzuGcSkKTtB/kuXkvW1m/0/M5BC8acNi0hs5fVEMEnKWXFhYweVMG85TXE026W52g8yFY7beJoigv9+JqZS9bx8FufhhyRSP5qmTef2tvvSJUrzv8CkXJVnHRWy/z5tC5YQKS8nNKDDgKgZOL+RKqqaF2yhOaPZnT7Z5ZGo9DcTOPzL6Sea37nXeKrV1M6eTKR4uJu/8xcpiRERLqstsGP0agq69m5LfqU+RP2+rQxIbAhgfhk1frUuJB4PMHcZbWMGFBORamPa6ehVTQ0bzwuJNl6svMwjQfpqkFVpRy554bZxn7/5Cxq6ptDjEgkf629wqDZ//8q2mUXSg85JOSIckvDU35AesnBBxMp9TMzRoqLKD1ksn89GLDennVXGCvPPGuTPzU3/a7Dzyw79FAoLKQxrUtWQ9DqUhZ015INlISISNZKrtAdiWw8u9V26eNClvuk4pPV62lobmWntBaOZLKS7JLV0NzKJ6s0HmRbHL3XMAZU+vE9a+v8FM0i0r0annqaxqee8oVIhD5Tp25yHpTNSzQ30/iCb41oOw4jmQw0vfQyifqGdvcvHj+e0sMO2+RP8W67dvi5BQP6Uzx+PC1z5tDyySLitbU0vf46haNHU7SjpjZvS1P0ikiX9QlaQGoaWraw5bapDVpAKkoKN3lt3LAqXp27itlLa9hzVP+NxoMk7TikD5GIb/04aq/hzF1WSzyRYEBlCdtpPMhWKSkq5LT9R6eSj7+/+jEnTxjFDkP6bGFPEemMRFMTa90VqXLp4VN0A9tFTa++SqK2loLhwynedePEoWiHHSgcO5bWBQtofOlFyg4/fJP9uzpFb7qyKVGa33yTxunTKRiyHTQ3qxVkM5SEiEiXbT+oglfnrmLhyk2nv+1On6z0rRYjBmw6/W96EgIbWjvSW0IqSosY0b88NS4kOTWvWkG2zb5jBjBuaBWzg3VYrntsBr+5YIJqakW6Qe2df0itIxGpqKDy3HNDjij3NDztu0Al6upY+5PLNnk9UV2d2q69JGRblEyYSKSqisbnnvPT8RYWUnroZ7v1M/KFumOJSJftMao/kQgsXlPPJ+2sw9EdWlrjvLnATwO824hNx2/snDYupK6xhbnLahnWr4yqso0H/o0btmFcSHIg+85KQrZJJBLhzAO3J5lzvDZvFc/OWB5uUCJ5oHXZMmquvyFVrjjrTAr69QsxotzTunIlze+9B/hko2XmzE3+xNf4KcZbZs6kdfHibv385LiT+Jo1tMybR8m+++rfcDOUhIhIlw3pW8aEYPrcv760kObWeIfbr1jXQHVdU5c+46E3F1Fd30xFSSEHj9tuk9cHV5UxMBgXEpuxnPo240GSktP5vr+omoUrk+NBNCh9W40cWMFndxmSKt/4+Ewam1s72ENEtmTd1b8gEUzvWjhyJGXHHBNyRLmn8ZnpkEhQvNdeDP77/Zv9U3KwnzEr2WrSncqmHE6kqopIVRWlR3RvS0s+URIiIlvlrIPGMLiqlAUr1/Obx2fy6Zq6TbZpbG7lqQ+W8sv/fMi6+s6NH1lW3cAfYnN5+oNlFETggs9+hvJ2xoTAhm5VT3+w1JeHtpOEBNvEPlpGPJFgYGUJg6tKOxWLdOyEfUZSWer/bRavqefeFxeEG5BIDmt68y3q/v6PVLly6lQiReo13xWJRIKGWAxgi12gSg89FIDGZ58lsYWKtK4q2mEsg/5wJ4P+cCelWhtks/TrFpGtUllaxHeP25U7p89l7vJarnroA4b1L2NYv3IKCyKsrWti4Yr1tMQTVJUVpW5Wk+Yur+VPz80DIJ6A+qYWllY3sLKmEYABlSV8YfJYdh2x+WbsccOqeGXuKuqCaXrbawmpKitmWL8yllY3pPaR7tGnrIgT9x3F315eCMAfn5vPCfuMZEg/DfoX6YpEPM7ayzaMXSjZf39Kxu8dYkS5qfn9D4gvWwalpZQceGCH25bssw+Rqiria9bQ/PZblEyYkKEoJUlJiIhstX4VJXz3+N1475O1vD5/FfOXr+fDT6uJxxP0KSti1xF92Xv7AUzcYSClxRsnIStrGlMJR1FBhLKSQgZUlDBp3GD2GNWPvUb3p7Cg48ba9LU+tqsqpX9FSbvb7TSsKi0JUVes7jR55+14fuZyPl1TT0NzKzc9MZOfnjE+7LBEckrd3/9B89vv+EJxMZUXXhBuQDkquRJ66cSJFJSXd7htpKiI0smTaZg2jYann1ESEoJIch5+EckOZjYdOGzMmDFcdNFFPfY5b8xf3WPvLb3L7KXruGHazFT5losPYJ8xA0KMSCR3xGtqWPbZw4ivWAFA+WmnUXnuOSFHJfmieLdd/SxdPa/L0yNqTIiIiGyTccP6st/YDRe56x79iNa4KrhEOqPmhhtTCUjBwIFUnHpKyBGJZIaSEBER2WanThxNcaG/pMxaWsN/3lwUckQi2a95zlxq77gzVa48/wtEyjSmSnoHJSEiIrLNBvYp5ei9hqXKv39qNuvqm0OMSCS7JRIJqq+4Alr8zIFFu+5KyeTJ4QYlkkFKQkREpFscuedwBlb6yQGq65q545k5IUckkr0annzKr2kBEInQ5+KpRCJd7lYvkrOUhIiISLcoKSrgtP1Hp8oPvPYJc4NV6kVkg0RjI9VXWKpcdsQRFO2wQ4gRiWSekhAREek2+4wZwM7BWiyt8QTXT5uBZmEU2VjtHXfSumABAJHKSirO0WxY0vsoCRERkW4TiUQ448DtKQh6lbw+bzXTP1oeblAiWaR16VJqbvxNqlxx1pkU9NP6RdL7KAkREZFuNXJABZ/dZUiqfOPjM2hobg0xIpHsUX3VL0isXw9A4ejRlB19dMgRiYRDSYiIiHS7E/YdSWVpEQBL1zZw7wsLwg1IJAs0vv4G9Q88kCpXTr2ISFFRiBGJhEdJiIiIdLvK0iJO2ndkqvzH5+exdG19iBGJhCsRj1N9+eWpcsmBB1Cy114hRiQSLiUhIiLSIybvvB0jB5QD0Ngc56YnZoUckUh46u6/n+Z33vWF4mIqL7gg3IBEQqYkREREekRBQYSzDhqTKj/5/lLeXLA6xIhEwhFft451V/8yVS7/3OcoHDKkgz1E8p+SEBER6TE7Da1iwg4DU+XrHv2IltZ4iBGJZF7N9TcQX7kSgIJBg6g49ZSQIxIJn5IQERHpUadOHEVxob/czFlWy0NvLAo5IpHMaZ49m9o/3JUqV55/PpHS0hAjEskOSkJERKRHDags5Zi9h6fKtz49h+q6phAjEsmMRCJBtbsCWloAKNptN0omHRxuUCJZQkmIiIj0uCP2GMagPiUArKtv5vZn5oQckUjPa3jiCRpjz/pCJEKfi6cSiUTCDUokSygJERGRHldSVMBp+2+fKj/42ifMWVYTYkQiPSvR0ED1FZYqlx11FEVjx4YXkEiWURIiIiIZMX77/uwyvC8A8YQfpJ5IJEKOSqRn1N5+B60LPwYgUllJxTlnhxyRSHZREiIiIhkRiUQ444DtKQh6o7y5YA3PfLgs3KBEekDrkiXU/Oa3qXLFOWdTUFUVYkQi2UdJiIiIZMyIAeUcuuuG9RF+8/hMGppaQ4xIpPtVX3U1ibo6AAq3356yo44KOSKR7KMkREREMuqEfUbSp7QIgKXVDfz5hfkhRyTSfRpfe436B/+ZKldOvYhIYWGIEYlkJyUhIiKSURWlRXxuwqhU+Z7n57NkbX2IEYl0j0RrK9WXuVS55KCDKNlzzxAjEsleSkJERCTjDt5pMKMHVgDQ2BLnpv/ODDkikW1X99e/0fzee75QXEzlBeeHG5BIFlMSIiIiGVdQEOHMAzdM2fvUB8t4Y/6qECMS2Tbx6mrW/eKXqXL5KSdTuN12IUYkkt2UhIiISCh2HFrFxM8MTJWve2wGLa3xECMS2Xrrrr2e+OrVABQMHkzFySeHHJFIdlMSIiIioTl1wmhKivylaO6yWv71+qKQIxLpuuZZs1h/992pcuUF5xMpLQ0vIJEcoCRERERC07+yhGP2Hp4q3/bMbKrrmkKMSKRrEokE1ZdfAa1+quniPfag5KCDwg1KJAcoCRERkVAdsfswBlf5WuN19S3c+vSckCMS6byGxx+n8bnnfCESoXLqVCKRSLhBieQAJSEiIhKq4qICTtt/dKr8r9c/YfbSdSFGJNI5iYYGqu3KVLns6KMpGrN9B3uISJKSEBERCd3eo/uz24i+AMQTcN2jM0gkEiFHJdKx2ltvo/XjjwGI9OlDxdlnhxyRSO5QEiIiIqGLRCKcccD2FATdWN5auIYnP1gaclQim9e6eAk1v70pVa445xwKqvqEGJFIblESIiIiWWFY/3Kiuw1JlW/67yzqm1pCjEhk86p//nMS9fUAFI4ZQ9mRR4YckUhuKQo7AJGeYGaDgFOBE4C9gJFAE/AecBdwl3Munrb9WGB+B2/5N+fcOZv5rAuBrwG7A63AW8A1zrmHt/mLiPQyx40fwavzVlHb0MKy6gbueX4+lxw+LuywRDbS+Mor1P/roVS5z8VTiRSqXlekK5SESL46E/g9sAR4BvgYGAqcBtwBHGdmZzrn2nY6fwf4Vzvv9357H2Jm1wD/AywCbgdKgHOA/5jZN5xzN7W3n4i0r6K0iJP3G8VfXlwAwN3PzuO+lxbS0NRKeUkhx44fwecnjWXUwIpwA5VepWXBAmpvvY26B/9JYv16SJv9qmTSJIp33z3E6ERyk5IQyVezgM8Bj7Rp8fgR8CpwOj4heaDNfm87567ozAeY2SR8AjIX2N85tyZ4/tfAG8A1Zvawc27Btn0Vkd7loHGD+e97S1hR00g8AfVNfv2FuqZW/v3GIh59+1OuOnsfJo3bLuRIpTdoePoZVl/yZRLNzdASdA9MmzShZN99Q4pMJLep7VDyknPuaefcf9ITkOD5pcAtQTG6jR/zleDx58kEJPiMBcDvgFJg6jZ+hkivs6qmkTWbWbCwJZ6goTnOj/72NotW12U4MultWhYs8AlIff2GBKSN2jvuoHWpJlEQ6Sq1hEhv1Bw8tndFGWFmXwYGAauAl5xz727mfQ4PHqe189pjwGXBNm4bYhXpdZ76YCnxeMfT87a0JrjvxQV8/0R1g5GeU3vrbb4FpCMtLdQ9/AhVX/piZoISyRNKQqRXMbMi4IKg2F7ycFTwJ32f6cCFzrmP056rxA92r3XOLWnnfWYHjzt3EMtFwEXtvLTP5vbpTiVFagiV7PTavFVsIQehJZ5g2rtLlIRIj6p78J+bbQFJaW2l6bnn4NKvZiYoka4oyN5rvZIQ6W1+AewJPOqcezzt+TrgSvyg9HnBc3sDVwBTgKfMbB/n3PrgtX7BY/VmPif5fP8OYhkLHNaV4LvTXqM7Ck0kPI3N8S1vBNRp+l7pYYn167e8EZCor6d04oQejkYkvygJkV7DzL6JH0g+Azg//TXn3HLg8ja7PGtmRwPPAwcCXwJu7OLHdlSfuwCItfP8ToMGDRo5bNiwLn6USH4oLymkLhiM3pGKEl3CpGdFKitJ1NZuebs+lRmIRiS/6AwuvYKZfQ2fQHwIHOGcW92Z/ZxzLWZ2Bz4JOZQNSUiypaNfuztuuaUE59zdwN2beXkLnVFE8tex40fw7zcW0dJBn6yiggjH7j08g1FJb1Rx2qmsv/e+jrtkFRVRcdrpmQtKJE9kb0cxkW5iZt8GbsKv9TElmCGrK1YEj6mqrqBb1qdAHzNr704oubrarC5+lkiv9/lJYykqjHS4TVFhhHMn+tleXwAAIABJREFUjc1MQNJr9fnyJUSKizvcJlJcTJ9LvpShiETyh5IQyWtm9r/A9cDb+ARk+Va8zUHB47w2zz8dPB7bzj7HtdlGRDpp1MAKrjp7H8qKCygq2DgZKSqIUFZcwFVn76MFC6XHFY0dy8DbbiVSXg5FbTqPFBURKS9n4G23UjR2bCjxieQyJSGSt8zsMvxA9DfwXbBWdrDtgWZW0s7zhwPfCYp/bvNycr2RH5vZgLR9xgJfAxqBu7Y2fpHebNK47fjzpZM5ecIoKkuLiESgsrSIkyeM4s+XTtZChZIxZYdPYciT/6XyvPOIVPWBSIRIVR8qzzuPIU/+l7LDp4QdokhOiiQS6nou+cfMLsSPt2gFfkv7YzMWBOMyktPw7gFMBxYFr+/NhrVALnPO/aydz7kW+G6wzz+AEuBs/Doj33DO3bSVX0H/MUVERCRXdNyHth0amC75aofgsRD49ma2ibFhYPg9wKnA/viuVMXAMuB+4Cbn3HPtvYFz7n/M7F3g68AlQBx4E/i1c+7hbf8aIiIiIvlHLSEi2Un/MUVERCRXdLklRGNCREREREQko5SEiIiIiIhIRikJERERERGRjFISIiIiIiIiGaUkREREREREMkpJiIiIiIiIZJSSEBERERERySgtVijSS02bNo2lS5eGHYaIiIj0kGHDhnHssceGHUa7lISIZKcuL/rTVa+88soMYJee/hwREREJx8KFC2cee+yxu4YdR3uUhIj0Xn2Cx2rg7TAD6aJ9gH7kXtxd0Ru+Y2fpWEi20W9yg95wLHL1Oybj7rOlDcOiJESk95oDjATeds5FQ46l08xsOnAYORZ3V/SG79hZOhaSbfSb3KA3HItc/Y5pcc8JOZTN0sB0ERERERHJKCUhIiIiIiKSUUpCREREREQko5SEiIiIiIhIRmlgukjvdTcwHVgQahRddze5GXdX3E3+f8fOuhsdC8kud6PfZNLd5P+xuJvc/I53k+VxRxKJRNgxiIiIiIhIL6LuWCIiIiIiklFKQkREREREJKOUhIiIiIiISEYpCRERERERkYxSEiIiIiIiIhmlJEREJA+YWSTsGLKJjoeEycxKwo4hW5iZ7jWlXZqiV0Q2YmYFzrl42HF0hZntAewA1APVzrnXQw4pY8zsROfcw2HHkQ3M7Aygwjn3p7Bjkd7LzL4CVAAPO+dmhR1PWMzsp8CtzrlPw46lp+Ti9TKbKAkREQDM7Gbgbufcq7l0YjWzW4GTgSFpT/8e+Jtz7tlwosoMM3sKmALs65x7J+x4wmRmdwHHAR8C5+fzjY9kLzO7FzgReB84xzn3ccghhcLMpgGT8f8X/xV2PN3BzI4FdgSGAW8BLznnloQbVeeZWcQ5l1U3/WoiExHM7K/AV4C/mNnezrl4LjShm9k/gQuAp4HzgO8Bc4GvAteZ2TdDDK9HmdljwAHA/5LFK+Jmgpn9Czgd+CtwsXPu0/TuWOqaJZlgZn/HV4hcR1oCYmaR5Pm0N/wWg3PTYYDDn5tznpndgz+//Ab4MfAP4BUzO9XMBoYa3BaY2e4AzrlEtv3+sv4mQ0R6lpn9EDgLWISv5XkwFxIRM/sBcALwK+BS59x9zrnrgC8CbwP7AV83s++HGGaPCC7yUeBy4DbnXPVmtsuqC05PMLMfA4cDvwCudM4tAH/BTW6TbbV/kn/M7MvAsfjz0W/atIAUAkWQ/7/F4Nw0BfgRcKdzbl3IIW2zILlMVnIcjj/33g+MAv4IfMvMxoUWYAfM7G/An83sUMi+RETdsUR6MTM7DLgPaAYOBK4ALgHmAac5597N1q5ZZvYfYCJwkHNuoZkVOedagte+CNwebPoJ8EPn3H0hhdqtgov8IYABdzjn1qa9tidQBqx1zs0Jnsu6JvjuYmaFwFNAJXCyc26xmZUB2+OT0e2ABPAn4APn3MrQgpW8FnTDmgzs75xbbmYVwK74FuY9gEZgGvCHfP0dBi3TR+MTkL8451Ymzz9mdhxQBSwBluTK+cnMLgLuBK4BfuWcW5X22p+AL+DHIv6eTZPPUJnZLfjreQvwHHC5c+6F4LWsOO5ZW8spIj3LzIrwF8di4NvOuaXOua/ga3Y+Qxa3iJjZAGBf/MVsYfB03MyKg7+/CawB7gUGARcENwU5LegScAxwlXPuGufcWjOrNLOjzOwR4F3gVeBFM/u7mfXNtpqvbrYDPiF7NEhAqoDzgUeA7wPnAlPxNZiXmdn2oUUqecvMhgAHA28HCUh//M3pQ8CXgN3xtee/AO4wswPDirWnBF0iTwb+CfwuSED6AyeZ2dP4/5N/xXfP+oeZnQc50TI0MXi8zTm3yswKgmsn+Eq7xfib/K/jW0uyYjYwM7sAf+57Hfg7vnXq52Y2GbKnRST0AyUi4QhaDZ7G1xg/kryBd85NZTOJSFDznA1agVpgn2BGJJxzcedcc/D65/C1U3cAj+Fv3E8KI9DuEtTwlwXFc9Jemoqv6d8f3yrwEP74nA7828z6ZMsFpwcU4ls6+gTlQ4CrgRXAGfiuE9cB1fga6W8GiYpId1oHrMfX9APsBPwcWIivLNkDOB54GX9u+h8z69PO++Sy5Ix0xwGnBX8/FfgDvpvvX4CbgOnA3vhk7NwMx9hpwTiecmA3IEJwvxz0Ckj2DGgCBgP/BVYCPzWzPcPuOWBmn8G3gDTjr+9T8dfCQ8myRERJiEgv5pybga9FbnLONSdreDaXiDjnWgHMbJ/wooagn/FtQfGHZvY58N1zghq284EPnXPTgbuD7Q4Ktsm5m/GgS1wDcBFwC7CXmb1tZicCP8QPxp8MnOicOxWYBHyAv+j8DnKixnFrfIrvbvfZoHw+sAo43Dn3oHPuJfzg2J/gbwjPwc9sI9ItgvNJEf4m9DAzmwR8GZ+UHOOce8c5t9g5Nw34NvAOPkE+L6yYu1Ny0L1z7kF8Rc8A4GYzuxr4KTATmOCcO985903g8/gWhFLgK2Y2MqTQO+ScSzjn6oE5wVNnmlm/4LVk74DT8RUePwXuwXcLvRhCv86swVfSfc859x6+peYK/DXzUOAqMzsEwk9ElISI9HLJcRTJv28mEfmnme0KYGZfAp43s/8LI960E+Y/8LVv+wEPmNmDQAx/k16CrwkCX/u4Fj9OICcFF71i59x6fDejW/G1if/GXwSnOOdmO+cag+3m4y+Q64D9zWxQaMH3rHr8VJkTzezX+GTkAedcQ5CQRoJj9gjwJDACX1Mr0i2Cm9VafI1/BN8Na1d818g6MytOnrOcc68Cvwx23T2MeLtTcK5JAJHg/9oj+JaegfhZ+z7BJ2Ir064rK/A3w68BE/DdZbNO2nXmAWApviX1orQunVOBr+GTz4+Aq4Ltxoc53iL47DX4yWbug1QvgcX4cYS34c+TP08mIpt5n4zkB0pCRGQj7SQif8L3vX/YzH6Cn56wAHg0pPgSwePH+BP/lfjuR6cAY/Hdrw5OzpIE1OFr3Vam758LzOxcMzsZIGipKghuqr+Hb+F5D/ha8Fph2nbF+FaCpcA4YLtcbAFqyzaedrcwaJn7Mb71I9nKkUyqC4JavqKgRvPB4PmcPw4SrvQbtLTxATF899ZL8K2SiSBBacbfpCe3mxE8VmYq3p4QVEb92MxGOOdakzXqzi+cejL+fHutc642OG+lV3YtxZ+fKvAzTGWdtOvEy/gEswK4HnjLzObhJz4pBk5J+26r8AlYaF3t0q6P65KzJqYlwUvYNBE5LLmPmV1sZlcE22akS5mSEBHZRJCIJG9qL8Lf8H4G3+zcHzjAZcHieM65Wc45h69VHI8fRHiB23ihukvwLSPPQujN5J1mfvG964EbzGy74AIfT0tEvgFci6+FI62rXIFzrjnYpgh4A5iVS8lXW2Y22cwuBX6WNgaoNbixm4P/XZbix4icZGblQTJWmnaDcHjwOKPt+4t0hpmdYWbX4MfQ/drMdkj+voIJMm7FL1IIcFza4Ot4m99hHHgxw+F3GzP7C75F5zCgvM1rEefcf4AjgJdgww1tm3PvdsDH+OnUs1LwXdYBvwa+AzyMr/Bagu/mOik5MYpzrgZ/LJYHf88abuPpytsmIleY2SQzOxv4GfBdM8tYl1VN0Ssi7UpvUjazc/AzTa0GDnXOfRhqcB2wtCmFgzETVwUvHeNyZHXbYKaZI/Bdy24Oulelv55sBWi7X/p3/yr+QnkjvmtEcy4mImZ2E76VI31BsMudcz9L22Y4frzMN/CtIf8Fzgi6yWBmp+JvmuqAo51zyzMTveQLM/sDvqtRH6AB6Iufie60oKtLcrsv4mdKGo9vqfyVc+4vwQ34GfiEuQA4wjm3KLPfYtuZ2QP4iT5+A/zeOfeJbZiGNwJE2qtFb3NuOh9/bnsA+Ipzri6DX6FL2natMrOx+Bmxkq1cyecvxg+8d865X4fZJaszzGwU8H/4hX0/xLdIJYDPOufe72jf7qSWEBFpV1oCcil+Aa5qQkhAuto3Ne1C9wv8jecI4NwcSkAuwycgVwG/bJuAwEatHoVp+6Vf5E/B3wjNB25wfuKBrL0gbk6QjF2IH9MxGT+YdxV+Fpq9k9sF/7Z34RdvXIhfq+BtM7vP/Hoyd+AHzJ6nBES6KhhvdiZ+gbpJ+PFYjwEHAPsE2yRnT7oTn2j8G9gLuMfMnsVPlXo7/nd4eo4mIF8DjsS3DFzjnPsENqppL0xPQJItH23OTWfiK0XWABZ2AtKma90mreRp18Hkawudc01smCEL8xOjfAvfxexv6ftlq+D391N8F8Ld8d/nkEwmIKCWEJG8tq21MUFtyYP4bk57Z+IEFVwUBgP16c3anf0uwY35ufib+EXAF51zH/VUvN0puNC9gK8gOsU5t9T8NJHD8AMhhwLL8IM6Hw5qHwvTkpIS4NLgT3/8LFEZvah0FzO7FTgbn0je6pxbHTz/P/iboAnOubfa7FMCjAn22QM/HmYefpDwD51zszL3DSQfmNmN+ET4V/jf4arg+SPxLW4XOOf+3M5+o/GVCV8HhuNvul/CVyzMabt9LjCz+/GDyQ91zn1qfu2lPfCzge2M7450O/CCc+6DNvsW4WeqOws/lfHR2XBuMj+FeW1audPXzOB8cyX+PFUGHJkN36mzzC/E+Ct8t93JYVwnlYSI5CEz28c593bw961ORIIBzkcA8zJxA2dmP8Uv6jUBP6j638Cfgfecc03WydXbzWwofpD6POdnY8kJZrYTMAv4vnPuWvNTQp6BrzncKW3T9fgpIb+WHHyNb07/Pb6rxOv4m6OcHP8Q9KW/Hr+4mbmNVym+Bn/TE8XXNNcAL7XpElOCH/j7GXwS0px+oyHSGWZ2Gv53+BTwA5e20rmZ/Rg/7enn8WtJFOHHDLzepjWgHF+pUI+fLCE1QDuXmNlg/Ex0Lzrnzja/zsl5+IkhRgHLgSH4iSGexCdbsWDfHfDrppyDr2T5knNuZua/xQZm9gPgQPz6Sq/gK3auTavQ2eJ108xOwre+Lge+k8lKjs5eCzvY/zT8gHvwCcgHHW3fU9QdSyTPmNlDwJtmdgxs2zzgwQDnaRlKQB7CTz87EHgGX5P/LXwS8n0zq3SdXL3dObfMOfdKLiUggWQf49HB4wH4Wv21+Nm/Pgdchh/b8BXgBkhNs7we+Ffw+mk5nIBU4JOLZfiuZOkJyBH4hdCK8Yuf/QG/GvB9FswiFtw8NDk/TeWbzrk1SkBkKw3FT2pxdZsE5Aj8mjRxfO3+d/Fr0TyDH5uUPmtWg3NufXDDuMk4rhySCP70C8rj8QOZF+C7qO2HXyPjSeBY/ADnMQBBl9K/41ePPyMLEpB/4WOfiB/fcyp+NftpZnZ8MLHFFq+bwQD88/HdPDOSgJjZeWbWt7PXws28RxH++job36oVSgICagkRySvBIN5Lg+Jq4Bzn3JPBa52p2RkD9HV+gaOMMbOf4xOQy4C7nHPLzWwvfE3bRfjE5DZ8l5ratrVAwWDBnfC1dFk7yHFLzKwvfpDgO865E4LEbC9gN+dcY7BNETAF3xKSwPcvfzF4LbnqfXN7758rzC+G2eic+yht0Osk/Gxg++Fv+l7BT7d7Hn5V4BhwpvPT8Yp0CzMb65xbkDznmNlB+IqBSfjf3QvOublm9g38rEPF+NkDc6ILaFeY2SP4GbHG49fIOA3Yq0232QPwN/hH4LuU/ifttXYn1MgkM/sN8P/wLTO34hf12xsfcxTfcnoNcK/zMwxu7n3KnF9ANmOC5OkkfMJ0dXvXwk68R/J82gcoSXZzDUvhFVdcEebni0g3MbNz8bVyr+K7MR0GfC4Wi70RjUbnRaNRzCwSjUY3t/9gfHcCi8Vi/41GoxkZOBmcDB1+wPGlzrk1wcVqaSwWewPfPelA4CigIhaLPRcMDEzuPwC/lokD3o1Go6HV6myLoFarFX+TfWosFivGX+zvd849bWal0Wi0NRqNxmOx2Cf4cSJHAq9Eo9E3AaLRaDwajWZkfveeFI1Gl0aj0ZVtLpjn4bumneqcuy8ajS6ORqOLY7HYDHyN5tHAk9FodGGYsUt+MLPCaDSaiEajawGi0WgCIBaLnYLvgvU559y/YrFYdbDdq7FYbARwCP489GZ40feMWCw2Ft/dczD+e77tgpm/YrFYJBqNEo1GP43FYn2B44HqWCz2WPBaInkMw2JmQ4Cr8dMCf885tyYWi0Wccx/HYrFn8effw/Dnk5WxWOyjaDTamrb/rrFY7JJoNPpcNBrNaLe6YKKVi/EtN/sDxbFY7FXnF6gt2NKxNbOyaDTaEtwHFDrnGqPRaOgVNuqOJZIHgjEQ5+AHBn7VOfdN/Mm2H/D3YBBlh12zgu4GyS4HmezGNAx/470iqNkpStaWBV1q/gV8E7/67hfxq9amZoUKtlkQxPwWOcr5tQSa8TM5gZ9udn/8BZ+0lpCCYLvXg+0GZzrWTHEbFt6qBaYB+zvnpplZgZlFgovpAnw/c/ALiolss83V2DvnbsL/Dp9Kax0pC15+OXgsa2/fXJV2zbgGeA7fArILkKwMSi0MGpQfCR4bgvNatlSMjAZ2BN53zq0zs5Jkq7Hz631ci5/SfDC+tXVf8Alp0Mr8K/xaRbdmMmjzsx1egl/j6Cv48ZLfBX4YDKzvsGuWmY0D/mJ+Fq/N/rbDoCREJD804ft3fik5O4dz7sf4Jud2E5H0ZMQ2TC95DDAiw7O3fArMBUYEF/WW9BNq0OrxBL6lowVfCzkgiDu5svslwB7OudkZjLtHOOeeBr6Nn0EGYEfz62AkX09e0PfGjyF5F9qfXjKfOOdedc59ELSOxIPnkhfT8fgEOqPdCKV3sQ0LuM4OHuPB7zHZLecY/FTmsZBC7BHJa0ZwLr4a+AB//3immR3s/MKhJWmD7s8MHt+BrDo3rcCPndsV/LUlPTbn3DL85B5/AvYE/id4vjVIVn6GnwL85kwFHCS4Z+MrGKc65+7BV8otCeLrTCJyPH7cy6/NrCKL/j2UhIjkg6A14Er8PPbpF8vLaCcRIai5CrZN1uYlb+iXZiru4GRYgO9ytSd+cCdtT6jBRX4afkrMSfhWH9ITlvSBo7kq7eLwO+BHwd+PB35sfrrk5Han4i/0H+Bndcn6eem7S3BDlP77vQDfNeQJ/DgokR7Rtga5ze/wHOBE4Hl8q21eSTu/TMe3GLyMH//yz2C8VjOAmZ2FH8c3Gz9IPZvOTbX4Sq/jzOxC2LR3QHD9uxF/TTrd/CxSBC30rwK7OOfeyVTAwbXvV/jZ2V4Jnn4S3yKymHYSkXaSjNvx/2anO+fqsujfQwPTRfKVbbx+xJX4qRSr8YPVHw+e/yqwA34F6owOsmsT6yR87WEt8A0XzLvfzgD0o4DH8auIfz2UYDMkuJB8CT94Enyt4kf4rh6H4AdlR8Oc2SQMtvHCZyfjk+y+wBTn3NxQg5Oc0+b31JU1IiJpCchZ+AqUIfgVp3OuRbYrxyGonZ+Eb7E9MXj6NaAQ38pQS5aumRH8W90DvAj8n3Pu5eD51KrvweMXgD8C33XO3Zi2fygroZtZsdt4hfZC4HB8y81IfJLxC7fxmidDXJYvzqqWEJE8FTSRt9cicp+ZHR7Upl8BfA8/+1QogpP6i8D/4bsg/cj8qrrJFpHCtDEgH+K7ZPUNJ9ru0VH/3STnXMI5dzt+lpl7gEH4Zvn98LWth+RDAtKZY5Eu+E2Umtn/4hct3A44XgmIbKXUOKKOxsy1FWw7MKjguRp/Dj0qFxOQQKePg3OuIeg2ejq+cusJfGUWwH2EsPJ2F0zDTxd8GPAdM9sXNvrOyfPRJ/iKnjHpO4fViuDazHgYVDA+DXyVDS0iP0r2aDCzLwGPmtmBmY61K9QSIpLn2rSIOPzYimp8rVUzcFg2XDDMbCT+RPotYA7wK+fcnW22uRi4BV87dVPmo9w6thWrwLepaS3DJ15j8RfHGpeja19szbFos/8I/OJx4/C1mZe4HF0TRcJj27hYXTBO6xf4dSKeBL7uMrhYXXfZ2uPQ5vxUCAx2zi0LxoY0td0+m5hfzf6P+Cl5/wn81jk3vc0238Inl19yzt2b6Rg7K61F5BZgOL5F5FN8cjgQ2M+FvC5LR5SEiPQC6RcGM/sncDKwhpAXKgriSe8GMBb4OvAdfC3UjfjZopYAJ+BnBOmH74b0cRjxdpV1wyrwndkmF3THsQje5zz8rGp/yeQYJskP5tdbOB5/XmkEPoOvAX8Kv0L6M865+i1UEhThJ0QYjV8rJNcWRt3m49BeF66wuit1VXCtuQ3f0vwuvgUnWbF1HH7Nl0J8t7JPQwix08ysBN897g78ebEcWIfvGhh6BWNHlISI5IE2tVKVbjOLLAX9XK8C+gCTXcgLaqVfuIBy51yd+XU/TsOvBl4J1ONn/6rAr6J9fLafWJPMLzZ4NH72rwXAwfiZvWbib75vcM6tz5ckoyPdfSwsCxY+k9xj3bdYXU7cbG9ONx6HIrdhVqycErSq/hA//W0JfjB9IUFLLb57XVZfa9ImlongF9H8HllSwdgZWqxQJMe1SUBOBy6JxWKzo9Ho6jbbnYS/2YvgT1AfZj7ajeJJxR2LxU4HvhKLxWY65xZHo9G3YrHYQ/i+rg34C+L9wLdzpc+1+VXgL8R3f/uOc+72WCz2GFCDvwE/DhgYi8Wede0sOGVmY2Ox2MRYLLY0Go3m+gro3X4swl74THKPde9idWF8hW7RzcchZytPotFoTSwWexI/tqIfvgVhPfAo8OVs7saUlLaI5lT8RAFx/JicUK/vnVW05U1EJFu1SUBOwrdyjME3Jbe1HL+a+jfCrt3pIO4r0l7/ED8QPeeYX+H7cPy6Fb9zfhHGQufce2b2S+BNfK3VpUCzmf3YOVeXtv8AfFeBI/HTEd+f8S/RTXQsJIskF6v7t9uwWF0T+MXqzOxafA34d/BdP2cALwf97gvwU6WeaGZjnHNfDucrdAsdh0Aw4Pt5M3ups+OBso2ZHYK/dg4EJuZKAgKaHUskp6XdyJ+MHyRZBezqnFvezqxDrwPHugzOcb45W4o77fXUd+jsrDVZQqvAb6BjIdki5xar6yE6DpvK2RYdfDeyR/EJSNZ3wUqnJEQkx5nZYPyAtKHAJOfcgqCmeaOTanABqWv3TULQmbjb/D1naqbQKvDpdCwkW+TcYnU9RMehjfTrS45da5JJ4zdyLQEBJSEiOc/5lcJPAQ5Mu5HP+gG7uRr3lphWgU/RsZBs4pxbDVyOn5r8IjM7KHg+dQMedMWZja/tT+C7LpE2+Dqnx2eBjkM+ytXJATQwXSQPRKPRT6LR6Jr0ri65IFfj7kg0GiUajTbHYrGP8YOxJ8RisU+j0ei70Wg0kT7oOhqN1sZisWr8WgPzo9Hoo8HzOVUTtzk6FpJtYrHYJ/iF9U4C+sZisbnRaHRpNBpNJc3RaDQRi8UGABcBM6LR6OPJ/XN5QHo6HQfJBmoJEckjuVobkqtxb471wlXgN0fHQrKJc24d/rc4HTgT+ImZRYPXEmmVIfvgZ+Z7PYQwe5yOg2QDrRMiItJDLI9Xge8qHQvJJvm0WN220HGQMCkJERHpZpbnq8B3hY6FZKt8WKyuO+g4SFiUhIiIdCPL81Xgu0LHQrKdmRUDB+IXehuDX6jvVeBG59zcMGPLJB0HCYOSEBGRbtLO6vVHANc55+YEz+2OnxFsf/y89G8Df3LOLQwp5B6jYyG5JH12vlxbrK476ThIJmnFdBGRbpDvq8B3hY6F5KBcXqyuO+k4SMaoJUREpBsFq8BfhV9wL7kIY/q4iPS/53VNo46FiIhsjpIQEZFuEqwC/xF+0PXEfFqEsat0LEREpCNKQkREupGZTQaWOufm9vabbh0LERHZHCUhIiI9IFgFPq8WYdxaOhYiItKWkhAREREREcmogrADEBERERGR3kVJiIiIiIiIZJSSEBERERERySglISIiIiIiklFKQkREREREJKOUhIiIiIiISEYpCRERERERkYxSEiIiIiIiIhlVFHYAIiIisvXMbDpwWJunpzjnpmc+mvaZ2VqgX/pzzrlISOGISBZQEiIiItJDzGwBMAYw59wV3bXtZqwD6oO/N23F/m3jmQI8HRQPdM692ol9BgBLgRLgq865W4KXlgENQCEweFtjE5HcpyREREQkP3zLOXd3N77fdGAhPjG6ANhiEgKcg09AGoG/JZ90zu0CYGZjgfndGKOI5CiNCREREZFNOOcSwJ+C4jlmVtyJ3S4IHv/tnFvTM5GJSD5QEiIiIiKbk0xCBgHHd7ShmY0DDgqKf+zJoEQk96k7loiISC9hZgXAefgWi33wg8VXAs8B1znnXknf3jk3x8xeACYH+zzUwdsnW0GWAY93c+gikmfUEiIiItILmFkVPjn4E3AkvnWjHhgOnAW8aGZfb2fXZKvGicHA8/beOwJ8ISj+xTnX0p2xi0j+URIiIiLSOySTj3eBE4BK51w/YADwI6AFuNHMJrc9OOHtAAADMElEQVTZ7378zFYlwNmbee9DgbFpnyMi0iElISIiInnOzI4ETgEW4NcQedQ5Vw/gnFvrnLsauAx/X/B/6fs656qBfwXFC2hf8vm3nXPvdHP4IpKHlISIiIjkvwuDx7udc6s3s829weMUMyts81qyS9bBZrZT+gtmVg6c0WY7EZEOaWC6iIhI/psUPH7HzL66hW0r8ONFlqc99wSwGBgBnA+4tNdOAfriu3Pdi4hIJ6glREREJP8NDx77AUM7+JNUkb6zc64V+HNQPD8YiJ6U7Io1zTmXnriIiGyWWkJERER6TkPwWN6JbZM3/vU9EEey0vFk59y/t/I9/gj8ANgBOAR4zsyGAUelvS4i0ilqCREREek5q4LH4R1tZGalwMA2+3SnZcHj7lv7Bs65D4HXg+L5weN5QCGwBvjPVkcnIr2OkhAREZGe81bwOKnDreAA/M18+j7d6aXg8fRtfJ9ka8dZZlbGhq5Yf3XONW7je4tIL6IkREREpOc8EDzuaGYnd7Ddd4PH+fRMEnJ38DjRzDY3zS4Am1uQMHAf0IQfW/ITYO/geXXFEpEuURIiIiLSQ5xzz+BnlgL4s5l92cz6JV83s13M7M/4GaYAfuKci/dAHNOAB4PiH8xLdREzswFmdrKZPQRc18H7rAIeCYrJ9URmOude6e6YRSS/aWC6iIhIz/o88BC+S9YtwO/NbC1+BfLKYJsEcJlzrienuL0AX/l4CnA5cLmZVQMR/BS7SXdv4X3+CJzKhopMtYKISJepJURERKQHOedWAofhB3M/gh8k3id4eSZwO7Cfc+7nPRzHeufcqcCJ+FaRT/GzdpUAc/BrfJwBXLqFt3oUWBH8Pc6GqXtFRDpNLSEiIiI9zDnXgr9ZD/2G3Tn3CBu6VG3N/s3AkO6LSER6I7WEiIiIiIhIRqklREREJD/cZWZ3BX+f4pybHmYw6YIxMP22uKGI9BpKQkRERHLbajYsRpjUFEYgHVjGhtXjRUSIJBKJsGMQEREREZFeRGNCREREREQko5SEiIiIiIhIRikJERERERGRjFISIiIiIiIiGaUkREREREREMkpJiIiIiIiIZNT/BwUzQtQxAdr0AAAAAElFTkSuQmCC\n", + "image/png": 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\n", 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" ] @@ -979,7 +979,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 24, "metadata": {}, "outputs": [ { @@ -993,11 +993,11 @@ "Two-Particle Response Function tool-box \n", "\n", "beta = 11.6045250062\n", - "nk = 64\n", + "nk = 1024\n", "nw = 100\n", "norb = 1\n", "\n", - "Approx. Memory Utilization: 0.00 GB\n", + "Approx. Memory Utilization: 0.01 GB\n", "\n", "--> fourier_wk_to_wr\n", "--> fourier_wr_to_tr\n", @@ -1025,7 +1025,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 25, "metadata": {}, "outputs": [], "source": [ @@ -1074,7 +1074,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 26, "metadata": {}, "outputs": [], "source": [ @@ -1124,7 +1124,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 27, "metadata": {}, "outputs": [], "source": [ @@ -1143,7 +1143,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 28, "metadata": {}, "outputs": [ { @@ -1152,13 +1152,13 @@ "Text(0.07,0.15,'SC')" ] }, - "execution_count": 26, + "execution_count": 28, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -1214,7 +1214,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 29, "metadata": {}, "outputs": [], "source": [ @@ -1226,7 +1226,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 30, "metadata": {}, "outputs": [ { @@ -1235,13 +1235,13 @@ "Text(0.52,0.6,'$|\\\\downarrow \\\\rangle$')" ] }, - "execution_count": 28, + "execution_count": 30, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -1273,7 +1273,7 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 31, "metadata": {}, "outputs": [], "source": [ @@ -1326,7 +1326,7 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 32, "metadata": {}, "outputs": [], "source": [ @@ -1363,7 +1363,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 38, "metadata": {}, "outputs": [ { @@ -1372,13 +1372,13 @@ "Text(0.5,1,'Hubbard with $\\\\mathrm{Zeeman}=\\\\xi$')" ] }, - "execution_count": 31, + "execution_count": 38, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -1435,6 +1435,488 @@ "ax_pd_right.set_title(r'Hubbard with $\\mathrm{Zeeman}=\\xi$', color='Grey', size=24)" ] }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(9,5))\n", + "\n", + "ax_pd_right = plt.subplot(122)\n", + "\n", + "ax_pd_right.plot(U_sx_cs, Ts, \"o\", ls=\"-\", color='C2')\n", + "ax_pd_right.fill_betweenx(Ts, U_sx_cs, np.max(U_sx_cs) , alpha=0.25, color='C2')\n", + "\n", + "ax_pd_left = plt.subplot(121)\n", + "\n", + "ax_pd_left.plot(U_sc_cs, Ts, \"o\", ls=\"-\", color='grey')\n", + "ax_pd_left.fill_betweenx(Ts, U_sc_cs, np.min(U_sc_cs), alpha=0.25, color='grey')\n", + "\n", + "ax_pd_left.set_ylabel('Temperature\\n[Kelvin]', rotation=0, ha='right', multialignment='center')\n", + "ax_pd_left.set_xlabel('U [eV]')\n", + "ax_pd_right.set_xlabel('U [eV]')\n", + "\n", + "ax_pd_left.set_yticks(Ts)\n", + "ax_pd_right.set_yticks([])\n", + "\n", + "ax_pd_left.set_xticks([np.round(ele,2) for ele in U_sc_cs])\n", + "ax_pd_left.set_xticklabels([np.round(ele,2) for ele in U_sc_cs])\n", + "ax_pd_right.set_xticks([np.round(ele,2) for ele in U_sx_cs])\n", + "ax_pd_right.set_xticklabels([np.round(ele,2) for ele in U_sx_cs])\n", + "\n", + "ax_pd_left.spines['left'].set_bounds(Ts[-1], Ts[0])\n", + "ax_pd_right.spines['left'].set_visible(False)\n", + "\n", + "ax_pd_left.spines['bottom'].set_bounds(min(ax_pd_left.get_xticks()), max(ax_pd_left.get_xticks()))\n", + "ax_pd_right.spines['bottom'].set_bounds(min(ax_pd_right.get_xticks()), max(ax_pd_right.get_xticks()))\n", + "\n", + "\n", + "ax_pd_left.text(0.3, 0.25, \"SC\", transform = ax_pd_left.transAxes, size=22, color='grey')\n", + "\n", + "ax_pd_right.text(0.35, 0.5, \"in-plane AFM\", transform = ax_pd_right.transAxes, size=22, color='C2', rotation=50)\n", + "\n", + "ax_pd_left.set_title(r'with $\\mu=\\xi$', color='grey', size=24)\n", + "ax_pd_right.set_title(r'with $\\mathrm{Zeeman}=\\xi$', color='Grey', size=24)\n", + "\n", + "fig.tight_layout()\n", + "\n", + "plt.savefig('test2.svg')" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": {}, + 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\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 60, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from IPython.core.display import SVG\n", + "SVG(filename='test.svg')" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -1445,7 +1927,7 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 34, "metadata": {}, "outputs": [], "source": [ @@ -1454,22 +1936,22 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 33, + "execution_count": 35, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] diff --git a/doc/documentation.rst b/doc/documentation.rst index 9625e6096..109b5d878 100644 --- a/doc/documentation.rst +++ b/doc/documentation.rst @@ -13,8 +13,8 @@ Tutorials user_guide/Bethe-Salpeter Equation on the Hubbard atom.ipynb user_guide/Lattice BSE on Hubbard atom.ipynb user_guide/dmft_susceptibility/dmft_susceptibility - user_guide/PHT_Hubbard_Model.ipynb - + user_guide/Linearized Eliashberg equation on the attractive Hubbard model.ipynb + Python reference manual ----------------------- diff --git a/doc/user_guide/Linearized Eliashberg equation on the attractive Hubbard model.ipynb b/doc/user_guide/Linearized Eliashberg equation on the attractive Hubbard model.ipynb new file mode 100644 index 000000000..367c0be09 --- /dev/null +++ b/doc/user_guide/Linearized Eliashberg equation on the attractive Hubbard model.ipynb @@ -0,0 +1,861 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "nbsphinx": "hidden" + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Starting run with 1 MPI threads at : 2019-05-15 18:39:07.048894\n" + ] + } + ], + "source": [ + "%matplotlib inline\n", + "\n", + "import numpy as np\n", + "\n", + "from pytriqs.plot.mpl_interface import plt\n", + "from triqs_tprf.tight_binding import create_square_lattice\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "nbsphinx": "hidden" + }, + "outputs": [], + "source": [ + "plt.style.use('notebook.mplstyle')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Linearized Eliashberg equation on the attractive Hubbard model\n", + "\n", + "A simple example for the usage of the linearized Eliashberg equation is the attractive Hubbard model on a square lattice.\n", + "It is not only fast and simple to setup, but the particle-hole symmetry of the Hubbard model also serves as a benchmark for the correctness of such a calculation.\n", + "\n", + "In the following we will first introduce the Hubbard model and present the semi particle-hole transformation and its usage.\n", + "Then we will show how to solve the linearized Eliashberg equation for this model to find the superconducting phase transition using TRIQS and TPRF routines.\n", + "\n", + "If you want a more detailed study of this problem, checkout this [notebook](https://github.com/TRIQS/tprf/blob/eliashberg/benchmark/eliashberg/particle_hole_transformation/PHT_Hubbard_Model.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Hubbard model on a square lattice\n", + "\n", + "The particle-hole symmetric Hamiltonian for the Hubbard model is given by\n", + "\n", + "$$\n", + "H=-t \\sum_{\\langle j, l\\rangle \\sigma}\\left(c_{j \\sigma}^{\\dagger} c_{l \\sigma}+c_{l \\sigma}^{\\dagger} c_{j \\sigma}\\right)+U \\sum_{j}\\left(n_{j \\uparrow}-\\frac{1}{2}\\right)\\left(n_{j \\downarrow}-\\frac{1}{2}\\right)-\\mu \\sum_{j}\\left(n_{j \\uparrow}+n_{j \\downarrow}\\right)\\,,\n", + "$$\n", + "\n", + "here $c_{j\\sigma}^{\\dagger}$ creates an electron on site $j$ with spin $\\sigma$ while $c_{j\\sigma}$ destroys such an electron, further the operator $n_{j\\sigma}$ count the number of electrons on site $j$ with spin $\\sigma$.\n", + "\n", + "The first term describes the kinetic energy of the electrons, which can be interpreted as an electron with spin $\\sigma$ *hopping* from site $l$ to site $j$ and vice versa.\n", + "Here the angular braket under the sum means that we only take *hopping* terms between neighboring lattice sites into account and the energy that is gained by such a *hopping* process is given by $t$.\n", + "\n", + "The second term describes the repulsive interaction between the electrons.\n", + "This repulsion is crudely approximated in the Hubbard model in the sense, that electrons only *see* each other if they occupy the same lattice site.\n", + "The energy that is needed to have a lattice site doubly occupied is given by $U$.\n", + "\n", + "The last term describes the filling of the lattice via an energy offset by the chemical potential $\\mu$.\n", + "\n", + "The Hubbard model is therefore defined by the parameters $t$, $U$ and $\\mu$, but we also need to know the temperature $T$ at which we shall observe the Hubbard model.\n", + "We will record these parameters using the `ParameterCollection` class of `triqs_tprf.ParameterCollection` module." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "T = 1000\n", + "U = 1.0\n", + "mu = 0.0\n", + "nk = 32\n", + "norb = 1\n", + "nw = 50\n", + "spin = False\n", + "t = 1.0" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from triqs_tprf.ParameterCollection import ParameterCollection\n", + "\n", + "hubbard = ParameterCollection( # -- Model Parameter\n", + " norb=1, # Number of orbitals.\n", + " t=1.0, # Hopping to nearest neighbor\n", + " U=1.0, # Strength of the on-site interaction\n", + " mu=0.0, # Chemical potential determining the filling.\n", + " T=1000, # Temperature.\n", + " spin=False, # Treat indices only for orbital character.\n", + " \n", + " # -- Technical parameter\n", + " nk=32, # Number of points in one dimension considered in the Brillouin zone.\n", + " nw=50, # Number of Matsubara points in positive dimension.\n", + " )\n", + "hubbard" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Semi particle-hole transformation\n", + "\n", + "The Hubbard model with only nearest neighbor hopping inhibts a useful semi particle-hole symmetry, which we will present without any rigorous derivations.\n", + "\n", + "First off, a bipartite lattice can be subdivided into two sublattices for which every lattice site on one of them only has neighboring sites from the other sublattice. This is the case for our square lattice.\n", + "With this knowledge we can define the particle-hole transformation (PHT) for the creation and annihilation operators as \n", + "\n", + "$$\n", + "c^\\dagger_{j \\sigma} \\xrightarrow{\\mathrm{PHT}} (-1)^{j} d_{j \\sigma} \\,,\\quad\n", + "\\mathrm{and}\\quad\n", + "c_{j \\sigma} \\xrightarrow{\\mathrm{PHT}}(-1)^{j}d_{j \\sigma}^{\\dagger}\\,,\\\\\n", + "$$\n", + "\n", + "where $j$ is either $0$ for one sublattice and $1$ for the other.\n", + "\n", + "If we use the PHT only on one spin specices it is called a semi particle-hole transformation (SPHT).\n", + "This means\n", + "\n", + "$$\n", + "c_{j \\uparrow}^{\\dagger} \\xrightarrow{\\mathrm{SPHT}} d_{j \\uparrow}^{\\dagger}\\quad\\mathrm{and}\\quad\n", + "c_{j \\uparrow} \\xrightarrow{\\mathrm{SPHT}} d_{j \\uparrow}\\\\\n", + "c_{j \\downarrow}^{\\dagger} \\xrightarrow{\\mathrm{SPHT}} (-1)^j d_{j \\downarrow}\\quad\\mathrm{and}\\quad\n", + "c_{j \\downarrow} \\xrightarrow{\\mathrm{SPHT}} (-1)^j d_{j \\downarrow}^{\\dagger}\\,,\n", + "$$\n", + "\n", + "and for the number operators\n", + "\n", + "$$\n", + "n_{j \\uparrow}\\xrightarrow{\\mathrm{SPHT}} \\tilde{n}_{j \\uparrow}\n", + "\\quad\\mathrm{and}\\quad\n", + "n_{j \\downarrow} \\xrightarrow{\\mathrm{SPHT}} 1-\\tilde{n}_{j \\downarrow}\\,.\n", + "$$\n", + "\n", + "One can convince themselves, that the kinetic part of the Hubbard model on a square lattice with only nearest neighbor hopping is invariant under a SPHT.\n", + "The interaction term on the other hand is not and changes sign\n", + "\n", + "$$\n", + "\\left(n_{j \\uparrow}-\\frac{1}{2}\\right)\\left(n_{j \\downarrow}-\\frac{1}{2}\\right) \\xrightarrow{\\mathrm{SPHT}}\n", + "-\\left(\\tilde{n}_{j \\uparrow} - \\frac{1}{2}\\right)\\left(\\tilde{n}_{j \\downarrow}-\\frac{1}{2}\\right)\\,.\n", + "$$\n", + "\n", + "Therefore the SPHT maps the repulsive Hubbard model with $U$ to the attractive one with $-U$.\n", + "Additionally to that, if our Hubbard model is not a half-filling, the chemical potential term is also not invariant under a SPHT\n", + "\n", + "$$\n", + "n_{j \\uparrow}+n_{j \\downarrow} \\xrightarrow{\\mathrm{SPHT}}\n", + "1 + \\left(\\tilde{n}_{j \\uparrow}-\\tilde{n}_{j \\downarrow}\\right)\\,,\n", + "$$\n", + "\n", + "and transforms into a Zeeman term.\n", + "\n", + "To summarize the SPHT maps the Hubbard Hamiltonian with interaction strength $U$ and chemical potential $\\mu$ to a Hubbard Hamiltonian with interaction strength $-U$, a chemical potential of $0$ and an additional Zeeman term of strength $\\mu$.\n", + "If we therefore calculate an observable $A$ in the attractive Hubbard model we know the observable $B\\xleftarrow{\\mathrm{SPHT}}A$ in the repulsive one.\n", + "\n", + "For example, the in-plane antiferromagnetic (AFM) phase of the repulsive model is connected to the superconducting (SC) phase in the attractive one, as can be seen by using the SPHT on the ladder operators of the spin\n", + "\n", + "$$\n", + "S^+_j = S^x_j + iS^y_j = c_{j \\uparrow}^{\\dagger}c_{j \\downarrow} \\xrightarrow{\\mathrm{SPHT}} (-1)^j d_{j \\uparrow}^{\\dagger}d_{j \\downarrow}^{\\dagger} = \\tilde{\\Delta}^{\\dagger}\\,,\\\\\n", + "S^-_j = S^x_j - iS^y_j = c_{j \\downarrow}^{\\dagger}c_{j \\uparrow} \\xrightarrow{\\mathrm{SPHT}} (-1)^j d_{j \\downarrow}d_{j \\uparrow} = \\tilde{\\Delta}\\,.\n", + "$$\n", + "\n", + "The $x$- and $y$-components of the spin operator are transformed to the complex superconducting oder parameter with a phase factor.\n", + "This means, that if we find a staggered in-plane spin phase in the repulsive model at some $U$, we will see a homogeneous superconducting phase at $-U$.\n", + "\n", + "The following plot shows this symmetry in a T-U phase diagram, which was previously calculated [here](https://github.com/TRIQS/tprf/blob/eliashberg/benchmark/eliashberg/particle_hole_transformation/PHT_Hubbard_Model.ipynb)." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + 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using an attractive Hubbard model at half-filling, i.e. $\\mu=0.0$, with an additional Zeeman term of strength $\\xi$.\n", + "The phase boundary was then calculated using the random phase approximation (RPA), i.e. using a frequency independent and local vertex $U$, to calculate $\\langle S^xS^x \\rangle$ and increasing $U$ until divergence.\n", + "For details on how to use TPRF for that see this [tutorial](Square lattice susceptibility.ipynb#Random-phase-approximation-(RPA)).\n", + "\n", + "The left hand side of the phase diagram was calculated using an repulsive Hubbard model with $\\mu=\\xi$, i.e. the SPHT mapping of the right hand side model.\n", + "Then the linearized Eliashberg equation was solved for this model for various interaction strengths until the superconducting phase transition was found." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Solving the linearized Eliashberg equation\n", + "\n", + "The linearized Eliashberg equation is given in a very simplified form by\n", + "\n", + "$$\n", + "\\lambda\\Delta = \\Lambda \\Delta\\,,\n", + "$$\n", + "\n", + "where $\\Delta$ is a gap function and $\\lambda$ the largest eigenvalue of the matrix $\\Lambda$.\n", + "Here $\\Lambda$ is the product of the particle-particle vertex $\\Gamma$ and the Green's function $G$.\n", + "If $\\lambda=1$ a phase transition to a superconducting state is found.\n", + "For further information see the documentation [here](../theory/eliashberg.rst).\n", + "\n", + "To solve it in the same order as the RPA we need the non-interacting Green's function $G^{(0)}$ and the particle-particle vertex $\\Gamma$ is approximated by a fequency independent and local vertex $U$.\n", + "\n", + "First we setup our model by using previously established `ParameterCollection` `hubbard` as a template and alter it to the parameters of the repulsive Hubbard model.\n", + "To do this use its method `alter` and supply the parameters that shall be changed as keywords.\n", + "We set the chemical potential to $\\mu=\\xi$ and the interaction strength to $U=-1.41$, which is close to the superconducting phase boundary for $T=1000\\,\\mathrm{K}$." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "T = 1000\n", + "U = -1.41\n", + "mu = 0.1\n", + "nk = 32\n", + "norb = 1\n", + "nw = 50\n", + "spin = False\n", + "t = 1.0" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xi = 0.1\n", + "\n", + "repl_hubbard = hubbard.alter(mu=xi, U=-1.41)\n", + "repl_hubbard" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To construct a representation of the kinetic part of the Hubbard model use the `create_square_lattice` function of the `triqs_tprf.tight_binding` module.\n", + "Give it as keywords the number of orbitals `norb` and the hopping energy `t`, which can comfortably be accessed from `repl_hubbard`.\n", + "It returns a `TBLattice` object." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "triqs_tprf.tight_binding.TBLattice" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from triqs_tprf.tight_binding import create_square_lattice\n", + "\n", + "H = create_square_lattice(norb=repl_hubbard.norb, t=repl_hubbard.t)\n", + "type(H)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To get the dispersion relation, use its member function `on_mesh_brillouin_zone` and enter a mesh on the Brillouin zone as a tuple.\n", + "It returns the dispersion relation stored as a `Gf` object." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "pytriqs.gf.gf.Gf" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "e_k = H.on_mesh_brillouin_zone(n_k=(repl_hubbard.nk, repl_hubbard.nk, 1))\n", + "type(e_k)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With the dispersion relation we can construct the non-interacting Green's function.\n", + "To do this first create a `MeshImFreq` object with a fermionic statistic and the wished inverse temperature $\\beta$ and number of points.\n", + "Then use the `lattice_dyson_g0_wk` function of the `triqs_tprf.lattice` module and supply it with the dispersion relation, the `MeshImFreq` object and a chemical potential.\n", + "This yields the non-interacting Green's function as a `Gf` object.\n", + "(You can use the `temperature_to_beta` function of the `triqs_tprf.utilities` to calculate the inverse temperature in $\\mathrm{eV}$ from the temperature in $\\mathrm{Kelvin}$.)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "pytriqs.gf.gf.Gf" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from triqs_tprf.lattice import lattice_dyson_g0_wk\n", + "from pytriqs.gf import MeshImFreq\n", + "from triqs_tprf.utilities import temperature_to_beta\n", + "\n", + "beta = temperature_to_beta(repl_hubbard.T)\n", + "wmesh = MeshImFreq(beta=beta, S='Fermion', n_max=repl_hubbard.nw)\n", + "g0_wk = lattice_dyson_g0_wk(mu=repl_hubbard.mu, e_k=e_k, mesh=wmesh)\n", + "type(g0_wk)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The particle-particle vertex $\\Gamma$ in this case must be manually created.\n", + "To do this first create a `MeshImFreq` in the same manner as before, but this time with a bosonic statistic.\n", + "Then use this `MeshImFreq` and combine it with the momentum mesh of the non-interacting Green's function to create a `MeshProduct` object.\n", + "Use this `MeshProduct` object to create a `Gf` object with a `target_shape` that corresponds to a two-particle object, e.g. `(1, 1, 1, 1)`.\n", + "Then overwrite its data to be constant to $U$." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "from pytriqs.gf import Gf, MeshProduct\n", + "\n", + "wmesh_boson = MeshImFreq(beta=temperature_to_beta(repl_hubbard.T), S='Boson', n_max=repl_hubbard.nw)\n", + "wmesh_boson_kmesh = MeshProduct(wmesh_boson, g0_wk.mesh[1])\n", + "gamma_pp = Gf(mesh=wmesh_boson_kmesh, target_shape=g0_wk.target_shape*2)\n", + "gamma_pp.data[:] = repl_hubbard.U" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With this we have all ingredients for the linearized Eliashberg equation.\n", + "To solve it use the `solve_eliashberg` function of the `triqs_tprf.eliashberg` module and supply it with the particle-particle vertex and the non-interacting Green's function.\n", + "It returns the eigenvalues and eigenvectors, i.e. the gap functions.\n", + "\n", + "The returned maximum eigenvalue is $\\lambda \\approx 1$ as expected, because we are close to the phase boundary." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.999970584562773" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from triqs_tprf.eliashberg import solve_eliashberg\n", + "\n", + "Es, eigen_modes = solve_eliashberg(gamma_pp, g0_wk)\n", + "Es[0]" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/doc/user_guide/plots/SPHT_hubbard_phase_diagram.svg b/doc/user_guide/plots/SPHT_hubbard_phase_diagram.svg new file mode 100644 index 000000000..d9c5aeb11 --- /dev/null +++ b/doc/user_guide/plots/SPHT_hubbard_phase_diagram.svg @@ -0,0 +1,1082 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + From 056a71a9c14f24e4b53dc707c2b7d30e8d263e71 Mon Sep 17 00:00:00 2001 From: Stefan Date: Thu, 23 May 2019 11:18:24 +0200 Subject: [PATCH 027/121] [plot] dont access zeroth element for dosplot --- python/triqs_tprf/plotting_tools.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/python/triqs_tprf/plotting_tools.py b/python/triqs_tprf/plotting_tools.py index 2c914de9d..3e1bff43a 100644 --- a/python/triqs_tprf/plotting_tools.py +++ b/python/triqs_tprf/plotting_tools.py @@ -64,7 +64,7 @@ def __dosplot_impl(top, obj, *opt_list, **opt_dict): lower_limit = np.min(obj.data.real) upper_limit = np.max(obj.data.real) - dos = gaussian_kde(obj.data[:,0,0].real) + dos = gaussian_kde(obj.data.real) xs = np.linspace(lower_limit, upper_limit, 500) dos.covariance_factor = lambda : .1 From 19339e9f9b3059dcef532e006cd26d490252fc71 Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 3 Jul 2019 22:47:32 +0200 Subject: [PATCH 028/121] Revert "[latutl] output k-points scaled by BZ input" This reverts commit 88989a321d5b80ef86c12aafc878e311fe380481. --- python/triqs_tprf/lattice_utils.py | 14 ++++++++------ 1 file changed, 8 insertions(+), 6 deletions(-) diff --git a/python/triqs_tprf/lattice_utils.py b/python/triqs_tprf/lattice_utils.py index 4c13c58b8..59d6629f6 100644 --- a/python/triqs_tprf/lattice_utils.py +++ b/python/triqs_tprf/lattice_utils.py @@ -439,22 +439,24 @@ def k_space_path(paths, num=100, bz=None): k_vecs = [] - def rel_to_abs(k_vec, cell): - return np.einsum('ba,ib->ia', cell, k_vec) - for path in paths: ki, kf = path x = np.linspace(0., 1., num=num)[:, None] k_vec = (1. - x) * ki[None, :] + x * kf[None, :] - k_vecs.append(rel_to_abs(k_vec, cell)) + k_vecs.append(k_vec) + + def rel_to_abs(k_vec, cell): + return np.einsum('ba,ib->ia', cell, k_vec) k_vec = k_vecs[0] - k_plot = np.linalg.norm(k_vec - k_vec[0][None, :], axis=1) + k_vec_abs = rel_to_abs(k_vec, cell) + k_plot = np.linalg.norm(k_vec_abs - k_vec_abs[0][None, :], axis=1) K_plot = [0.] for kidx, k_vec in enumerate(k_vecs[1:]): - k_plot_new = np.linalg.norm(k_vec - k_vec[0][None, :], axis=1) + k_plot[-1] + k_vec_abs = rel_to_abs(k_vec, cell) + k_plot_new = np.linalg.norm(k_vec_abs - k_vec_abs[0][None, :], axis=1) + k_plot[-1] K_plot.append(k_plot[-1]) k_plot = np.concatenate((k_plot, k_plot_new)) From 3664094530db43554c8412d16003c6c725a46a29 Mon Sep 17 00:00:00 2001 From: Stefan Date: Tue, 9 Jul 2019 17:32:39 +0200 Subject: [PATCH 029/121] [latutil] generalize chi contraction The two-particle Green's functions do not require to have a omega and momentum mesh but can have an arbitrary one. --- python/triqs_tprf/lattice_utils.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/python/triqs_tprf/lattice_utils.py b/python/triqs_tprf/lattice_utils.py index 59d6629f6..7ff343769 100644 --- a/python/triqs_tprf/lattice_utils.py +++ b/python/triqs_tprf/lattice_utils.py @@ -238,7 +238,7 @@ def chi_contraction(chi, op1, op2): ' must fit the shape of chi %s.'%(chi.target_shape,)) chi_op1op2 = chi[0, 0, 0, 0].copy() - chi_op1op2.data[:] = np.einsum('wqabcd,ab,cd->wq', chi.data, op1, op2) + chi_op1op2.data[:] = np.einsum('...abcd,ab,cd->...', chi.data, op1, op2) return chi_op1op2 From eaf407ef260292a641a20b974633ce9e2f489a1c Mon Sep 17 00:00:00 2001 From: Stefan Date: Tue, 9 Jul 2019 17:36:30 +0200 Subject: [PATCH 030/121] [eli] refactor gamma creation Instead of using loops over the indicies we are reordering indices to use matrix products. This speeds up the construction significantly. Also the singlet and triplet function now call the same creation function but with different factors for charge and spin. --- c++/triqs_tprf/lattice/eliashberg.cpp | 64 ++++++++++++++++----------- 1 file changed, 37 insertions(+), 27 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index 885a4a134..71a80d0b2 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -180,46 +180,56 @@ g_wk_t eliashberg_product_fft_constant(chi_r_vt Gamma_pp_const_r, return delta_wk_out; } - -chi_wk_t gamma_PP_singlet(chi_wk_vt chi_c, chi_wk_vt chi_s, \ - array_view, 4> U_c, array_view, 4> U_s) { +chi_wk_t gamma_PP_spin_charge(chi_wk_vt chi_c, chi_wk_vt chi_s, \ + array_view, 4> U_c, array_view, 4> U_s, \ + double charge_factor, double spin_factor) { + + using scalar_t = chi_wk_t::scalar_t; + + size_t nb = chi_c.target_shape()[0]; auto [wmesh, kmesh] = chi_c.mesh(); auto Gamma_pp_wk = make_gf(chi_c); Gamma_pp_wk *= 0; - for (const auto [w, k] : Gamma_pp_wk.mesh()) - for (auto [a, b, c, d] : Gamma_pp_wk.target_indices()){ - for (auto [A, B, C, D] : chi_c.target_indices()){ - Gamma_pp_wk[w,k](a, b, c, d) += - 1.5 * U_s(a, b, A, B) * chi_s[w, k](B, A, C, D) * U_s(D, C, c, d) \ - - 0.5 * U_c(a, b, A, B) * chi_c[w, k](B, A, C, D) * U_c(D, C, c, d); - } - Gamma_pp_wk[w,k](a, b, c, d) += 0.5 * (U_s(a, b, c, d) + U_c(a, b, c, d)); - } + // PH grouping of the vertex, from cc+cc+, permuting the last two indices. + auto U_c_matrix = make_matrix_view(group_indices_view(U_c, {0, 1}, {3, 2})); + auto U_s_matrix = make_matrix_view(group_indices_view(U_s, {0, 1}, {3, 2})); + + for (const auto [w, k] : Gamma_pp_wk.mesh()) { + + array Gamma_pp_arr{nb, nb, nb, nb, memory_layout_t<4>{0, 1, 2, 3}}; + array chi_c_arr{chi_c[w, k], memory_layout_t<4>{0, 1, 2, 3}}; + array chi_s_arr{chi_s[w, k], memory_layout_t<4>{0, 1, 2, 3}}; + + // PH grouping of the vertex, from cc+cc+, permuting the last two indices. + auto Gamma_pp_matrix = make_matrix_view(group_indices_view(Gamma_pp_arr, {0, 1}, {3, 2})); + // PH grouping of the susceptibilites, from c+cc+c, permuting the last two indices. + auto chi_c_matrix = make_matrix_view(group_indices_view(chi_c_arr, {0, 1}, {3, 2})); + auto chi_s_matrix = make_matrix_view(group_indices_view(chi_s_arr, {0, 1}, {3, 2})); + + Gamma_pp_matrix = spin_factor * U_s_matrix * chi_s_matrix * U_s_matrix \ + + charge_factor * U_c_matrix * chi_c_matrix * U_c_matrix \ + + 0.5 * (U_s_matrix + U_c_matrix); + + Gamma_pp_wk[w, k] = Gamma_pp_arr; + } return Gamma_pp_wk; } - -chi_wk_t gamma_PP_triplet(chi_wk_vt chi_c, chi_wk_vt chi_s, \ + +chi_wk_t gamma_PP_singlet(chi_wk_vt chi_c, chi_wk_vt chi_s, \ array_view, 4> U_c, array_view, 4> U_s) { - auto [wmesh, kmesh] = chi_c.mesh(); - - auto Gamma_pp_wk = make_gf(chi_c); - Gamma_pp_wk *= 0; + auto Gamma_pp_wk = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, -0.5, 1.5); + return Gamma_pp_wk; +} - for (const auto [w, k] : Gamma_pp_wk.mesh()) - for (auto [a, b, c, d] : Gamma_pp_wk.target_indices()){ - for (auto [A, B, C, D] : chi_c.target_indices()){ - Gamma_pp_wk[w,k](a, b, c, d) += - - 0.5 * U_s(a, b, A, B) * chi_s[w, k](B, A, C, D) * U_s(D, C, c, d) \ - - 0.5 * U_c(a, b, A, B) * chi_c[w, k](B, A, C, D) * U_c(D, C, c, d); - } - Gamma_pp_wk[w,k](a, b, c, d) += 0.5 * (U_s(a, b, c, d) + U_c(a, b, c, d)); - } +chi_wk_t gamma_PP_triplet(chi_wk_vt chi_c, chi_wk_vt chi_s, \ + array_view, 4> U_c, array_view, 4> U_s) { + auto Gamma_pp_wk = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, -0.5, -0.5); return Gamma_pp_wk; } From 56de94c2c2f76f34fafd436a22a704f0013e6682 Mon Sep 17 00:00:00 2001 From: Stefan Kaser Date: Tue, 9 Jul 2019 17:58:34 -0400 Subject: [PATCH 031/121] [eli] parallelize gamma creation --- c++/triqs_tprf/lattice/eliashberg.cpp | 14 ++++++++++---- 1 file changed, 10 insertions(+), 4 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index 71a80d0b2..b9bf12acf 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -21,6 +21,8 @@ ******************************************************************************/ #include "eliashberg.hpp" +#include "common.hpp" +#include "../mpi.hpp" namespace triqs_tprf { @@ -188,7 +190,6 @@ chi_wk_t gamma_PP_spin_charge(chi_wk_vt chi_c, chi_wk_vt chi_s, \ using scalar_t = chi_wk_t::scalar_t; size_t nb = chi_c.target_shape()[0]; - auto [wmesh, kmesh] = chi_c.mesh(); auto Gamma_pp_wk = make_gf(chi_c); Gamma_pp_wk *= 0; @@ -197,7 +198,11 @@ chi_wk_t gamma_PP_spin_charge(chi_wk_vt chi_c, chi_wk_vt chi_s, \ auto U_c_matrix = make_matrix_view(group_indices_view(U_c, {0, 1}, {3, 2})); auto U_s_matrix = make_matrix_view(group_indices_view(U_s, {0, 1}, {3, 2})); - for (const auto [w, k] : Gamma_pp_wk.mesh()) { + auto meshes_mpi = mpi_view(Gamma_pp_wk.mesh()); + +#pragma omp parallel for + for (int idx = 0; idx < meshes_mpi.size(); idx++){ + auto &[w, k] = meshes_mpi(idx); array Gamma_pp_arr{nb, nb, nb, nb, memory_layout_t<4>{0, 1, 2, 3}}; array chi_c_arr{chi_c[w, k], memory_layout_t<4>{0, 1, 2, 3}}; @@ -209,12 +214,13 @@ chi_wk_t gamma_PP_spin_charge(chi_wk_vt chi_c, chi_wk_vt chi_s, \ auto chi_c_matrix = make_matrix_view(group_indices_view(chi_c_arr, {0, 1}, {3, 2})); auto chi_s_matrix = make_matrix_view(group_indices_view(chi_s_arr, {0, 1}, {3, 2})); - Gamma_pp_matrix = spin_factor * U_s_matrix * chi_s_matrix * U_s_matrix \ - + charge_factor * U_c_matrix * chi_c_matrix * U_c_matrix \ + Gamma_pp_matrix = charge_factor * U_c_matrix * chi_c_matrix * U_c_matrix \ + + spin_factor * U_s_matrix * chi_s_matrix * U_s_matrix \ + 0.5 * (U_s_matrix + U_c_matrix); Gamma_pp_wk[w, k] = Gamma_pp_arr; } + Gamma_pp_wk = mpi_all_reduce(Gamma_pp_wk); return Gamma_pp_wk; } From 4801944c8ae6d2889ade481c3964661ad4330bce Mon Sep 17 00:00:00 2001 From: Stefan Date: Tue, 9 Jul 2019 20:00:08 -0400 Subject: [PATCH 032/121] [rpa] parallelize rpa function --- c++/triqs_tprf/lattice/rpa.cpp | 15 +++++++++------ 1 file changed, 9 insertions(+), 6 deletions(-) diff --git a/c++/triqs_tprf/lattice/rpa.cpp b/c++/triqs_tprf/lattice/rpa.cpp index a33544f4d..2503f5de8 100644 --- a/c++/triqs_tprf/lattice/rpa.cpp +++ b/c++/triqs_tprf/lattice/rpa.cpp @@ -22,6 +22,7 @@ #include "rpa.hpp" #include "common.hpp" +#include "../mpi.hpp" namespace triqs_tprf { @@ -31,18 +32,20 @@ chi_wk_t solve_rpa_PH(chi_wk_vt chi0_wk, using scalar_t = chi_wk_t::scalar_t; size_t nb = chi0_wk.target_shape()[0]; - auto wmesh = std::get<0>(chi0_wk.mesh()); - auto kmesh = std::get<1>(chi0_wk.mesh()); - chi_wk_t chi_wk{{wmesh, kmesh}, chi0_wk.target_shape()}; + auto chi_wk = make_gf(chi0_wk); + chi_wk *=0; // PH grouping of the vertex, from cc+cc+, permuting the last two indices. auto U = make_matrix_view(group_indices_view(U_arr, {0, 1}, {3, 2})); auto I = make_unit_matrix(U.shape()[0]); - for (auto const &w : wmesh) { - for (auto const &k : kmesh) { + auto meshes_mpi = mpi_view(chi0_wk.mesh()); + +#pragma omp parallel for + for (int idx = 0; idx < meshes_mpi.size(); idx++){ + auto &[w, k] = meshes_mpi(idx); array chi_arr{nb, nb, nb, nb, memory_layout_t<4>{0, 1, 2, 3}}; @@ -58,7 +61,7 @@ chi_wk_t solve_rpa_PH(chi_wk_vt chi0_wk, chi_wk[w, k] = chi_arr; // assign back using the array_view } - } + chi_wk = mpi_all_reduce(chi_wk); return chi_wk; } From b13e0621990061d11ff8e2b4b519768908efe582 Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 10 Jul 2019 14:34:04 -0400 Subject: [PATCH 033/121] [eli] add two band test to protect from indices errors --- test/python/eliashberg/CMakeLists.txt | 1 + .../eliashberg_benchmark_two_band.tar.gz | Bin 0 -> 91145 bytes .../previous_implementation_two_band.py | 124 ++++++++++++++++++ 3 files changed, 125 insertions(+) create mode 100644 test/python/eliashberg/eliashberg_benchmark_two_band.tar.gz create mode 100644 test/python/eliashberg/previous_implementation_two_band.py diff --git a/test/python/eliashberg/CMakeLists.txt b/test/python/eliashberg/CMakeLists.txt index cbecb83cc..7a1970577 100644 --- a/test/python/eliashberg/CMakeLists.txt +++ b/test/python/eliashberg/CMakeLists.txt @@ -6,4 +6,5 @@ set(PREFIX eliashberg-) add_python_test(product_summation_vs_fft ${PREFIX}) add_python_test(eigenvalue_solver ${PREFIX}) add_python_test(previous_implementation ${PREFIX}) +add_python_test(previous_implementation_two_band ${PREFIX}) add_python_test(fft_product_constant_vs_full ${PREFIX}) diff --git a/test/python/eliashberg/eliashberg_benchmark_two_band.tar.gz b/test/python/eliashberg/eliashberg_benchmark_two_band.tar.gz new file mode 100644 index 0000000000000000000000000000000000000000..3c96b3b943cf4e920196f2e5928cd579acfbe442 GIT binary patch literal 91145 zcmZU4X*`r~*mfmbB_Sjs*^*@v5{7B9REng?I&Bg{wiwGyM52(CohfUDhHP2Ku53e= z$vXDIU}iA;a=-I`f6tfa_k6l%`EZ}tb)M&O9@lZ)x58T?AuDZF*L{HdGtUQsPanDm zct9Vz`#yT=^B}+*8WiFOefYrlG1S*RL_6p~z@Cj}VX*zoEPzn7)B6^4VBofYit5Hq 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zZuCmU*78T}Z8Ew)DHFUsOkbVzM_%~T?gKbL;c9Rl6kanUQ6_P@GL%n858SR3AH@JJ z(h-Ds&|ShtaM&|!d#d61(hT|#nJAzRg9lWtm$dfW#-o>9Yp7ooOWGyMU)`*+`tO^w zgF+>vLyFJAJ9KgT2Mm9#&t|AJRnq_o^ELWro)ZVE*64~ElXH!{EBd}&ux}Kq+`547 zAbl#PUMa2ZG~4)q*i}VjLXdx*^pH(7+}bUYt2&H#GEVU#@+Jc4uF2xQz^hoozLFVq zKX4j!>DLH~pM|KB0iDX9E<5`N2xQ;}P>CMHkqA`sP7t%1_5b|oN!>wz-@l&3M&V%l EAJB9P@Bjb+ literal 0 HcmV?d00001 diff --git a/test/python/eliashberg/previous_implementation_two_band.py b/test/python/eliashberg/previous_implementation_two_band.py new file mode 100644 index 000000000..da1a6ac45 --- /dev/null +++ b/test/python/eliashberg/previous_implementation_two_band.py @@ -0,0 +1,124 @@ + +# ---------------------------------------------------------------------- + +""" Goes through the steps of solving the linearized Eliashberg equation for singlet pairing in +RPA limit in model with two orbitals, saves the results and compares to previously established +benchmark data. """ + +# ---------------------------------------------------------------------- + +import itertools + +# ---------------------------------------------------------------------- + +import numpy as np + +# ---------------------------------------------------------------------- + +from pytriqs.gf import MeshImFreq + +from triqs_tprf.ParameterCollection import ParameterCollection +from triqs_tprf.tight_binding import TBLattice +from triqs_tprf.lattice import lattice_dyson_g0_wk +from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk +from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors +from triqs_tprf.lattice import solve_rpa_PH +from triqs_tprf.lattice import gamma_PP_singlet +from triqs_tprf.lattice import eliashberg_product_fft +from triqs_tprf.eliashberg import preprocess_gamma_for_fft, solve_eliashberg + +# ---------------------------------------------------------------------- + +from triqs_tprf.utilities import write_TarGZ_HDFArchive, read_TarGZ_HDFArchive, show_version_info +import triqs_tprf.version as version + +# ---------------------------------------------------------------------- + +p = ParameterCollection( + filename = 'eliashberg_benchmark_two_band_new.tar.gz', + dim = 2, + norbs = 2, + t = 1.0, + mu = 0.0, + beta = 1, + U = 1.0, + nk = 2, + nw = 100, + version_info = version.info, + ) + +# -- Setup model, RPA susceptibilities and spin/charge interaction + +full_units = [(1, 0, 0), (0, 1, 0), (0, 0, 1)] +all_nn_hoppings = list(itertools.product([-1, 0, 1], repeat=p.dim)) +non_diagonal_hoppings = [ele for ele in all_nn_hoppings if sum(np.abs(ele)) == 1] + +# -- Make off-diagonal hoppings 10 percent the strength of diagonal ones. +t = -p.t * (0.9 * np.eye(p.norbs) + 0.1*np.ones((p.norbs, p.norbs))) + +H = TBLattice( + units = full_units[:p.dim], + hopping = {hop : t for hop in non_diagonal_hoppings}, + orbital_positions = [(0,0,0)]*p.norbs, + ) + +e_k = H.on_mesh_brillouin_zone(n_k=[p.nk]*p.dim + [1]*(3-p.dim)) + +wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nw) + +g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh) + +chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw) + +U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norbs, p.U, 0, 0, 0) + +chi_s = solve_rpa_PH(chi0_wk, U_s) +chi_c = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation + +# -- The output of the following three functions shall be tested + +gamma = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) +Gamma_pp_dyn_tr, Gamma_pp_const_r = preprocess_gamma_for_fft(gamma) # This one is not tested +next_delta = eliashberg_product_fft(Gamma_pp_dyn_tr, Gamma_pp_const_r, g0_wk, g0_wk) +E, eigen_modes = solve_eliashberg(gamma, g0_wk, product='FFT', solver='IRAM', initial_delta=g0_wk) + +# -- Save results + +p.gamma = gamma +p.next_delta = next_delta +p.E = E[0] +p.eigen_mode = eigen_modes[0] + +write_TarGZ_HDFArchive(p.filename, p=p) + +# -- Load benchmark data + +filename = './eliashberg_benchmark_two_band.tar.gz' +p_benchmark = read_TarGZ_HDFArchive(filename)['p'] + +# -- Check if the benchmark data was calculated for the same model, +# -- otherwise a comparison does not make sense. + +model_parameters = ['dim', 'norbs', 't', 'mu', 'beta', 'U'] + +for model_parameter in model_parameters: + run_time, benchmark = p[model_parameter], p_benchmark[model_parameter] + if run_time != benchmark: + error = 'The model of the benchmark and the one used now are not the same.\n' + error += '\t\tNow: {0} = {1}, benchmark: {0} = {2}.'.format(model_parameter, run_time, + benchmark) + raise AssertionError, error + +# -- Compare the results. Raise an error if the are not the same within a tolerance. + +print('\nThe benchmark data was obtained with %s.'%show_version_info(p_benchmark.version_info)) + +np.testing.assert_allclose(p_benchmark.gamma.data, p.gamma.data) +np.testing.assert_allclose(p_benchmark.next_delta.data, p.next_delta.data) +np.testing.assert_allclose(p_benchmark.E, p.E) +try: + np.testing.assert_allclose(p_benchmark.eigen_mode.data, p.eigen_mode.data, atol=1e-6) +except AssertionError: + np.testing.assert_allclose(-p_benchmark.eigen_mode.data, p.eigen_mode.data, atol=1e-6) + +print('\nThis (new) version with %s yields the same results!'%show_version_info(p.version_info)) From fbb73dba9c41a40e5cb836cef95a6c837b816e9e Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 10 Jul 2019 15:21:55 -0400 Subject: [PATCH 034/121] [eli] add functionality to compare eigenvectors Adds a function that checks if two eigenvectors are equal if multiplied by a scalar. --- python/triqs_tprf/eliashberg.py | 39 +++++++++++++++++++ test/python/eliashberg/eigenvalue_solver.py | 16 ++++---- .../eliashberg/previous_implementation.py | 8 ++-- .../previous_implementation_two_band.py | 9 ++--- 4 files changed, 53 insertions(+), 19 deletions(-) diff --git a/python/triqs_tprf/eliashberg.py b/python/triqs_tprf/eliashberg.py index 7349baab5..3a68cf16d 100644 --- a/python/triqs_tprf/eliashberg.py +++ b/python/triqs_tprf/eliashberg.py @@ -329,3 +329,42 @@ def power_method(init, offset=0.0, tol=tol, max_it=max_it): norm, v_k = power_method(init, offset=-norm, tol=tol) return norm, v_k +def allclose_by_scalar_multiplication(delta_1, delta_2, atol=1e-10): + """Test if two eigenvectors are equal if multiplied by a scalar + + Eigenvectors are not unique and can be multiplied by any complex scalar. + Therfore two eigenvalue solver could output different eigenvectors for + the same non-degenerate eigenvalue. + This function checks if two eigenvectors are only different, because of a multiplication + by a scalar. + + Parameters + ---------- + delta_1 : Gf + delta_2 : Gf + tol : float, optional + The tolerance at which the eigenvector are considered to be equal up to a scalar + + Returns + ------- + have_common_scalar_factor : bool, + True if the two eigenvectors are equal up to a scalar. + False otherwise. + """ + delta_1_arr = delta_1.data.flatten() + delta_2_arr = delta_2.data.flatten() + + # Remove numerical zeroes + delta_1_arr = delta_1_arr[np.abs(delta_1_arr) > 1e-8] + delta_2_arr = delta_2_arr[np.abs(delta_2_arr) > 1e-8] + + try: + division_of_deltas = np.divide(delta_1_arr, delta_2_arr) + except ValueError: # Arrays do not contain the same # of zeroes and are therefore not equal + return False + + # Check if elements share common scalar factor + have_common_scalar_factor = np.allclose(division_of_deltas, division_of_deltas[0], atol=atol) + + return have_common_scalar_factor + diff --git a/test/python/eliashberg/eigenvalue_solver.py b/test/python/eliashberg/eigenvalue_solver.py index df07472ee..7bbefdb49 100644 --- a/test/python/eliashberg/eigenvalue_solver.py +++ b/test/python/eliashberg/eigenvalue_solver.py @@ -23,7 +23,8 @@ from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors from triqs_tprf.lattice import gamma_PP_singlet -from triqs_tprf.eliashberg import solve_eliashberg +from triqs_tprf.eliashberg import solve_eliashberg, semi_random_initial_delta +from triqs_tprf.eliashberg import allclose_by_scalar_multiplication # ---------------------------------------------------------------------- @@ -73,9 +74,10 @@ def run_solve_eliashberg(p): gamma_const = None else: gamma_const = 0.5*(U_s + U_c) - + + initial_delta = semi_random_initial_delta(g0_wk, seed=1337) Es, eigen_modes = solve_eliashberg(gamma, g0_wk, Gamma_pp_const_k=gamma_const, - product=p.product, solver=p.solver) + product=p.product, solver=p.solver, initial_delta=initial_delta) return Es, eigen_modes @@ -106,13 +108,9 @@ def run_solve_eliashberg(p): Es_iram, eigen_modes_iram = run_solve_eliashberg(p.alter(solver='IRAM')) print(Es_pm[0], Es_iram[0]) - np.testing.assert_allclose(Es_pm[0], Es_iram[0]) - try: - np.testing.assert_allclose(eigen_modes_pm[0].data, eigen_modes_iram[0].data, atol=1e-8) - except AssertionError: - np.testing.assert_allclose(-eigen_modes_pm[0].data, eigen_modes_iram[0].data, atol=1e-8) + assert allclose_by_scalar_multiplication(eigen_modes_pm[0], eigen_modes_iram[0]),\ + "Eigenvectors are not the same." print('Both solvers yield the same results.') - diff --git a/test/python/eliashberg/previous_implementation.py b/test/python/eliashberg/previous_implementation.py index 6f85b2530..0b7238604 100644 --- a/test/python/eliashberg/previous_implementation.py +++ b/test/python/eliashberg/previous_implementation.py @@ -24,7 +24,7 @@ from triqs_tprf.lattice import solve_rpa_PH from triqs_tprf.lattice import gamma_PP_singlet from triqs_tprf.lattice import eliashberg_product -from triqs_tprf.eliashberg import solve_eliashberg +from triqs_tprf.eliashberg import solve_eliashberg, allclose_by_scalar_multiplication # ---------------------------------------------------------------------- @@ -122,9 +122,7 @@ np.testing.assert_allclose(p_benchmark.gamma.data, p.gamma.data) np.testing.assert_allclose(p_benchmark.next_delta.data, p.next_delta.data) np.testing.assert_allclose(p_benchmark.E, p.E) -try: - np.testing.assert_allclose(p_benchmark.eigen_mode.data, p.eigen_mode.data, atol=1e-6) -except AssertionError: - np.testing.assert_allclose(-p_benchmark.eigen_mode.data, p.eigen_mode.data, atol=1e-6) +assert allclose_by_scalar_multiplication(p_benchmark.eigen_mode, p.eigen_mode),\ + "Eigenvectors are not the same." print('\nThis (new) version with %s yields the same results!'%show_version_info(p.version_info)) diff --git a/test/python/eliashberg/previous_implementation_two_band.py b/test/python/eliashberg/previous_implementation_two_band.py index da1a6ac45..1ce2b68b7 100644 --- a/test/python/eliashberg/previous_implementation_two_band.py +++ b/test/python/eliashberg/previous_implementation_two_band.py @@ -26,6 +26,7 @@ from triqs_tprf.lattice import gamma_PP_singlet from triqs_tprf.lattice import eliashberg_product_fft from triqs_tprf.eliashberg import preprocess_gamma_for_fft, solve_eliashberg +from triqs_tprf.eliashberg import allclose_by_scalar_multiplication # ---------------------------------------------------------------------- @@ -80,7 +81,7 @@ gamma = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) Gamma_pp_dyn_tr, Gamma_pp_const_r = preprocess_gamma_for_fft(gamma) # This one is not tested next_delta = eliashberg_product_fft(Gamma_pp_dyn_tr, Gamma_pp_const_r, g0_wk, g0_wk) -E, eigen_modes = solve_eliashberg(gamma, g0_wk, product='FFT', solver='IRAM', initial_delta=g0_wk) +E, eigen_modes = solve_eliashberg(gamma, g0_wk, product='FFT', solver='IRAM')#, initial_delta=g0_wk) # -- Save results @@ -116,9 +117,7 @@ np.testing.assert_allclose(p_benchmark.gamma.data, p.gamma.data) np.testing.assert_allclose(p_benchmark.next_delta.data, p.next_delta.data) np.testing.assert_allclose(p_benchmark.E, p.E) -try: - np.testing.assert_allclose(p_benchmark.eigen_mode.data, p.eigen_mode.data, atol=1e-6) -except AssertionError: - np.testing.assert_allclose(-p_benchmark.eigen_mode.data, p.eigen_mode.data, atol=1e-6) +assert allclose_by_scalar_multiplication(p_benchmark.eigen_mode, p.eigen_mode),\ + "Eigenvectors are not the same." print('\nThis (new) version with %s yields the same results!'%show_version_info(p.version_info)) From 9f9214f6229c5fbe73736e78cda8a6046029b4b5 Mon Sep 17 00:00:00 2001 From: Stefan Date: Thu, 11 Jul 2019 15:09:01 -0400 Subject: [PATCH 035/121] [eli] update two band test Make test more generic by variable hopping rates. Also handle exceptions in model parameter lookup and slightly adjust tolerance in testing. --- python/triqs_tprf/eliashberg.py | 6 ++++-- .../eliashberg_benchmark_two_band.tar.gz | Bin 91145 -> 107519 bytes .../previous_implementation_two_band.py | 20 ++++++++++++------ 3 files changed, 17 insertions(+), 9 deletions(-) diff --git a/python/triqs_tprf/eliashberg.py b/python/triqs_tprf/eliashberg.py index 3a68cf16d..166b9946d 100644 --- a/python/triqs_tprf/eliashberg.py +++ b/python/triqs_tprf/eliashberg.py @@ -301,6 +301,7 @@ def power_method(init, offset=0.0, tol=tol, max_it=max_it): it = 1 while True: norm, new_v_k = iteration(v_k, offset) + print(norm) # -- Convergence criterion add = np.max(np.abs(v_k + new_v_k)) @@ -355,12 +356,13 @@ def allclose_by_scalar_multiplication(delta_1, delta_2, atol=1e-10): delta_2_arr = delta_2.data.flatten() # Remove numerical zeroes - delta_1_arr = delta_1_arr[np.abs(delta_1_arr) > 1e-8] - delta_2_arr = delta_2_arr[np.abs(delta_2_arr) > 1e-8] + delta_1_arr = delta_1_arr[np.abs(delta_1_arr) > 1e-7] + delta_2_arr = delta_2_arr[np.abs(delta_2_arr) > 1e-7] try: division_of_deltas = np.divide(delta_1_arr, delta_2_arr) except ValueError: # Arrays do not contain the same # of zeroes and are therefore not equal + print('FUUUCK') return False # Check if elements share common scalar factor diff --git a/test/python/eliashberg/eliashberg_benchmark_two_band.tar.gz b/test/python/eliashberg/eliashberg_benchmark_two_band.tar.gz index 3c96b3b943cf4e920196f2e5928cd579acfbe442..45d974382caf23679ed9ffc5d2cf115add5ae3cd 100644 GIT binary patch literal 107519 zcmY&!<#g%g*gh&4?^VOmv0Yi>#oLr`wog(j1jHJ4wIm|s-9x1kRQuqMF7=;$bn z@lE)djD{ly#qN%#Sv>pV6bip~?H)P?jb8QfVcFbb<#>jU188XahL%2w3-=sbIc;op zl89r(1;o(CMg|<3A~bBg^2i}+lmB*P;s{szLs`{gT?RuwbrBahZ4T- z7@bWVg9z;^t1%c~B9A6A>JpnN^G)Z^D1bk!X?wwy(seXF~A;O6TE(j&cW4BXM0SuZi zv2hMQp*zIGail_E7lcbBZLFvsV^V+&ugBZRAW|@rV5qy72%dZK|iRyGc*yc0*^)|OFb!%N<@k5^rUPD&=NtuYNUUptQ~EFuNgFD8Vb-i 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norbs = 2, - t = 1.0, + t1 = 1.0, + t2 = 0.5, + t12 = 0.1, + t21 = 0.1, mu = 0.0, beta = 1, U = 1.0, @@ -54,8 +57,8 @@ all_nn_hoppings = list(itertools.product([-1, 0, 1], repeat=p.dim)) non_diagonal_hoppings = [ele for ele in all_nn_hoppings if sum(np.abs(ele)) == 1] -# -- Make off-diagonal hoppings 10 percent the strength of diagonal ones. -t = -p.t * (0.9 * np.eye(p.norbs) + 0.1*np.ones((p.norbs, p.norbs))) +# -- Create hopping matrix for two-band model +t = -np.array([[p.t1, p.t12], [p.t21, p.t2]]) H = TBLattice( units = full_units[:p.dim], @@ -81,7 +84,7 @@ gamma = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) Gamma_pp_dyn_tr, Gamma_pp_const_r = preprocess_gamma_for_fft(gamma) # This one is not tested next_delta = eliashberg_product_fft(Gamma_pp_dyn_tr, Gamma_pp_const_r, g0_wk, g0_wk) -E, eigen_modes = solve_eliashberg(gamma, g0_wk, product='FFT', solver='IRAM')#, initial_delta=g0_wk) +E, eigen_modes = solve_eliashberg(gamma, g0_wk, product='FFT', solver='IRAM') # -- Save results @@ -100,11 +103,14 @@ # -- Check if the benchmark data was calculated for the same model, # -- otherwise a comparison does not make sense. -model_parameters = ['dim', 'norbs', 't', 'mu', 'beta', 'U'] +model_parameters = ['dim', 'norbs', 't1', 't2', 't12', 't21', 'mu', 'beta', 'U'] for model_parameter in model_parameters: - run_time, benchmark = p[model_parameter], p_benchmark[model_parameter] - if run_time != benchmark: + try: + run_time, benchmark = p[model_parameter], p_benchmark[model_parameter] + except KeyError: + raise AssertionError, "The model parameter %s does not exist."%model_parameter + if (run_time != benchmark): error = 'The model of the benchmark and the one used now are not the same.\n' error += '\t\tNow: {0} = {1}, benchmark: {0} = {2}.'.format(model_parameter, run_time, benchmark) From 0b95716e38e7965ccc9d05fd9e1a3fd03b37d7b0 Mon Sep 17 00:00:00 2001 From: Stefan Date: Thu, 11 Jul 2019 16:50:44 -0400 Subject: [PATCH 036/121] [eli] refactor eliashberg product The function `eliashberg_g_delta_g_product` and the dynamic part in `eliashberg_product_fft` were refactored due to issue #725 of TRIQS. Also their outerloop was parallelized with openmp. --- c++/triqs_tprf/lattice/eliashberg.cpp | 119 +++++++++++++++++++++++--- 1 file changed, 106 insertions(+), 13 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index b9bf12acf..db9d66995 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -23,29 +23,75 @@ #include "eliashberg.hpp" #include "common.hpp" #include "../mpi.hpp" +#include +#include "../fourier/fourier.hpp" namespace triqs_tprf { + namespace { + using namespace fourier; + } + // Helper function computing F = GG \Delta - + g_wk_t eliashberg_g_delta_g_product(g_wk_vt g_wk, g_wk_vt delta_wk) { + triqs::utility::timer t_all, t_parallel; + t_all.start(); + + size_t norb = g_wk.target_shape()[0]; auto [wmesh, kmesh] = delta_wk.mesh(); - auto gf_wmesh = std::get<0>(g_wk.mesh()); + auto wmesh_gf = std::get<0>(g_wk.mesh()); - if (wmesh.size() > gf_wmesh.size()) + if (wmesh.size() > wmesh_gf.size()) TRIQS_RUNTIME_ERROR << "The size of the Matsubara frequency mesh of the Green's function" - " (" << gf_wmesh.size() << ") must be atleast the size of the mesh of Delta (" << + " (" << wmesh_gf.size() << ") must be atleast the size of the mesh of Delta (" << wmesh.size() << ")."; auto F_wk = make_gf(delta_wk); F_wk *= 0.; - for (const auto [w, k] : delta_wk.mesh()) +/* The rest of this function contains a lot boiler plate code due to issue + #725 in the TRIQS library and not yet avaible functionality to use + 'pragma omp parallel loop for' over mesh objects. + It will be changed later +*/ + array::mesh_point_t, 1> k_arr(kmesh.size()); + auto k_iter = kmesh.begin(); + for (auto idx : range(0, kmesh.size())) { + auto k = *k_iter; + k_arr(idx) = k; + k_iter++; + } + + auto _ = all_t{}; + t_parallel.start(); +#pragma omp parallel for + for(int idx_k = 0; idx_k < kmesh.size(); idx_k++){ + auto k = k_arr(idx_k); + + auto g_left_w = make_gf(wmesh, g_wk.target()); + auto g_right_w = make_gf(wmesh, g_wk.target()); + auto delta_w = make_gf(wmesh, delta_wk.target()); + auto F_w = make_gf(wmesh, F_wk.target()); + + g_left_w = g_wk[_, k]; + g_right_w = g_wk[_, -k]; + delta_w = delta_wk[_, k]; + + for (const auto w : wmesh) { for (auto [A, B] : F_wk.target_indices()) for (auto [c, d] : delta_wk.target_indices()) - F_wk[w, k](A, B) += - g_wk[w, k](A, c) * g_wk[-w, -k](B, d) * delta_wk[w, k](c, d); + F_w[w](A, B) += + g_left_w[w](A, c) * g_right_w[-w](B, d) * delta_w[w](c, d); + } + F_wk[_, k] = F_w; + } + t_parallel.stop(); + t_all.stop(); + std::cout << "all:\t" << double(t_all) << "\n" \ + << "parallel:\t" << double(t_parallel) << "\n" \ + << "sequential:\t" << double(t_all - t_parallel) << "\n"; return F_wk; } @@ -128,8 +174,15 @@ e_k_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, g_tr_t F_tr g_wk_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const_r, g_wk_vt g_wk, g_wk_vt delta_wk) { + triqs::utility::timer t_g_delta_g_product, t_fft_F, t_dynamic_product, t_fft_delta, t_constant_product, t_combine; + + t_g_delta_g_product.start(); auto F_wk = eliashberg_g_delta_g_product(g_wk, delta_wk); + t_g_delta_g_product.stop(); + + t_fft_F.start(); auto F_tr = make_gf_from_fourier<0, 1>(F_wk); + t_fft_F.stop(); auto [tmesh, rmesh] = F_tr.mesh(); @@ -137,30 +190,70 @@ g_wk_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const auto delta_tr_out = make_gf(F_tr); delta_tr_out *= 0.; - auto gamma_tmesh = std::get<0>(Gamma_pp_dyn_tr.mesh()); + auto tmesh_gamma = std::get<0>(Gamma_pp_dyn_tr.mesh()); // Test if the tau meshs of delta and gamma are compatible. If not raise an error, because // it would lead to wrong results. - if (tmesh.size() != gamma_tmesh.size()) + if (tmesh.size() != tmesh_gamma.size()) TRIQS_RUNTIME_ERROR << "The size of the imaginary time mesh of Gamma" - " (" << gamma_tmesh.size() << ") must be the size of the mesh of Delta (" << + " (" << tmesh_gamma.size() << ") must be the size of the mesh of Delta (" << tmesh.size() << ")."; - for (const auto [t, r] : triqs::utility::product(tmesh, rmesh)) { - for (auto [A, a, B, b] : Gamma_pp_dyn_tr.target_indices()) - delta_tr_out[t, r](a, b) += -Gamma_pp_dyn_tr[t, r](A, a, B, b) * F_tr[t, r](A, B); + t_dynamic_product.start(); +/* This function contains a lot boiler plate code due to issue + #725 in the TRIQS library and not yet avaible functionality to use + 'pragma omp parallel loop for' over mesh objects. + It will be changed later +*/ + + array::mesh_point_t, 1> r_arr(rmesh.size()); + auto r_iter = rmesh.begin(); + for (auto idx : range(0, rmesh.size())) { + auto r = *r_iter; + r_arr(idx) = r; + r_iter++; + } + auto _ = all_t{}; +#pragma omp parallel for + for(int idx_r = 0; idx_r < rmesh.size(); idx_r++){ + auto r = r_arr(idx_r); + + auto delta_t = make_gf(tmesh, delta_tr_out.target()); + + auto Gamma_pp_dyn_t = Gamma_pp_dyn_tr[_, r]; + auto F_t = F_tr[_, r]; + + for (const auto t : tmesh) { + for (auto [A, a, B, b] : Gamma_pp_dyn_tr.target_indices()) + delta_t[t](a, b) += -Gamma_pp_dyn_t[t](A, a, B, b) * F_t[t](A, B); + } + delta_tr_out[_, r] = delta_t; } + t_dynamic_product.stop(); // FIXME // This raises warnings when used with random delta input, e.g. eigenvalue finder + t_fft_delta.start(); auto delta_wk_out = make_gf_from_fourier<0, 1>(delta_tr_out); + t_fft_delta.stop(); // Constant part + t_constant_product.start(); auto delta_k_out = eliashberg_constant_gamma_f_product(Gamma_pp_const_r, F_tr); + t_constant_product.stop(); // Combine dynamic and constant part + t_combine.start(); for (const auto [w , k]: delta_wk_out.mesh()) delta_wk_out[w, k] += delta_k_out[k]; + t_combine.stop(); + + std::cout << "g_delta_g_product:\t" << double(t_g_delta_g_product) << "\n" \ + << "fft_F:\t" << double(t_fft_F) << "\n" \ + << "dynamic_product:\t" << double(t_dynamic_product) << "\n" \ + << "fft_delta:\t" << double(t_fft_delta) << "\n" \ + << "constant_product:\t" << double(t_constant_product) << "\n" \ + << "combin:\t" << double(t_combine) << "\n" ; return delta_wk_out; } From c5ff3b9112440ca0cb90abb23063296fcaeb91f6 Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 22 Jul 2019 16:46:31 -0400 Subject: [PATCH 037/121] [eli] add parallelized fft helper functions Because the `make_gf_from_fourier` function of TRIQS is not parallelized for mesh products helper functions were introduced. This is a overlap with some functions in `gf.cpp` and will be changed later. --- c++/triqs_tprf/lattice/eliashberg.cpp | 160 +++++++++++++++++++++++++- 1 file changed, 158 insertions(+), 2 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index db9d66995..4f03a3eae 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -171,6 +171,158 @@ e_k_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, g_tr_t F_tr return delta_k_out; } +// BOILER PLATE CODE FOR FFT STARTS HERE ============================================================ + +g_tr_t g_tr_from_g_wr(g_wr_cvt g_wr, int nt = -1) { + + auto _ = all_t{}; + int nb = g_wr.target().shape()[0]; + + auto [wmesh, rmesh] = g_wr.mesh(); + + auto tmesh = make_adjoint_mesh(wmesh, nt); + g_tr_t g_tr{{tmesh, rmesh}, {nb, nb}}; + + auto r0 = *rmesh.begin(); + auto p = _fourier_plan<0>(gf_const_view(g_wr[_, r0]), gf_view(g_tr[_, r0])); + + array::mesh_point_t, 1> r_arr(rmesh.size()); + auto r_iter = rmesh.begin(); + for (auto idx : range(0, rmesh.size())) { + auto r = *r_iter; + r_arr(idx) = r; + r_iter++; + } + +#pragma omp parallel for + for (int idx = 0; idx < r_arr.size(); idx++) { + auto &r = r_arr(idx); + + auto g_w = make_gf(wmesh, g_wr.target()); + auto g_t = make_gf(tmesh, g_tr.target()); + + g_w = g_wr[_, r]; + + _fourier_with_plan<0>(gf_const_view(g_w), gf_view(g_t), p); + + g_tr[_, r] = g_t; + } + return g_tr; +} + +g_wr_t g_wr_from_g_wk(g_wk_cvt g_wk) { + + auto _ = all_t{}; + int nb = g_wk.target().shape()[0]; + + auto [wmesh, kmesh] = g_wk.mesh(); + + auto rmesh = make_adjoint_mesh(kmesh); + g_wr_t g_wr{{wmesh, rmesh}, {nb, nb}}; + + auto w0 = *wmesh.begin(); + auto p = _fourier_plan<0>(gf_const_view(g_wk[w0, _]), gf_view(g_wr[w0, _])); + + array::mesh_point_t, 1> w_arr(wmesh.size()); + auto w_iter = wmesh.begin(); + for (auto idx : range(0, wmesh.size())) { + auto w = *w_iter; + w_arr(idx) = w; + w_iter++; + } + +#pragma omp parallel for + for (int idx = 0; idx < w_arr.size(); idx++) { + auto &w = w_arr(idx); + + auto g_k = make_gf(kmesh, g_wk.target()); + auto g_r = make_gf(rmesh, g_wr.target()); + + g_k = g_wk[w, _]; + + _fourier_with_plan<0>(gf_const_view(g_k), gf_view(g_r), p); + + g_wr[w, _] = g_r; + } + return g_wr; +} + +g_wr_t g_wr_from_g_tr(g_tr_cvt g_tr) { + + auto _ = all_t{}; + int nb = g_tr.target().shape()[0]; + + auto [tmesh, rmesh] = g_tr.mesh(); + + auto wmesh = make_adjoint_mesh(tmesh); + g_wr_t g_wr{{wmesh, rmesh}, {nb, nb}}; + + auto r0 = *rmesh.begin(); + auto p = _fourier_plan<0>(gf_const_view(g_tr[_, r0]), gf_view(g_wr[_, r0])); + + array::mesh_point_t, 1> r_arr(rmesh.size()); + auto r_iter = rmesh.begin(); + for (auto idx : range(0, rmesh.size())) { + auto r = *r_iter; + r_arr(idx) = r; + r_iter++; + } + +#pragma omp parallel for + for (int idx = 0; idx < r_arr.size(); idx++) { + auto &r = r_arr(idx); + + auto g_t = make_gf(tmesh, g_tr.target()); + auto g_w = make_gf(wmesh, g_wr.target()); + + g_t = g_tr[_, r]; + + _fourier_with_plan<0>(gf_const_view(g_t), gf_view(g_w), p); + + g_wr[_, r] = g_w; + } + return g_wr; +} + +g_wk_t g_wk_from_g_wr(g_wr_cvt g_wr) { + + auto _ = all_t{}; + int nb = g_wr.target().shape()[0]; + + auto [wmesh, rmesh] = g_wr.mesh(); + + auto kmesh = make_adjoint_mesh(rmesh); + g_wk_t g_wk{{wmesh, kmesh}, {nb, nb}}; + + auto w0 = *wmesh.begin(); + auto p = _fourier_plan<0>(gf_const_view(g_wr[w0, _]), gf_view(g_wk[w0, _])); + + array::mesh_point_t, 1> w_arr(wmesh.size()); + auto w_iter = wmesh.begin(); + for (auto idx : range(0, wmesh.size())) { + auto w = *w_iter; + w_arr(idx) = w; + w_iter++; + } + +#pragma omp parallel for + for (int idx = 0; idx < w_arr.size(); idx++) { + auto &w = w_arr(idx); + + auto g_r = make_gf(rmesh, g_wr.target()); + auto g_k = make_gf(kmesh, g_wk.target()); + + g_r = g_wr[w, _]; + + _fourier_with_plan<0>(gf_const_view(g_r), gf_view(g_k), p); + + g_wk[w, _] = g_k; + } + return g_wk; +} + +// BOILER PLATE CODE FOR FFT ENDS HERE ============================================================ + g_wk_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const_r, g_wk_vt g_wk, g_wk_vt delta_wk) { @@ -181,7 +333,9 @@ g_wk_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const t_g_delta_g_product.stop(); t_fft_F.start(); - auto F_tr = make_gf_from_fourier<0, 1>(F_wk); + //auto F_tr = make_gf_from_fourier<0, 1>(F_wk); + auto F_wr = g_wr_from_g_wk(F_wk); + auto F_tr = g_tr_from_g_wr(F_wr); t_fft_F.stop(); auto [tmesh, rmesh] = F_tr.mesh(); @@ -234,7 +388,9 @@ g_wk_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const // FIXME // This raises warnings when used with random delta input, e.g. eigenvalue finder t_fft_delta.start(); - auto delta_wk_out = make_gf_from_fourier<0, 1>(delta_tr_out); + //auto delta_wk_out = make_gf_from_fourier<0, 1>(delta_tr_out); + auto delta_wr_out = g_wr_from_g_tr(delta_tr_out); + auto delta_wk_out = g_wk_from_g_wr(delta_wr_out); t_fft_delta.stop(); // Constant part From 5d270ef3135a150f91a52d41c72221993e19d07f Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 22 Jul 2019 16:48:31 -0400 Subject: [PATCH 038/121] [eli] ease numerical tolerance in two band test --- test/python/eliashberg/previous_implementation_two_band.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/test/python/eliashberg/previous_implementation_two_band.py b/test/python/eliashberg/previous_implementation_two_band.py index 911440e0c..7738fa2ad 100644 --- a/test/python/eliashberg/previous_implementation_two_band.py +++ b/test/python/eliashberg/previous_implementation_two_band.py @@ -121,7 +121,7 @@ print('\nThe benchmark data was obtained with %s.'%show_version_info(p_benchmark.version_info)) np.testing.assert_allclose(p_benchmark.gamma.data, p.gamma.data) -np.testing.assert_allclose(p_benchmark.next_delta.data, p.next_delta.data) +np.testing.assert_allclose(p_benchmark.next_delta.data, p.next_delta.data, atol=1e-9) np.testing.assert_allclose(p_benchmark.E, p.E) assert allclose_by_scalar_multiplication(p_benchmark.eigen_mode, p.eigen_mode),\ "Eigenvectors are not the same." From 6c04d397204240362700418f3ffa7597752ae00f Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 24 Jul 2019 14:34:30 -0400 Subject: [PATCH 039/121] [fourier] introduce lattice fourier for general target Added a template that uses the omp parallelized fourier transformation for Gfs with a general target in fourier_gf.hpp This template was then used is gf.cpp and chi_imtime.cpp where duplicate definitions of a parallelized fourier transformation existed. The naming a placement of fourier_gf.hpp, or further generalizations are up for debate. --- c++/triqs_tprf/lattice.hpp | 1 + c++/triqs_tprf/lattice/chi_imtime.cpp | 134 +---------------- c++/triqs_tprf/lattice/eliashberg.cpp | 167 +-------------------- c++/triqs_tprf/lattice/fourier_gf.hpp | 161 ++++++++++++++++++++ c++/triqs_tprf/lattice/gf.cpp | 208 +------------------------- 5 files changed, 179 insertions(+), 492 deletions(-) create mode 100644 c++/triqs_tprf/lattice/fourier_gf.hpp diff --git a/c++/triqs_tprf/lattice.hpp b/c++/triqs_tprf/lattice.hpp index 215443db2..10df57353 100644 --- a/c++/triqs_tprf/lattice.hpp +++ b/c++/triqs_tprf/lattice.hpp @@ -28,6 +28,7 @@ #include "./lattice/gw.hpp" #include "./lattice/eliashberg.hpp" #include "./lattice/fourier_interpolation.hpp" +#include "./lattice/fourier_gf.hpp" #include "./lattice/chi_imtime.hpp" #include "./lattice/chi_imfreq.hpp" diff --git a/c++/triqs_tprf/lattice/chi_imtime.cpp b/c++/triqs_tprf/lattice/chi_imtime.cpp index b1c297b60..3fd4147cd 100644 --- a/c++/triqs_tprf/lattice/chi_imtime.cpp +++ b/c++/triqs_tprf/lattice/chi_imtime.cpp @@ -24,6 +24,7 @@ #include "chi_imtime.hpp" #include "../fourier/fourier.hpp" +#include "fourier_gf.hpp" namespace triqs_tprf { @@ -186,147 +187,22 @@ chi_wr_t chi_w0r_from_chi_tr(chi_tr_cvt chi_tr) { } chi_wr_t chi_wr_from_chi_tr(chi_tr_cvt chi_tr, int nw) { - - auto _ = all_t{}; - int nb = chi_tr.target().shape()[0]; - - auto tmesh = std::get<0>(chi_tr.mesh()); - auto rmesh = std::get<1>(chi_tr.mesh()); - - double beta = tmesh.domain().beta; - - auto wmesh = gf_mesh(beta, Boson, nw); - chi_wr_t chi_wr{{wmesh, rmesh}, {nb, nb, nb, nb}}; - - //for (auto const &r : rmesh) { - - /* -#pragma omp parallel for - for (int idx = 0; idx < rmesh.size(); idx++) { - auto iter = rmesh.begin(); iter += idx; auto r = *iter; - */ - - auto r0 = *rmesh.begin(); - auto p = _fourier_plan<0>(gf_const_view(chi_tr[_, r0]), gf_view(chi_wr[_, r0])); - - auto arr = mpi_view(rmesh); - -#pragma omp parallel for - for (int idx = 0; idx < arr.size(); idx++) { - auto & r = arr(idx); - - auto chi_w = make_gf(wmesh, chi_wr.target()); - auto chi_t = make_gf(tmesh, chi_wr.target()); - -#pragma omp critical - chi_t = chi_tr[_, r]; - - _fourier_with_plan<0>(gf_const_view(chi_t), gf_view(chi_w), p); - -#pragma omp critical - chi_wr[_, r] = chi_w; - - //chi_wr[_, r] = fourier(chi_tr[_, r]); - } - - chi_wr = mpi::all_reduce(chi_wr); + auto chi_wr = fourier_tr_to_wr_general_target(chi_tr, nw); return chi_wr; } chi_tr_t chi_tr_from_chi_wr(chi_wr_cvt chi_wr, int ntau) { - std::cout << "WARNING: chi_tr_from_chi_wr is not parallellized. FIXME\n"; - - auto wmesh = std::get<0>(chi_wr.mesh()); - double beta = wmesh.domain().beta; - - if( ntau <= 0 ) - ntau = wmesh.size() * 6; - - auto tmesh = gf_mesh(beta, Boson, ntau); - - auto chi_tr = make_gf_from_fourier<0>(chi_wr, tmesh); - + auto chi_tr = fourier_wr_to_tr_general_target(chi_wr, ntau); return chi_tr; } chi_wk_t chi_wk_from_chi_wr(chi_wr_cvt chi_wr) { - - auto _ = all_t{}; - - // auto target = chi_wr.target(); - int nb = chi_wr.target().shape()[0]; - - auto wmesh = std::get<0>(chi_wr.mesh()); - auto rmesh = std::get<1>(chi_wr.mesh()); - - auto kmesh = gf_mesh{brillouin_zone{rmesh.domain()}, rmesh.periodization_matrix}; - - chi_wk_t chi_wk{{wmesh, kmesh}, {nb, nb, nb, nb}}; - - auto w0 = *wmesh.begin(); - auto p = _fourier_plan<0>(gf_const_view(chi_wr[w0, _]), gf_view(chi_wk[w0, _])); - - auto arr = mpi_view(wmesh); - -#pragma omp parallel for - for (int idx = 0; idx < arr.size(); idx++) { - auto & w = arr(idx); - - auto chi_r = make_gf(rmesh, chi_wr.target()); - auto chi_k = make_gf(kmesh, chi_wr.target()); - -#pragma omp critical - chi_r = chi_wr[w, _]; - - _fourier_with_plan<0>(gf_const_view(chi_r), gf_view(chi_k), p); - -#pragma omp critical - chi_wk[w, _] = chi_k; - - } - - chi_wk = mpi::all_reduce(chi_wk); + auto chi_wk = fourier_wr_to_wk_general_target(chi_wr); return chi_wk; } chi_wr_t chi_wr_from_chi_wk(chi_wk_cvt chi_wk) { - - auto _ = all_t{}; - - int nb = chi_wk.target().shape()[0]; - - auto wmesh = std::get<0>(chi_wk.mesh()); - auto kmesh = std::get<1>(chi_wk.mesh()); - - auto rmesh = gf_mesh{bravais_lattice{kmesh.domain()}, kmesh.periodization_matrix}; - - chi_wr_t chi_wr{{wmesh, rmesh}, {nb, nb, nb, nb}}; - - auto w0 = *wmesh.begin(); - auto p = _fourier_plan<0>(gf_const_view(chi_wk[w0, _]), gf_view(chi_wr[w0, _])); - - auto arr = mpi_view(wmesh); - -#pragma omp parallel for - for (int idx = 0; idx < arr.size(); idx++) { - auto & w = arr(idx); - - auto chi_k = make_gf(kmesh, chi_wr.target()); - auto chi_r = make_gf(rmesh, chi_wr.target()); - -#pragma omp critical - chi_k = chi_wk[w, _]; - - _fourier_with_plan<0>(gf_const_view(chi_k), gf_view(chi_r), p); - -#pragma omp critical - chi_wr[w, _] = chi_r; - - //for (auto const &w : wmesh) - //chi_wr[w, _] = triqs::gfs::fourier(chi_wk[w, _]); - } - - chi_wr = mpi::all_reduce(chi_wr); + auto chi_wr = fourier_wk_to_wr_general_target(chi_wk); return chi_wr; } diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index 4f03a3eae..e33fdf4d5 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -24,13 +24,10 @@ #include "common.hpp" #include "../mpi.hpp" #include -#include "../fourier/fourier.hpp" -namespace triqs_tprf { +#include "gf.hpp" - namespace { - using namespace fourier; - } +namespace triqs_tprf { // Helper function computing F = GG \Delta @@ -171,158 +168,6 @@ e_k_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, g_tr_t F_tr return delta_k_out; } -// BOILER PLATE CODE FOR FFT STARTS HERE ============================================================ - -g_tr_t g_tr_from_g_wr(g_wr_cvt g_wr, int nt = -1) { - - auto _ = all_t{}; - int nb = g_wr.target().shape()[0]; - - auto [wmesh, rmesh] = g_wr.mesh(); - - auto tmesh = make_adjoint_mesh(wmesh, nt); - g_tr_t g_tr{{tmesh, rmesh}, {nb, nb}}; - - auto r0 = *rmesh.begin(); - auto p = _fourier_plan<0>(gf_const_view(g_wr[_, r0]), gf_view(g_tr[_, r0])); - - array::mesh_point_t, 1> r_arr(rmesh.size()); - auto r_iter = rmesh.begin(); - for (auto idx : range(0, rmesh.size())) { - auto r = *r_iter; - r_arr(idx) = r; - r_iter++; - } - -#pragma omp parallel for - for (int idx = 0; idx < r_arr.size(); idx++) { - auto &r = r_arr(idx); - - auto g_w = make_gf(wmesh, g_wr.target()); - auto g_t = make_gf(tmesh, g_tr.target()); - - g_w = g_wr[_, r]; - - _fourier_with_plan<0>(gf_const_view(g_w), gf_view(g_t), p); - - g_tr[_, r] = g_t; - } - return g_tr; -} - -g_wr_t g_wr_from_g_wk(g_wk_cvt g_wk) { - - auto _ = all_t{}; - int nb = g_wk.target().shape()[0]; - - auto [wmesh, kmesh] = g_wk.mesh(); - - auto rmesh = make_adjoint_mesh(kmesh); - g_wr_t g_wr{{wmesh, rmesh}, {nb, nb}}; - - auto w0 = *wmesh.begin(); - auto p = _fourier_plan<0>(gf_const_view(g_wk[w0, _]), gf_view(g_wr[w0, _])); - - array::mesh_point_t, 1> w_arr(wmesh.size()); - auto w_iter = wmesh.begin(); - for (auto idx : range(0, wmesh.size())) { - auto w = *w_iter; - w_arr(idx) = w; - w_iter++; - } - -#pragma omp parallel for - for (int idx = 0; idx < w_arr.size(); idx++) { - auto &w = w_arr(idx); - - auto g_k = make_gf(kmesh, g_wk.target()); - auto g_r = make_gf(rmesh, g_wr.target()); - - g_k = g_wk[w, _]; - - _fourier_with_plan<0>(gf_const_view(g_k), gf_view(g_r), p); - - g_wr[w, _] = g_r; - } - return g_wr; -} - -g_wr_t g_wr_from_g_tr(g_tr_cvt g_tr) { - - auto _ = all_t{}; - int nb = g_tr.target().shape()[0]; - - auto [tmesh, rmesh] = g_tr.mesh(); - - auto wmesh = make_adjoint_mesh(tmesh); - g_wr_t g_wr{{wmesh, rmesh}, {nb, nb}}; - - auto r0 = *rmesh.begin(); - auto p = _fourier_plan<0>(gf_const_view(g_tr[_, r0]), gf_view(g_wr[_, r0])); - - array::mesh_point_t, 1> r_arr(rmesh.size()); - auto r_iter = rmesh.begin(); - for (auto idx : range(0, rmesh.size())) { - auto r = *r_iter; - r_arr(idx) = r; - r_iter++; - } - -#pragma omp parallel for - for (int idx = 0; idx < r_arr.size(); idx++) { - auto &r = r_arr(idx); - - auto g_t = make_gf(tmesh, g_tr.target()); - auto g_w = make_gf(wmesh, g_wr.target()); - - g_t = g_tr[_, r]; - - _fourier_with_plan<0>(gf_const_view(g_t), gf_view(g_w), p); - - g_wr[_, r] = g_w; - } - return g_wr; -} - -g_wk_t g_wk_from_g_wr(g_wr_cvt g_wr) { - - auto _ = all_t{}; - int nb = g_wr.target().shape()[0]; - - auto [wmesh, rmesh] = g_wr.mesh(); - - auto kmesh = make_adjoint_mesh(rmesh); - g_wk_t g_wk{{wmesh, kmesh}, {nb, nb}}; - - auto w0 = *wmesh.begin(); - auto p = _fourier_plan<0>(gf_const_view(g_wr[w0, _]), gf_view(g_wk[w0, _])); - - array::mesh_point_t, 1> w_arr(wmesh.size()); - auto w_iter = wmesh.begin(); - for (auto idx : range(0, wmesh.size())) { - auto w = *w_iter; - w_arr(idx) = w; - w_iter++; - } - -#pragma omp parallel for - for (int idx = 0; idx < w_arr.size(); idx++) { - auto &w = w_arr(idx); - - auto g_r = make_gf(rmesh, g_wr.target()); - auto g_k = make_gf(kmesh, g_wk.target()); - - g_r = g_wr[w, _]; - - _fourier_with_plan<0>(gf_const_view(g_r), gf_view(g_k), p); - - g_wk[w, _] = g_k; - } - return g_wk; -} - -// BOILER PLATE CODE FOR FFT ENDS HERE ============================================================ - g_wk_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const_r, g_wk_vt g_wk, g_wk_vt delta_wk) { @@ -334,8 +179,8 @@ g_wk_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const t_fft_F.start(); //auto F_tr = make_gf_from_fourier<0, 1>(F_wk); - auto F_wr = g_wr_from_g_wk(F_wk); - auto F_tr = g_tr_from_g_wr(F_wr); + auto F_wr = fourier_wk_to_wr(F_wk); + auto F_tr = fourier_wr_to_tr(F_wr); t_fft_F.stop(); auto [tmesh, rmesh] = F_tr.mesh(); @@ -389,8 +234,8 @@ g_wk_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const // This raises warnings when used with random delta input, e.g. eigenvalue finder t_fft_delta.start(); //auto delta_wk_out = make_gf_from_fourier<0, 1>(delta_tr_out); - auto delta_wr_out = g_wr_from_g_tr(delta_tr_out); - auto delta_wk_out = g_wk_from_g_wr(delta_wr_out); + auto delta_wr_out = fourier_tr_to_wr(delta_tr_out); + auto delta_wk_out = fourier_wr_to_wk(delta_wr_out); t_fft_delta.stop(); // Constant part diff --git a/c++/triqs_tprf/lattice/fourier_gf.hpp b/c++/triqs_tprf/lattice/fourier_gf.hpp new file mode 100644 index 000000000..28ee6935d --- /dev/null +++ b/c++/triqs_tprf/lattice/fourier_gf.hpp @@ -0,0 +1,161 @@ +/******************************************************************************* + * + * TRIQS: a Toolbox for Research in Interacting Quantum Systems + * + * Copyright (C) 2017, H. U.R. Strand + * + * TRIQS is free software: you can redistribute it and/or modify it under the + * terms of the GNU General Public License as published by the Free Software + * Foundation, either version 3 of the License, or (at your option) any later + * version. + * + * TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY + * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more + * details. + * + * You should have received a copy of the GNU General Public License along with + * TRIQS. If not, see . + * + ******************************************************************************/ +#pragma once + +#include "../types.hpp" +#include "../fourier/fourier.hpp" +#include +#include "../mpi.hpp" + +namespace triqs_tprf { + + + namespace { + using namespace fourier; + } + +template +auto fourier_wr_to_tr_general_target(gf_const_view, Target> g_wr, int n_tau = -1) { + + auto _ = all_t{}; + auto [wmesh, rmesh] = g_wr.mesh(); + + auto tmesh = make_adjoint_mesh(wmesh, n_tau); + auto g_tr = gf, Target>{{tmesh, rmesh}, g_wr.target_shape()}; + + auto r0 = *rmesh.begin(); + auto p = _fourier_plan<0>(gf_const_view(g_wr[_, r0]), gf_view(g_tr[_, r0])); + + auto r_arr = mpi_view(rmesh); + +#pragma omp parallel for + for (unsigned int idx = 0; idx < r_arr.size(); idx++) { + auto &r = r_arr(idx); + + auto g_w = make_gf(wmesh, g_wr.target()); + auto g_t = make_gf(tmesh, g_tr.target()); + + g_w = g_wr[_, r]; + + _fourier_with_plan<0>(gf_const_view(g_w), gf_view(g_t), p); + + g_tr[_, r] = g_t; + } + g_tr = mpi_all_reduce(g_tr); + return g_tr; +} + +template +auto fourier_tr_to_wr_general_target(gf_const_view, Target> g_tr, int n_w = -1) { + + auto _ = all_t{}; + auto [tmesh, rmesh] = g_tr.mesh(); + + auto wmesh = make_adjoint_mesh(tmesh, n_w); + auto g_wr = gf, Target>{{wmesh, rmesh}, g_tr.target_shape()}; + + auto r0 = *rmesh.begin(); + auto p = _fourier_plan<0>(gf_const_view(g_tr[_, r0]), gf_view(g_wr[_, r0])); + + auto r_arr = mpi_view(rmesh); + +#pragma omp parallel for + for (unsigned int idx = 0; idx < r_arr.size(); idx++) { + auto &r = r_arr(idx); + + auto g_t = make_gf(tmesh, g_tr.target()); + auto g_w = make_gf(wmesh, g_wr.target()); + + g_t = g_tr[_, r]; + + _fourier_with_plan<0>(gf_const_view(g_t), gf_view(g_w), p); + + g_wr[_, r] = g_w; + } + g_wr = mpi_all_reduce(g_wr); + return g_wr; +} + +template +auto fourier_wk_to_wr_general_target(gf_const_view, Target> g_wk) { + + auto _ = all_t{}; + + auto [wmesh, kmesh] = g_wk.mesh(); + + auto rmesh = make_adjoint_mesh(kmesh); + auto g_wr = gf, Target>{{wmesh, rmesh}, g_wk.target_shape()}; + + auto w0 = *wmesh.begin(); + auto p = _fourier_plan<0>(gf_const_view(g_wk[w0, _]), gf_view(g_wr[w0, _])); + + auto w_arr = mpi_view(wmesh); + +#pragma omp parallel for + for (unsigned int idx = 0; idx < w_arr.size(); idx++) { + auto &w = w_arr(idx); + + auto g_k = make_gf(kmesh, g_wk.target()); + auto g_r = make_gf(rmesh, g_wr.target()); + + g_k = g_wk[w, _]; + + _fourier_with_plan<0>(gf_const_view(g_k), gf_view(g_r), p); + + g_wr[w, _] = g_r; + } + g_wr = mpi_all_reduce(g_wr); + return g_wr; +} + +template +auto fourier_wr_to_wk_general_target(gf_const_view, Target> g_wr) { + + auto _ = all_t{}; + + auto [wmesh, rmesh] = g_wr.mesh(); + + auto kmesh = make_adjoint_mesh(rmesh); + auto g_wk = gf, Target>{{wmesh, kmesh}, g_wr.target_shape()}; + + auto w0 = *wmesh.begin(); + auto p = _fourier_plan<0>(gf_const_view(g_wr[w0, _]), gf_view(g_wk[w0, _])); + + auto w_arr = mpi_view(wmesh); + +#pragma omp parallel for + for (unsigned int idx = 0; idx < w_arr.size(); idx++) { + auto &w = w_arr(idx); + + auto g_r = make_gf(rmesh, g_wr.target()); + auto g_k = make_gf(kmesh, g_wk.target()); + + g_r = g_wr[w, _]; + + _fourier_with_plan<0>(gf_const_view(g_r), gf_view(g_k), p); + + g_wk[w, _] = g_k; + } + g_wk = mpi_all_reduce(g_wk); + return g_wk; +} + +} // namespace triqs_tprf diff --git a/c++/triqs_tprf/lattice/gf.cpp b/c++/triqs_tprf/lattice/gf.cpp index 226f94198..40f26c08a 100644 --- a/c++/triqs_tprf/lattice/gf.cpp +++ b/c++/triqs_tprf/lattice/gf.cpp @@ -26,7 +26,7 @@ using triqs::arrays::inverse; #include "common.hpp" #include "gf.hpp" -#include "../fourier/fourier.hpp" +#include "fourier_gf.hpp" namespace triqs_tprf { @@ -143,225 +143,29 @@ g_w_t lattice_dyson_g_w(double mu, e_k_cvt e_k, g_w_cvt sigma_w) { } // ---------------------------------------------------- +// Transformations: real space <-> reciprocal space -#ifdef TPRF_OMP - -g_wr_t fourier_wk_to_wr(g_wk_cvt g_wk) { - - auto _ = all_t{}; - auto target = g_wk.target(); - - //const auto & [ wmesh, kmesh ] = g_wk.mesh(); - auto wmesh = std::get<0>(g_wk.mesh()); - auto kmesh = std::get<1>(g_wk.mesh()); - auto rmesh = make_adjoint_mesh(kmesh); - - g_wr_t g_wr({wmesh, rmesh}, g_wk.target_shape()); - - auto w0 = *wmesh.begin(); - auto p = _fourier_plan<0>(gf_const_view(g_wk[w0, _]), gf_view(g_wr[w0, _])); - - auto arr = mpi_view(wmesh); - - #pragma omp parallel for - for (int idx = 0; idx < arr.size(); idx++) { - auto & w = arr(idx); - - auto g_r = make_gf(rmesh, target); - auto g_k = make_gf(kmesh, target); - - #pragma omp critical - g_k = g_wk[w, _]; - - _fourier_with_plan<0>(gf_const_view(g_k), gf_view(g_r), p); - - #pragma omp critical - g_wr[w, _] = g_r; - - } - - g_wr = mpi::all_reduce(g_wr); - return g_wr; -} - -#else - g_wr_t fourier_wk_to_wr(g_wk_cvt g_wk) { - - auto [wmesh, kmesh] = g_wk.mesh(); - auto rmesh = make_adjoint_mesh(kmesh); - - g_wr_t g_wr({wmesh, rmesh}, g_wk.target_shape()); - - auto _ = all_t{}; - for ( auto const &w : mpi_view(wmesh) ) - g_wr[w, _]() = triqs::gfs::fourier(g_wk[w, _]); - - g_wr = mpi::all_reduce(g_wr); - + auto g_wr = fourier_wk_to_wr_general_target(g_wk); return g_wr; } - -#endif - -// ---------------------------------------------------- - -#ifdef TPRF_OMP - -g_wk_t fourier_wr_to_wk(g_wr_cvt g_wr) { - - auto _ = all_t{}; - auto target = g_wr.target(); - - //auto [wmesh, rmesh] = g_wr.mesh(); - auto wmesh = std::get<0>(g_wr.mesh()); - auto rmesh = std::get<1>(g_wr.mesh()); - auto kmesh = make_adjoint_mesh(rmesh); - - g_wk_t g_wk({wmesh, kmesh}, g_wr.target_shape()); - - auto w0 = *wmesh.begin(); - auto p = _fourier_plan<0>(gf_const_view(g_wr[w0, _]), gf_view(g_wk[w0, _])); - - auto arr = mpi_view(wmesh); - - #pragma omp parallel for - for (int idx = 0; idx < arr.size(); idx++) { - auto & w = arr(idx); - - auto g_r = make_gf(rmesh, target); - auto g_k = make_gf(kmesh, target); - -#pragma omp critical - g_r = g_wr[w, _]; - - _fourier_with_plan<0>(gf_const_view(g_r), gf_view(g_k), p); - -#pragma omp critical - g_wk[w, _] = g_k; - - } - - g_wk = mpi::all_reduce(g_wk); - return g_wk; -} -#else - g_wk_t fourier_wr_to_wk(g_wr_cvt g_wr) { - - auto [wmesh, rmesh] = g_wr.mesh(); - auto kmesh = make_adjoint_mesh(rmesh); - - g_wk_t g_wk({wmesh, kmesh}, g_wr.target_shape()); - - auto _ = all_t{}; - for (auto const &w : mpi_view(wmesh)) - g_wk[w, _]() = triqs::gfs::fourier(g_wr[w, _]); - - g_wk = mpi::all_reduce(g_wk); - + auto g_wk = fourier_wr_to_wk_general_target(g_wr); return g_wk; } -#endif - // ---------------------------------------------------- // Transformations: Matsubara frequency <-> imaginary time g_wr_t fourier_tr_to_wr(g_tr_cvt g_tr, int nw) { - std::cout << "WARNING: fourier_tr_to_wr is not parallellized. FIXME\n"; - - auto tmesh = std::get<0>(g_tr.mesh()); - double beta = tmesh.domain().beta; - auto S = tmesh.domain().statistic; - - if( nw <= 0 ) nw = tmesh.size() / 4; - - auto wmesh = gf_mesh(beta, S, nw); - - auto g_wr = make_gf_from_fourier<0>(g_tr, wmesh); - + auto g_wr = fourier_tr_to_wr_general_target(g_tr, nw); return g_wr; } -#ifdef TPRF_OMP - -g_tr_t fourier_wr_to_tr(g_wr_cvt g_wr, int nt) { - - auto wmesh = std::get<0>(g_wr.mesh()); - auto rmesh = std::get<1>(g_wr.mesh()); - - double beta = wmesh.domain().beta; - auto S = wmesh.domain().statistic; - - int nw = wmesh.last_index() + 1; - if( nt <= 0 ) nt = 4 * nw; - - g_tr_t g_tr({{beta, S, nt}, rmesh}, g_wr.target_shape()); - - auto tmesh = std::get<0>(g_tr.mesh()); - - auto _ = all_t{}; - - auto r0 = *rmesh.begin(); - auto p = _fourier_plan<0>(gf_const_view(g_wr[_, r0]), gf_view(g_tr[_, r0])); - - auto arr = mpi_view(rmesh); - -#pragma omp parallel for - for (int idx = 0; idx < arr.size(); idx++) { - auto & r = arr(idx); - - auto g_w = make_gf(wmesh, g_wr.target()); - auto g_t = make_gf(tmesh, g_wr.target()); - -#pragma omp critical - g_w = g_wr[_, r]; - - _fourier_with_plan<0>(gf_const_view(g_w), gf_view(g_t), p); - -#pragma omp critical - g_tr[_, r] = g_t; - - } - - g_tr = mpi::all_reduce(g_tr); - return g_tr; -} - -#else - g_tr_t fourier_wr_to_tr(g_wr_cvt g_wr, int nt) { - - auto wmesh = std::get<0>(g_wr.mesh()); - auto rmesh = std::get<1>(g_wr.mesh()); - - double beta = wmesh.domain().beta; - - int nw = wmesh.last_index() + 1; - if( nt <= 0 ) nt = 4 * nw; - - g_tr_t g_tr({{beta, wmesh.domain().statistic, nt}, rmesh}, g_wr.target_shape()); - - auto _ = all_t{}; - auto r0 = *rmesh.begin(); - auto zero_tail = make_zero_tail(g_wr[_, r0], 2); - auto zero_tail_r0 = make_zero_tail(g_wr[_, r0], 2); - - zero_tail_r0(1, range(), range()) = - make_unit_matrix(g_wr.target_shape()[0]); - - for (auto const &r : rmesh) { - if(r.linear_index() == 0) - g_tr[_, r]() = triqs::gfs::fourier<0>(g_wr[_, r], make_const_view(zero_tail_r0)); - else - g_tr[_, r]() = triqs::gfs::fourier<0>(g_wr[_, r], make_const_view(zero_tail)); - } - + auto g_tr = fourier_wr_to_tr_general_target(g_wr, nt); return g_tr; } -#endif - } // namespace triqs_tprf From 4be81970f1b12ed2f704b4f9cdee6c7afd9e9683 Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 26 Jul 2019 15:20:57 -0400 Subject: [PATCH 040/121] [eli] ease numercial tolerance for gamma in two band test --- test/python/eliashberg/previous_implementation_two_band.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/test/python/eliashberg/previous_implementation_two_band.py b/test/python/eliashberg/previous_implementation_two_band.py index 7738fa2ad..5de5635dd 100644 --- a/test/python/eliashberg/previous_implementation_two_band.py +++ b/test/python/eliashberg/previous_implementation_two_band.py @@ -120,7 +120,7 @@ print('\nThe benchmark data was obtained with %s.'%show_version_info(p_benchmark.version_info)) -np.testing.assert_allclose(p_benchmark.gamma.data, p.gamma.data) +np.testing.assert_allclose(p_benchmark.gamma.data, p.gamma.data, atol=1e-9) np.testing.assert_allclose(p_benchmark.next_delta.data, p.next_delta.data, atol=1e-9) np.testing.assert_allclose(p_benchmark.E, p.E) assert allclose_by_scalar_multiplication(p_benchmark.eigen_mode, p.eigen_mode),\ From 177c365271d0ef1007b1482a928cea68e897b6a3 Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 26 Jul 2019 15:21:54 -0400 Subject: [PATCH 041/121] fix -Wsign-compare compiler warnings We no longer compare signed to unsigned integer. --- c++/triqs_tprf/fourier/fourier_lattice.cpp | 4 ++-- c++/triqs_tprf/lattice/chi_imfreq.cpp | 16 ++++++++-------- c++/triqs_tprf/lattice/chi_imtime.cpp | 6 +++--- c++/triqs_tprf/lattice/eliashberg.cpp | 12 +++++------- c++/triqs_tprf/lattice/gf.cpp | 4 ++-- c++/triqs_tprf/lattice/gw.cpp | 4 ++-- c++/triqs_tprf/lattice/lindhard_chi00.cpp | 2 +- c++/triqs_tprf/lattice/rpa.cpp | 2 +- test/c++/mpi_and_openmp.cpp | 6 +++--- 9 files changed, 27 insertions(+), 29 deletions(-) diff --git a/c++/triqs_tprf/fourier/fourier_lattice.cpp b/c++/triqs_tprf/fourier/fourier_lattice.cpp index 771c21b29..ba774118d 100644 --- a/c++/triqs_tprf/fourier/fourier_lattice.cpp +++ b/c++/triqs_tprf/fourier/fourier_lattice.cpp @@ -49,8 +49,8 @@ namespace triqs_tprf::fourier { template fourier_plan __impl_plan(int fftw_backward_forward, gf_mesh const &out_mesh, gf_vec_cvt g_in) { //check periodization_matrix is diagonal - for (int i = 0; i < g_in.mesh().periodization_matrix.shape()[0]; i++) - for (int j = 0; j < g_in.mesh().periodization_matrix.shape()[1]; j++) + for (unsigned int i = 0; i < g_in.mesh().periodization_matrix.shape()[0]; i++) + for (unsigned int j = 0; j < g_in.mesh().periodization_matrix.shape()[1]; j++) if (i != j and g_in.mesh().periodization_matrix(i, j) != 0) TRIQS_RUNTIME_ERROR << "Periodization matrix must be diagonal for FFTW to work"; diff --git a/c++/triqs_tprf/lattice/chi_imfreq.cpp b/c++/triqs_tprf/lattice/chi_imfreq.cpp index 07a8aff27..85d95d30b 100644 --- a/c++/triqs_tprf/lattice/chi_imfreq.cpp +++ b/c++/triqs_tprf/lattice/chi_imfreq.cpp @@ -88,7 +88,7 @@ chi_wnr_t chi0r_from_gr_PH(int nw, int nn, g_wr_cvt g_nr) { t_calc.start(); #pragma omp parallel for - for (int idx = 0; idx < arr.size(); idx++) { + for (unsigned int idx = 0; idx < arr.size(); idx++) { auto &r = arr(idx); auto chi0_wn = @@ -167,7 +167,7 @@ chi_wnr_t chi0r_from_gr_PH_nompi(int nw, int nn, g_wr_cvt g_nr) { t_calc.start(); #pragma omp parallel for - for (int idx = 0; idx < rmesh.size(); idx++) { + for (unsigned int idx = 0; idx < rmesh.size(); idx++) { auto iter = rmesh.begin(); iter += idx; auto r = *iter; auto chi0_wn = @@ -349,7 +349,7 @@ chi_wnr_t chi0r_from_chi0q(chi_wnk_cvt chi_wnk) { auto arr = mpi_view(gf_mesh{bmesh, fmesh}); #pragma omp parallel for shared(kmesh, rmesh) - for (int idx = 0; idx < arr.size(); idx++) { + for (unsigned int idx = 0; idx < arr.size(); idx++) { //auto &[w, n] = arr(idx); auto w = std::get<0>(arr(idx)); auto n = std::get<1>(arr(idx)); @@ -422,7 +422,7 @@ chi_wnk_t chi0q_from_chi0r(chi_wnr_cvt chi_wnr) { t_calc.start(); #pragma omp parallel for - for (int idx = 0; idx < arr.size(); idx++) { + for (unsigned int idx = 0; idx < arr.size(); idx++) { //auto &[w, n] = arr(idx); auto w = std::get<0>(arr(idx)); auto n = std::get<1>(arr(idx)); @@ -473,7 +473,7 @@ chi_wk_t chi0q_sum_nu(chi_wnk_cvt chi_wnk) { auto arr = mpi_view(gf_mesh{wmesh, kmesh}); #pragma omp parallel for - for (int idx = 0; idx < arr.size(); idx++) { + for (unsigned int idx = 0; idx < arr.size(); idx++) { auto &[w, k] = arr(idx); for( auto &n : nmesh) chi_wk[w, k] += chi_wnk[w, n, k]; chi_wk[w, k] /= beta * beta; @@ -507,7 +507,7 @@ chi_wk_t chi0q_sum_nu_tail_corr_PH(chi_wnk_cvt chi_wnk) { auto arr = mpi_view(wq_mesh); // FIXME Use library implementation #pragma omp parallel for - for (int idx = 0; idx < arr.size(); idx++) { + for (unsigned int idx = 0; idx < arr.size(); idx++) { //auto &[w, q] = arr(idx); auto w = std::get<0>(arr(idx)); auto q = std::get<1>(arr(idx)); @@ -614,7 +614,7 @@ chi_kwnn_t chiq_from_chi0q_and_gamma_PH(chi_wnk_cvt chi0_wnk, chi_wnn_cvt gamma_ // for (auto const &k : mbz) { #pragma omp parallel for - for (int idx = 0; idx < mbz.size(); idx++) { + for (unsigned int idx = 0; idx < mbz.size(); idx++) { auto iter = mbz.begin(); iter += idx; auto k = *iter; @@ -670,7 +670,7 @@ chi_kw_t chiq_sum_nu_from_chi0q_and_gamma_PH(chi_wnk_cvt chi0_wnk, chi_wnn_cvt g t.start(); #pragma omp parallel for - for (int idx = 0; idx < arr.size(); idx++) { + for (unsigned int idx = 0; idx < arr.size(); idx++) { //auto &[k, w] = arr(idx); auto k = std::get<0>(arr(idx)); auto w = std::get<1>(arr(idx)); diff --git a/c++/triqs_tprf/lattice/chi_imtime.cpp b/c++/triqs_tprf/lattice/chi_imtime.cpp index 3fd4147cd..07f4959d3 100644 --- a/c++/triqs_tprf/lattice/chi_imtime.cpp +++ b/c++/triqs_tprf/lattice/chi_imtime.cpp @@ -61,7 +61,7 @@ chi_tr_t chi0_tr_from_grt_PH(g_tr_cvt g_tr) { auto arr = mpi_view(rmesh); #pragma omp parallel for - for (int idx = 0; idx < arr.size(); idx++) { + for (unsigned int idx = 0; idx < arr.size(); idx++) { auto & r = arr(idx); auto chi0_t = make_gf({beta, Boson, ntau}, chi_target); @@ -107,7 +107,7 @@ chi_wr_t chi0_w0r_from_grt_PH(g_tr_cvt g_tr) { auto arr = mpi_view(rmesh); #pragma omp parallel for - for (int idx = 0; idx < arr.size(); idx++) { + for (unsigned int idx = 0; idx < arr.size(); idx++) { auto & r = arr(idx); auto chi0_t = make_gf({beta, Boson, ntau}, chi_target); @@ -172,7 +172,7 @@ chi_wr_t chi_w0r_from_chi_tr(chi_tr_cvt chi_tr) { auto arr = mpi_view(rmesh); #pragma omp parallel for - for (int idx = 0; idx < arr.size(); idx++) { + for (unsigned int idx = 0; idx < arr.size(); idx++) { auto & r = arr(idx); auto _ = all_t{}; diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index e33fdf4d5..50bc57fc1 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -21,7 +21,7 @@ ******************************************************************************/ #include "eliashberg.hpp" -#include "common.hpp" +#include #include "../mpi.hpp" #include @@ -35,8 +35,6 @@ g_wk_t eliashberg_g_delta_g_product(g_wk_vt g_wk, g_wk_vt delta_wk) { triqs::utility::timer t_all, t_parallel; t_all.start(); - size_t norb = g_wk.target_shape()[0]; - auto [wmesh, kmesh] = delta_wk.mesh(); auto wmesh_gf = std::get<0>(g_wk.mesh()); @@ -64,7 +62,7 @@ g_wk_t eliashberg_g_delta_g_product(g_wk_vt g_wk, g_wk_vt delta_wk) { auto _ = all_t{}; t_parallel.start(); #pragma omp parallel for - for(int idx_k = 0; idx_k < kmesh.size(); idx_k++){ + for(unsigned int idx_k = 0; idx_k < kmesh.size(); idx_k++){ auto k = k_arr(idx_k); auto g_left_w = make_gf(wmesh, g_wk.target()); @@ -132,7 +130,7 @@ std::tuple split_into_dynamic_wk_and_constant_k(chi_wk_vt G for (const auto k : kmesh) { auto Gamma_w = Gamma_pp[_, k]; - auto [tail, err] = fit_tail(Gamma_w); + auto tail = std::get<0>(fit_tail(Gamma_w)); for (auto [a, b, c, d] : Gamma_pp.target_indices()) Gamma_pp_const_k[k](a, b, c, d) = tail(0, a, b, c, d); for( const auto w : wmesh ) Gamma_pp_dyn_wk[w, k] = Gamma_pp[w, k] - Gamma_pp_const_k[k]; @@ -214,7 +212,7 @@ g_wk_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const } auto _ = all_t{}; #pragma omp parallel for - for(int idx_r = 0; idx_r < rmesh.size(); idx_r++){ + for(unsigned int idx_r = 0; idx_r < rmesh.size(); idx_r++){ auto r = r_arr(idx_r); auto delta_t = make_gf(tmesh, delta_tr_out.target()); @@ -295,7 +293,7 @@ chi_wk_t gamma_PP_spin_charge(chi_wk_vt chi_c, chi_wk_vt chi_s, \ auto meshes_mpi = mpi_view(Gamma_pp_wk.mesh()); #pragma omp parallel for - for (int idx = 0; idx < meshes_mpi.size(); idx++){ + for (unsigned int idx = 0; idx < meshes_mpi.size(); idx++){ auto &[w, k] = meshes_mpi(idx); array Gamma_pp_arr{nb, nb, nb, nb, memory_layout_t<4>{0, 1, 2, 3}}; diff --git a/c++/triqs_tprf/lattice/gf.cpp b/c++/triqs_tprf/lattice/gf.cpp index 40f26c08a..d6fcc4a61 100644 --- a/c++/triqs_tprf/lattice/gf.cpp +++ b/c++/triqs_tprf/lattice/gf.cpp @@ -47,7 +47,7 @@ g_wk_t lattice_dyson_g0_wk(double mu, e_k_cvt e_k, gf_mesh mesh) { auto arr = mpi_view(g0_wk.mesh()); #pragma omp parallel for - for (int idx = 0; idx < arr.size(); idx++) { + for (unsigned int idx = 0; idx < arr.size(); idx++) { auto &[w, k] = arr(idx); g0_wk[w, k] = inverse((w + mu)*I - e_k(k)); } @@ -97,7 +97,7 @@ g_wk_t lattice_dyson_g_wk(double mu, e_k_cvt e_k, g_w_cvt sigma_w) { auto arr = mpi_view(g_wk.mesh()); #pragma omp parallel for - for (int idx = 0; idx < arr.size(); idx++) { + for (unsigned int idx = 0; idx < arr.size(); idx++) { auto &[w, k] = arr(idx); g_wk[w, k] = inverse((w + mu)*I - e_k(k) - sigma_w[w]); } diff --git a/c++/triqs_tprf/lattice/gw.cpp b/c++/triqs_tprf/lattice/gw.cpp index de42fe998..f6908832d 100644 --- a/c++/triqs_tprf/lattice/gw.cpp +++ b/c++/triqs_tprf/lattice/gw.cpp @@ -40,7 +40,7 @@ chi_wk_t dynamical_screened_interaction_W_wk(chi_wk_cvt PI_wk, chi_k_cvt V_k) { // MPI and openMP parallell loop auto arr = mpi_view(W_wk.mesh()); #pragma omp parallel for - for (int idx = 0; idx < arr.size(); idx++) { + for (unsigned int idx = 0; idx < arr.size(); idx++) { auto &[w, k] = arr(idx); array V_arr{V_k[k], memory_layout_t<4>{0, 1, 2, 3}}; @@ -114,7 +114,7 @@ g_tr_t gw_sigma_tr(chi_tr_cvt Wr_tr, g_tr_cvt g_tr) { // MPI and openMP parallell loop auto arr = mpi_view(g_tr.mesh()); #pragma omp parallel for - for (int idx = 0; idx < arr.size(); idx++) { + for (unsigned int idx = 0; idx < arr.size(); idx++) { auto &[t, r] = arr(idx); //for (const auto &[t, r] : g_tr.mesh()) { diff --git a/c++/triqs_tprf/lattice/lindhard_chi00.cpp b/c++/triqs_tprf/lattice/lindhard_chi00.cpp index 662934518..a6223748f 100644 --- a/c++/triqs_tprf/lattice/lindhard_chi00.cpp +++ b/c++/triqs_tprf/lattice/lindhard_chi00.cpp @@ -50,7 +50,7 @@ chi_wk_t lindhard_chi00_wk(e_k_cvt e_k, int nw, //for (auto const &q : kmesh) { // can not do range-based for loops with OpenMP #pragma omp parallel for - for (int qidx = 0; qidx < kmesh.size(); qidx++) { + for (unsigned int qidx = 0; qidx < kmesh.size(); qidx++) { auto q_iter = kmesh.begin(); q_iter += qidx; auto q = *q_iter; diff --git a/c++/triqs_tprf/lattice/rpa.cpp b/c++/triqs_tprf/lattice/rpa.cpp index 2503f5de8..3e4bd5a45 100644 --- a/c++/triqs_tprf/lattice/rpa.cpp +++ b/c++/triqs_tprf/lattice/rpa.cpp @@ -44,7 +44,7 @@ chi_wk_t solve_rpa_PH(chi_wk_vt chi0_wk, auto meshes_mpi = mpi_view(chi0_wk.mesh()); #pragma omp parallel for - for (int idx = 0; idx < meshes_mpi.size(); idx++){ + for (unsigned int idx = 0; idx < meshes_mpi.size(); idx++){ auto &[w, k] = meshes_mpi(idx); array chi_arr{nb, nb, nb, nb, diff --git a/test/c++/mpi_and_openmp.cpp b/test/c++/mpi_and_openmp.cpp index 89d32639f..639059554 100644 --- a/test/c++/mpi_and_openmp.cpp +++ b/test/c++/mpi_and_openmp.cpp @@ -79,7 +79,7 @@ TEST(mpi, mpi_view_openmp) { { auto arr = mpi_view(g_wk.mesh()); #pragma omp parallel for - for (int idx = 0; idx < arr.size(); idx++) { + for (unsigned int idx = 0; idx < arr.size(); idx++) { auto &[w, k] = arr(idx); int tid = omp_get_thread_num(); @@ -96,7 +96,7 @@ TEST(mpi, mpi_view_openmp) { { auto arr = mpi_view(wmesh); #pragma omp parallel for - for (int idx = 0; idx < arr.size(); idx++) { + for (unsigned int idx = 0; idx < arr.size(); idx++) { auto &w = arr(idx); int tid = omp_get_thread_num(); @@ -112,7 +112,7 @@ TEST(mpi, mpi_view_openmp) { { auto arr = mpi_view(kmesh); #pragma omp parallel for - for (int idx = 0; idx < arr.size(); idx++) { + for (unsigned int idx = 0; idx < arr.size(); idx++) { auto &k = arr(idx); int tid = omp_get_thread_num(); From f4e10d94de3d2de407c2daa5a8f767591fb95379 Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 24 Jul 2019 17:26:52 -0400 Subject: [PATCH 042/121] fix -Wunused-variable compiler warnings --- c++/triqs_tprf/lattice/chi_imfreq.cpp | 13 ++++++++----- c++/triqs_tprf/lattice/common.hpp | 12 ++++++------ c++/triqs_tprf/lattice/gf.cpp | 4 ++-- c++/triqs_tprf/lattice/rpa.cpp | 2 +- 4 files changed, 17 insertions(+), 14 deletions(-) diff --git a/c++/triqs_tprf/lattice/chi_imfreq.cpp b/c++/triqs_tprf/lattice/chi_imfreq.cpp index 85d95d30b..32edd52ee 100644 --- a/c++/triqs_tprf/lattice/chi_imfreq.cpp +++ b/c++/triqs_tprf/lattice/chi_imfreq.cpp @@ -35,6 +35,7 @@ namespace triqs_tprf { namespace { using fourier::_fourier_plan; using fourier::_fourier_with_plan; +placeholder<1> inu; } // namespace // ---------------------------------------------------- @@ -216,7 +217,7 @@ gf> chi0_n_from_g_wk_PH(mesh_point> w, g_wk_cvt g_wk) { int nb = g_wk.target().shape()[0]; - auto [fmesh_large, kmesh] = g_wk.mesh(); + auto kmesh = std::get<1>(g_wk.mesh()); double beta = fmesh.domain().beta; @@ -287,7 +288,7 @@ chi0_n_from_e_k_sigma_w_PH(mesh_point> w, chi_wnk_t chi0q_from_g_wk_PH(int nw, int nn, g_wk_cvt g_wk) { - auto [fmesh_large, kmesh] = g_wk.mesh(); + auto kmesh = std::get<1>(g_wk.mesh()); int nb = g_wk.target().shape()[0]; double beta = std::get<0>(g_wk.mesh()).domain().beta; @@ -776,8 +777,9 @@ chiq_sum_nu_from_g_wk_and_gamma_PH(gk_iw_t g_wk, g2_iw_vt gamma_ph_wnn, auto _ = all_t{}; auto target = gamma_ph_wnn.target(); - auto [fmesh_large, kmesh] = g_wk.mesh(); - auto [bmesh, fmesh, fmesh2] = gamma_ph_wnn.mesh(); + auto kmesh = std::get<1>(g_wk.mesh()); + auto bmesh = std::get<0>(gamma_ph_wnn.mesh()); + auto fmesh = std::get<1>(gamma_ph_wnn.mesh()); double beta = fmesh.domain().beta; @@ -904,7 +906,8 @@ chiq_sum_nu_from_e_k_sigma_w_and_gamma_PH(double mu, ek_vt e_k, g_iw_vt sigma_w, auto kmesh = e_k.mesh(); auto fmesh_large = sigma_w.mesh(); - auto [bmesh, fmesh, fmesh2] = gamma_ph_wnn.mesh(); + auto bmesh = std::get<0>(gamma_ph_wnn.mesh()); + auto fmesh = std::get<1>(gamma_ph_wnn.mesh()); double beta = fmesh.domain().beta; diff --git a/c++/triqs_tprf/lattice/common.hpp b/c++/triqs_tprf/lattice/common.hpp index 358879948..c237261d0 100644 --- a/c++/triqs_tprf/lattice/common.hpp +++ b/c++/triqs_tprf/lattice/common.hpp @@ -27,17 +27,17 @@ using namespace triqs::clef; namespace { -placeholder<0> iw; -placeholder<1> inu; -placeholder<2> k; -placeholder<3> r; +//placeholder<0> iw; +//placeholder<1> inu; +//placeholder<2> k; +//placeholder<3> r; placeholder<4> a; placeholder<5> b; placeholder<6> c; placeholder<7> d; -placeholder<8> inup; -placeholder<9> tau; +//placeholder<8> inup; +//placeholder<9> tau; } // namespace diff --git a/c++/triqs_tprf/lattice/gf.cpp b/c++/triqs_tprf/lattice/gf.cpp index d6fcc4a61..1c9683156 100644 --- a/c++/triqs_tprf/lattice/gf.cpp +++ b/c++/triqs_tprf/lattice/gf.cpp @@ -22,10 +22,10 @@ #include using triqs::arrays::inverse; -#include "../mpi.hpp" -#include "common.hpp" #include "gf.hpp" +#include +#include "../mpi.hpp" #include "fourier_gf.hpp" namespace triqs_tprf { diff --git a/c++/triqs_tprf/lattice/rpa.cpp b/c++/triqs_tprf/lattice/rpa.cpp index 3e4bd5a45..b33a51df0 100644 --- a/c++/triqs_tprf/lattice/rpa.cpp +++ b/c++/triqs_tprf/lattice/rpa.cpp @@ -21,7 +21,7 @@ ******************************************************************************/ #include "rpa.hpp" -#include "common.hpp" +#include #include "../mpi.hpp" namespace triqs_tprf { From 8ae3f7db6c8e76679719f4d0279faa3d97b80857 Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 24 Jul 2019 17:44:24 -0400 Subject: [PATCH 043/121] [fourier] rename fourier template file and update licence --- c++/triqs_tprf/lattice.hpp | 1 - c++/triqs_tprf/lattice/chi_imtime.cpp | 2 +- c++/triqs_tprf/lattice/{fourier_gf.hpp => fourier.hpp} | 3 ++- c++/triqs_tprf/lattice/gf.cpp | 2 +- 4 files changed, 4 insertions(+), 4 deletions(-) rename c++/triqs_tprf/lattice/{fourier_gf.hpp => fourier.hpp} (98%) diff --git a/c++/triqs_tprf/lattice.hpp b/c++/triqs_tprf/lattice.hpp index 10df57353..215443db2 100644 --- a/c++/triqs_tprf/lattice.hpp +++ b/c++/triqs_tprf/lattice.hpp @@ -28,7 +28,6 @@ #include "./lattice/gw.hpp" #include "./lattice/eliashberg.hpp" #include "./lattice/fourier_interpolation.hpp" -#include "./lattice/fourier_gf.hpp" #include "./lattice/chi_imtime.hpp" #include "./lattice/chi_imfreq.hpp" diff --git a/c++/triqs_tprf/lattice/chi_imtime.cpp b/c++/triqs_tprf/lattice/chi_imtime.cpp index 07f4959d3..60f66e634 100644 --- a/c++/triqs_tprf/lattice/chi_imtime.cpp +++ b/c++/triqs_tprf/lattice/chi_imtime.cpp @@ -24,7 +24,7 @@ #include "chi_imtime.hpp" #include "../fourier/fourier.hpp" -#include "fourier_gf.hpp" +#include "fourier.hpp" namespace triqs_tprf { diff --git a/c++/triqs_tprf/lattice/fourier_gf.hpp b/c++/triqs_tprf/lattice/fourier.hpp similarity index 98% rename from c++/triqs_tprf/lattice/fourier_gf.hpp rename to c++/triqs_tprf/lattice/fourier.hpp index 28ee6935d..f48fcb057 100644 --- a/c++/triqs_tprf/lattice/fourier_gf.hpp +++ b/c++/triqs_tprf/lattice/fourier.hpp @@ -2,7 +2,8 @@ * * TRIQS: a Toolbox for Research in Interacting Quantum Systems * - * Copyright (C) 2017, H. U.R. Strand + * Copyright (C) 2019, The Simons Foundation and S. Käser + * Authors: S. Käser * * TRIQS is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software diff --git a/c++/triqs_tprf/lattice/gf.cpp b/c++/triqs_tprf/lattice/gf.cpp index 1c9683156..985a3b16f 100644 --- a/c++/triqs_tprf/lattice/gf.cpp +++ b/c++/triqs_tprf/lattice/gf.cpp @@ -26,7 +26,7 @@ using triqs::arrays::inverse; #include #include "../mpi.hpp" -#include "fourier_gf.hpp" +#include "fourier.hpp" namespace triqs_tprf { From 566cf70aeaea1f0a5d4f28dd7619b1e12b23c7af Mon Sep 17 00:00:00 2001 From: Stefan Date: Thu, 25 Jul 2019 11:28:53 -0400 Subject: [PATCH 044/121] [chi] make spin tests in spin and charge split optional --- python/triqs_tprf/rpa_tensor.py | 47 +++++++++++++++++++-------------- 1 file changed, 27 insertions(+), 20 deletions(-) diff --git a/python/triqs_tprf/rpa_tensor.py b/python/triqs_tprf/rpa_tensor.py index a0933dccd..5b2a4fe5f 100644 --- a/python/triqs_tprf/rpa_tensor.py +++ b/python/triqs_tprf/rpa_tensor.py @@ -295,16 +295,24 @@ def general_susceptibility_from_charge_and_spin(chi_c, chi_s, spin_fast=True): return chi_general # ---------------------------------------------------------------------- -def charge_and_spin_susceptibility_from_general(chi, spin_fast=True): - """Construct a chi spin and charge from a general susceptibility +def charge_and_spin_susceptibility_from_general(chi, spin_fast=True, check_spin_conservation=True): + r"""Construct a chi spin and charge from a generalized susceptibility - Parameters: + Should only be used for a :math:`SU(2)` susceptibility. - chi: Greens function, the general susceptibility - spin_fast: bool, True if spin is the fast index, e.g. - xz up, xz down, xy up, xy down, yz up, yz down, - or False if spin is the slow index, e.g. - xz up, xy up, yz up, xz down, xy down, yz down. + Parameters + ---------- + chi : Gf, + Generalized susceptibility :math:`\chi_{a,b,c,d}` where :math:`a,b,c,d` are + combined indices of spin and orbital. + spin_fast : bool, optional + True if spin is the fast index, e.g. + xz up, xz down, xy up, xy down, yz up, yz down. + False if spin is the slow index, e.g. + xz up, xy up, yz up, xz down, xy down, yz down. + check_spin_conservation : bool, optional + True if the susceptibility should be checked for spin + conservation, False otherwise. """ norb = chi.target_shape[-1] / 2 @@ -321,20 +329,19 @@ def charge_and_spin_susceptibility_from_general(chi, spin_fast=True): up = slice(norb) down = slice(norb, None) - # -- Check spin-conservation - - np.testing.assert_allclose(chi[(up, up, up, down)].data, 0) - np.testing.assert_allclose(chi[(up, up, down, up)].data, 0) - np.testing.assert_allclose(chi[(up, down, up, up)].data, 0) - np.testing.assert_allclose(chi[(down, up, up, up)].data, 0) + if check_spin_conservation: + np.testing.assert_allclose(chi[(up, up, up, down)].data, 0) + np.testing.assert_allclose(chi[(up, up, down, up)].data, 0) + np.testing.assert_allclose(chi[(up, down, up, up)].data, 0) + np.testing.assert_allclose(chi[(down, up, up, up)].data, 0) - np.testing.assert_allclose(chi[(down, down, down, up)].data, 0) - np.testing.assert_allclose(chi[(down, down, up, down)].data, 0) - np.testing.assert_allclose(chi[(down, up, down, down)].data, 0) - np.testing.assert_allclose(chi[(up, down, down, down)].data, 0) + np.testing.assert_allclose(chi[(down, down, down, up)].data, 0) + np.testing.assert_allclose(chi[(down, down, up, down)].data, 0) + np.testing.assert_allclose(chi[(down, up, down, down)].data, 0) + np.testing.assert_allclose(chi[(up, down, down, down)].data, 0) - np.testing.assert_allclose(chi[(up, down, up, down)].data, 0) - np.testing.assert_allclose(chi[(down, up, down, up)].data, 0) + np.testing.assert_allclose(chi[(up, down, up, down)].data, 0) + np.testing.assert_allclose(chi[(down, up, down, up)].data, 0) chi_uu = chi[(up, up, up, up)] chi_ud = chi[(up, up, down, down)] From 4ee4fa9e729d14cc74c09970cefb95f5e6fdf423 Mon Sep 17 00:00:00 2001 From: Stefan Date: Thu, 25 Jul 2019 15:52:24 -0400 Subject: [PATCH 045/121] [fourier] change template for generic Gf type The parallelized template fourier function can now not only be used by `const_view` types, but by any Gf type. Also these fourier functions are now used to prepare Gamma in `eliashberg.cpp` and the numerical tolerance was eased in a test. --- c++/triqs_tprf/lattice/eliashberg.cpp | 5 +++- c++/triqs_tprf/lattice/fourier.hpp | 25 ++++++++++--------- .../eliashberg/product_summation_vs_fft.py | 2 +- 3 files changed, 18 insertions(+), 14 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index 50bc57fc1..a0b2ce045 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -26,6 +26,7 @@ #include #include "gf.hpp" +#include "fourier.hpp" namespace triqs_tprf { @@ -142,7 +143,9 @@ std::tuple split_into_dynamic_wk_and_constant_k(chi_wk_vt G std::tuple dynamic_and_constant_to_tr(chi_wk_vt Gamma_pp_dyn_wk, chi_k_vt Gamma_pp_const_k) { - auto Gamma_pp_dyn_tr = make_gf_from_fourier<0, 1>(Gamma_pp_dyn_wk); + auto Gamma_pp_dyn_wr = fourier_wk_to_wr_general_target(Gamma_pp_dyn_wk); + auto Gamma_pp_dyn_tr = fourier_wr_to_tr_general_target(Gamma_pp_dyn_wr); + auto Gamma_pp_const_r = make_gf_from_fourier<0>(Gamma_pp_const_k); return {Gamma_pp_dyn_tr, Gamma_pp_const_r}; diff --git a/c++/triqs_tprf/lattice/fourier.hpp b/c++/triqs_tprf/lattice/fourier.hpp index f48fcb057..fbecefaba 100644 --- a/c++/triqs_tprf/lattice/fourier.hpp +++ b/c++/triqs_tprf/lattice/fourier.hpp @@ -33,14 +33,14 @@ namespace triqs_tprf { using namespace fourier; } -template -auto fourier_wr_to_tr_general_target(gf_const_view, Target> g_wr, int n_tau = -1) { +template +auto fourier_wr_to_tr_general_target(Gf_type g_wr, int n_tau = -1) { auto _ = all_t{}; auto [wmesh, rmesh] = g_wr.mesh(); auto tmesh = make_adjoint_mesh(wmesh, n_tau); - auto g_tr = gf, Target>{{tmesh, rmesh}, g_wr.target_shape()}; + auto g_tr = make_gf>({tmesh, rmesh}, g_wr.target()); auto r0 = *rmesh.begin(); auto p = _fourier_plan<0>(gf_const_view(g_wr[_, r0]), gf_view(g_tr[_, r0])); @@ -64,14 +64,14 @@ auto fourier_wr_to_tr_general_target(gf_const_view -auto fourier_tr_to_wr_general_target(gf_const_view, Target> g_tr, int n_w = -1) { +template +auto fourier_tr_to_wr_general_target(Gf_type g_tr, int n_w = -1) { auto _ = all_t{}; auto [tmesh, rmesh] = g_tr.mesh(); auto wmesh = make_adjoint_mesh(tmesh, n_w); - auto g_wr = gf, Target>{{wmesh, rmesh}, g_tr.target_shape()}; + auto g_wr = make_gf>({wmesh, rmesh}, g_tr.target()); auto r0 = *rmesh.begin(); auto p = _fourier_plan<0>(gf_const_view(g_tr[_, r0]), gf_view(g_wr[_, r0])); @@ -95,15 +95,16 @@ auto fourier_tr_to_wr_general_target(gf_const_view -auto fourier_wk_to_wr_general_target(gf_const_view, Target> g_wk) { +template +auto fourier_wk_to_wr_general_target(Gf_type g_wk) { auto _ = all_t{}; auto [wmesh, kmesh] = g_wk.mesh(); auto rmesh = make_adjoint_mesh(kmesh); - auto g_wr = gf, Target>{{wmesh, rmesh}, g_wk.target_shape()}; + //auto g_wr = gf, Target>{{wmesh, rmesh}, g_wk.target_shape()}; + auto g_wr = make_gf>({wmesh, rmesh}, g_wk.target()); auto w0 = *wmesh.begin(); auto p = _fourier_plan<0>(gf_const_view(g_wk[w0, _]), gf_view(g_wr[w0, _])); @@ -127,15 +128,15 @@ auto fourier_wk_to_wr_general_target(gf_const_view -auto fourier_wr_to_wk_general_target(gf_const_view, Target> g_wr) { +template +auto fourier_wr_to_wk_general_target(Gf_type g_wr) { auto _ = all_t{}; auto [wmesh, rmesh] = g_wr.mesh(); auto kmesh = make_adjoint_mesh(rmesh); - auto g_wk = gf, Target>{{wmesh, kmesh}, g_wr.target_shape()}; + auto g_wk = make_gf>({wmesh, kmesh}, g_wr.target()); auto w0 = *wmesh.begin(); auto p = _fourier_plan<0>(gf_const_view(g_wr[w0, _]), gf_view(g_wk[w0, _])); diff --git a/test/python/eliashberg/product_summation_vs_fft.py b/test/python/eliashberg/product_summation_vs_fft.py index 84172b30a..0ff7891f7 100644 --- a/test/python/eliashberg/product_summation_vs_fft.py +++ b/test/python/eliashberg/product_summation_vs_fft.py @@ -197,7 +197,7 @@ def compare_next_delta(p): nr_factor = 0.5, fit_const = False, big_factor = 2, - atol = 1e-9, + atol = 1e-8, plot = False, ) From 6d7c0567dd2356e485357a4ba8e1a66a47657071 Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 26 Jul 2019 14:33:56 -0400 Subject: [PATCH 046/121] [eli] clean up code Functionality of `eliashberg_product_fft` was pulled out and put into a seperate function. The function mpi_view is now used again to create arrays for multi threaded enviroments. --- c++/triqs_tprf/lattice/eliashberg.cpp | 116 ++++++++++++-------------- c++/triqs_tprf/lattice/eliashberg.hpp | 2 +- c++/triqs_tprf/types.hpp | 4 + 3 files changed, 59 insertions(+), 63 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index a0b2ce045..38e433fc3 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -33,8 +33,6 @@ namespace triqs_tprf { // Helper function computing F = GG \Delta g_wk_t eliashberg_g_delta_g_product(g_wk_vt g_wk, g_wk_vt delta_wk) { - triqs::utility::timer t_all, t_parallel; - t_all.start(); auto [wmesh, kmesh] = delta_wk.mesh(); auto wmesh_gf = std::get<0>(g_wk.mesh()); @@ -47,21 +45,13 @@ g_wk_t eliashberg_g_delta_g_product(g_wk_vt g_wk, g_wk_vt delta_wk) { auto F_wk = make_gf(delta_wk); F_wk *= 0.; -/* The rest of this function contains a lot boiler plate code due to issue - #725 in the TRIQS library and not yet avaible functionality to use - 'pragma omp parallel loop for' over mesh objects. +/* The rest of this function contains a lot of boiler plate code due to issue + #725 in the TRIQS library. It will be changed later */ - array::mesh_point_t, 1> k_arr(kmesh.size()); - auto k_iter = kmesh.begin(); - for (auto idx : range(0, kmesh.size())) { - auto k = *k_iter; - k_arr(idx) = k; - k_iter++; - } - + auto k_arr = mpi_view(kmesh); auto _ = all_t{}; - t_parallel.start(); + #pragma omp parallel for for(unsigned int idx_k = 0; idx_k < kmesh.size(); idx_k++){ auto k = k_arr(idx_k); @@ -83,11 +73,6 @@ g_wk_t eliashberg_g_delta_g_product(g_wk_vt g_wk, g_wk_vt delta_wk) { } F_wk[_, k] = F_w; } - t_parallel.stop(); - t_all.stop(); - std::cout << "all:\t" << double(t_all) << "\n" \ - << "parallel:\t" << double(t_parallel) << "\n" \ - << "sequential:\t" << double(t_all - t_parallel) << "\n"; return F_wk; } @@ -151,7 +136,7 @@ std::tuple dynamic_and_constant_to_tr(chi_wk_vt Gamma_pp_dy return {Gamma_pp_dyn_tr, Gamma_pp_const_r}; } -e_k_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, g_tr_t F_tr) { +e_r_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, g_tr_t F_tr) { auto _ = all_t{}; @@ -164,29 +149,13 @@ e_k_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, g_tr_t F_tr delta_r_out[r](a, b) += -Gamma_pp_const_r[r](A, a, B, b) * F_t(0)(A, B); } - auto delta_k_out = make_gf_from_fourier<0>(delta_r_out); - - return delta_k_out; + return delta_r_out; } -g_wk_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const_r, - g_wk_vt g_wk, g_wk_vt delta_wk) { - - triqs::utility::timer t_g_delta_g_product, t_fft_F, t_dynamic_product, t_fft_delta, t_constant_product, t_combine; - - t_g_delta_g_product.start(); - auto F_wk = eliashberg_g_delta_g_product(g_wk, delta_wk); - t_g_delta_g_product.stop(); - - t_fft_F.start(); - //auto F_tr = make_gf_from_fourier<0, 1>(F_wk); - auto F_wr = fourier_wk_to_wr(F_wk); - auto F_tr = fourier_wr_to_tr(F_wr); - t_fft_F.stop(); +g_tr_t eliashberg_dynamic_gamma_f_product(chi_tr_vt Gamma_pp_dyn_tr, g_tr_vt F_tr) { auto [tmesh, rmesh] = F_tr.mesh(); - // Dynamic part auto delta_tr_out = make_gf(F_tr); delta_tr_out *= 0.; @@ -199,20 +168,12 @@ g_wk_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const " (" << tmesh_gamma.size() << ") must be the size of the mesh of Delta (" << tmesh.size() << ")."; - t_dynamic_product.start(); /* This function contains a lot boiler plate code due to issue - #725 in the TRIQS library and not yet avaible functionality to use - 'pragma omp parallel loop for' over mesh objects. + #725 in the TRIQS library. It will be changed later */ - array::mesh_point_t, 1> r_arr(rmesh.size()); - auto r_iter = rmesh.begin(); - for (auto idx : range(0, rmesh.size())) { - auto r = *r_iter; - r_arr(idx) = r; - r_iter++; - } + auto r_arr = mpi_view(rmesh); auto _ = all_t{}; #pragma omp parallel for for(unsigned int idx_r = 0; idx_r < rmesh.size(); idx_r++){ @@ -229,28 +190,56 @@ g_wk_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const } delta_tr_out[_, r] = delta_t; } + + return delta_tr_out; +} + +g_wk_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const_r, + g_wk_vt g_wk, g_wk_vt delta_wk) { + + triqs::utility::timer t_all, t_g_delta_g_product, t_fft_F, t_dynamic_product, t_fft_delta, t_constant_product, t_combine; + t_all.start(); + + t_g_delta_g_product.start(); + auto F_wk = eliashberg_g_delta_g_product(g_wk, delta_wk); + t_g_delta_g_product.stop(); + + t_fft_F.start(); + auto F_wr = fourier_wk_to_wr(F_wk); + auto F_tr = fourier_wr_to_tr(F_wr); + t_fft_F.stop(); + + // Dynamic part + t_dynamic_product.start(); + auto delta_tr_out = eliashberg_dynamic_gamma_f_product(Gamma_pp_dyn_tr, F_tr); t_dynamic_product.stop(); + + // Constant part + t_constant_product.start(); + auto delta_r_out = eliashberg_constant_gamma_f_product(Gamma_pp_const_r, F_tr); + t_constant_product.stop(); // FIXME // This raises warnings when used with random delta input, e.g. eigenvalue finder t_fft_delta.start(); - //auto delta_wk_out = make_gf_from_fourier<0, 1>(delta_tr_out); auto delta_wr_out = fourier_tr_to_wr(delta_tr_out); - auto delta_wk_out = fourier_wr_to_wk(delta_wr_out); t_fft_delta.stop(); - // Constant part - t_constant_product.start(); - auto delta_k_out = eliashberg_constant_gamma_f_product(Gamma_pp_const_r, F_tr); - t_constant_product.stop(); - // Combine dynamic and constant part t_combine.start(); - for (const auto [w , k]: delta_wk_out.mesh()) - delta_wk_out[w, k] += delta_k_out[k]; + auto _ = all_t{}; + for (const auto w : std::get<0>(delta_wr_out.mesh())) + delta_wr_out[w, _] += delta_r_out; t_combine.stop(); - std::cout << "g_delta_g_product:\t" << double(t_g_delta_g_product) << "\n" \ + t_fft_delta.start(); + t_fft_delta.stop(); + auto delta_wk_out = fourier_wr_to_wk(delta_wr_out); + + t_all.stop(); + + std::cout << "all:\t" << double(t_all) << "\n" \ + << "g_delta_g_product:\t" << double(t_g_delta_g_product) << "\n" \ << "fft_F:\t" << double(t_fft_F) << "\n" \ << "dynamic_product:\t" << double(t_dynamic_product) << "\n" \ << "fft_delta:\t" << double(t_fft_delta) << "\n" \ @@ -265,15 +254,18 @@ g_wk_t eliashberg_product_fft_constant(chi_r_vt Gamma_pp_const_r, g_wk_vt g_wk, g_wk_vt delta_wk) { auto F_wk = eliashberg_g_delta_g_product(g_wk, delta_wk); - auto F_tr = make_gf_from_fourier<0, 1>(F_wk); + auto F_wr = fourier_wk_to_wr(F_wk); + auto F_tr = fourier_wr_to_tr(F_wr); - auto delta_k_out = eliashberg_constant_gamma_f_product(Gamma_pp_const_r, F_tr); + auto delta_r_out = eliashberg_constant_gamma_f_product(Gamma_pp_const_r, F_tr); + auto delta_k_out = make_gf_from_fourier<0>(delta_r_out); auto delta_wk_out = make_gf(F_wk); delta_wk_out *= 0.; - for (const auto [w , k]: delta_wk_out.mesh()) - delta_wk_out[w, k] += delta_k_out[k]; + auto _ = all_t{}; + for (const auto w : std::get<0>(delta_wk_out.mesh())) + delta_wk_out[w, _] += delta_k_out; return delta_wk_out; } diff --git a/c++/triqs_tprf/lattice/eliashberg.hpp b/c++/triqs_tprf/lattice/eliashberg.hpp index 0bc273b1e..10a3867fe 100644 --- a/c++/triqs_tprf/lattice/eliashberg.hpp +++ b/c++/triqs_tprf/lattice/eliashberg.hpp @@ -95,7 +95,7 @@ namespace triqs_tprf { g_wk_t eliashberg_g_delta_g_product(g_wk_vt g_wk, g_wk_vt delta_wk); std::tuple split_into_dynamic_wk_and_constant_k(chi_wk_vt Gamma_pp); std::tuple dynamic_and_constant_to_tr(chi_wk_vt Gamma_pp_dyn_wk, chi_k_vt Gamma_pp_const_k); - e_k_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, g_tr_t F_tr); + e_r_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, g_tr_t F_tr); /** Gamma particle-particle singlet diff --git a/c++/triqs_tprf/types.hpp b/c++/triqs_tprf/types.hpp index 6742a0b38..3375e8213 100644 --- a/c++/triqs_tprf/types.hpp +++ b/c++/triqs_tprf/types.hpp @@ -103,6 +103,10 @@ typedef gf e_k_t; typedef e_k_t::const_view_type e_k_cvt; typedef e_k_t::view_type e_k_vt; +typedef gf e_r_t; +typedef e_r_t::const_view_type e_r_cvt; +typedef e_r_t::view_type e_r_vt; + typedef gf g_w_t; typedef g_w_t::const_view_type g_w_cvt; typedef g_w_t::view_type g_w_vt; From 770a5c9611b61a2df9e5bb4ad1d59ca51ce0b296 Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 2 Sep 2019 14:10:23 +0200 Subject: [PATCH 047/121] [sym] add restricted symmetrizing operations One can now use the functions `enforce_symmetry` and `check_symmetry` one- particle fermionic Green's function with a MeshProduct with a MeshImFreq on first and a MeshBrillouinZone on second position to symmetrize or check the momentum, frequency or orbital space. --- python/triqs_tprf/symmetries.py | 396 ++++++++++++++++++++++++++++++++ test/python/CMakeLists.txt | 1 + test/python/symmetrize_gf.py | 119 ++++++++++ 3 files changed, 516 insertions(+) create mode 100644 python/triqs_tprf/symmetries.py create mode 100644 test/python/symmetrize_gf.py diff --git a/python/triqs_tprf/symmetries.py b/python/triqs_tprf/symmetries.py new file mode 100644 index 000000000..acb141610 --- /dev/null +++ b/python/triqs_tprf/symmetries.py @@ -0,0 +1,396 @@ +import numpy as np + +def enforce_symmetry(gf, variables, symmetries): + """Symmetrize Green's function in the given variables + + Parameters + ---------- + gf : Gf, + One-particle fermionic Green's function with a MeshProduct containing + a MeshImFreq on first and a MeshBrillouinZone in second position. + variables : str or list of str, + Tells what variable(s) shall be symmetrized, e.g. "momentum" + or ["frequency", "momentum"] + symmetries : str or list of str, + Gives the symmetry for the respective variable, e.g. "even" + or ["odd", "even"] + + Returns + ------- + gf : Gf + """ + if type(variables) != list: + variables = [variables] + if type(symmetries) != list: + symmetries = [symmetries] + if len(variables) != len(symmetries): + raise ValueError("Variables and symmetries must be of equal length.") + + variable_symmetrize_fct = {"frequency" : _symmetrize_frequency, + "momentum" : _symmetrize_momentum, + "orbital" : _symmetrize_orbital,} + + for variable in variables: + if variable not in variable_symmetrize_fct.keys(): + raise ValueError("No symmetrize function for this variable exists.") + + for symmetry in symmetries: + if symmetry not in ['even', 'odd']: + raise ValueError("Symmetry can only be 'even' or 'odd'.") + + gf_symmetrized = gf.copy() + + for variable, symmetry in zip(variables, symmetries): + symmetrize_fct = variable_symmetrize_fct[variable] + symmetrize_fct(gf_symmetrized, symmetry) + + return gf_symmetrized + +def check_symmetry(gf, atol=1e-08): + """Check the symmetry of a Green's function for various variables + + Parameters + ---------- + gf : Gf, + One-particle fermionic Green's function with a MeshProduct containing + a MeshImFreq on first and a MeshBrillouinZone in second position. + atol : float, + Absolute tolerance used as parameter `atol` in `np.allclose`. + + Returns + ------- + variable_symmetry : dict, + Keys give the variable and values the symmetry. + If even, +1, if odd, -1, else None. + """ + variable_check_symmetry = {"frequency" : _check_frequency_symmetry, + "momentum" : _check_momentum_symmetry, + "orbital" : _check_orbital_symmetry,} + + variable_symmetry = {} + for variable, check_symmetry_fct in variable_check_symmetry.items(): + variable_symmetry[variable] = check_symmetry_fct(gf, atol) + + return variable_symmetry + +def _average_halfs(half_1, half_2): + """Stub that can be used as an averager + """ + return half_2 + +def _overall_sign(signs): + """Return +/- 1 if all elements of signs are +/- 1, None else + + Parameters + ---------- + signs : list of +/- 1 + """ + signs = set(signs) + if len(signs) == 1: + return signs.pop() + return None + +# -- Frequency +# ============================================================================ +def _split_frequency(gf): + """Split Green's function data in positive and negative frequencies + + Parameters + --------- + gf : Gf, + Fermionic Green's function with a MeshProduct containing + a MeshImFreq on first position. + + Returns + ------- + negative_half : np.array, + positive_half : np.array, + """ + if not gf.mesh[0].statistic == 'Fermion': + raise ValueError("The Green's function must be a fermionic one") + + nw_half = gf.data.shape[0]/2 + + negative_half = gf.data[:nw_half] + positive_half = gf.data[nw_half:] + + return negative_half, positive_half + +def _check_frequency_symmetry(gf, atol=1e-08): + """Check if frequency symmetry of Green's function is even or odd + + Parameters + ---------- + gf : Gf, + Fermionic Green's function with a MeshProduct containing + a MeshImFreq on first position. + atol : float, + Absolute tolerance used as parameter `atol` in `np.allclose`. + + Returns + ------- + +1 if the Green's function is even in frequency space, -1 if odd, + and None if undefined. + """ + negative_half, positive_half = _split_frequency(gf) + + if np.allclose(negative_half, positive_half, atol=atol): + return +1 + elif np.allclose(negative_half, -1*positive_half, atol=atol): + return -1 + return None + +def _symmetrize_frequency(gf, symmetry='even'): + r"""Symmetrize the data of a Green's function in frequency space + + Parameters + --------- + gf : Gf, + Fermionic Green's function with a MeshProduct containing + a MeshImFreq on first position. + symmetry : str, ['even', 'odd'], optional + What frequency symmetry shall be enforced: + + 'even' : no sign change :math:`\nu_n\rightarrow\nu_{-n}` + 'odd' : sign change :math:`\nu_n\rightarrow\nu_{-n}` + """ + negative_half, positive_half = _split_frequency(gf) + avg = _average_halfs(negative_half, positive_half) + + # Use slice access so that the data in the Green's function get changed + positive_half[:] = avg + if symmetry == "even": + negative_half[:] = avg + else: + negative_half[:] = -1* avg + +# -- Momentum +# ============================================================================ +def _invert_momentum(momentum, momentum_mesh): + """Returns the indices corresponding to the inverted momentum + + Parameters + ---------- + momentum : array_like, + The indices that correspond to a momentum, e.g. (0, 3). + momentum_mesh : array_like, + The number of points used in the corresponding dimension, + e.g. [4, 4]. + + Returns + ------- + inv_k : tuple, + The indices that correspond to the inverted momentum, + e.g. (0, 1). + """ + momentum = np.array(momentum) + momentum_mesh = np.array(momentum_mesh) + inv_k = momentum_mesh - momentum + inv_k = inv_k % momentum_mesh + inv_k = tuple(inv_k) + return inv_k + +def _split_momentum(gf): + """Split Green's function data in momentum and inversed momentum + + Parameters + ---------- + gf : Gf, + Green's function with a MeshProduct containing and a + MeshBrillouinZone in second position. + + Yields + ------ + positive_half : np.array + negative_half : np.array + """ + nk = gf.data.shape[1] + momentum_mesh = gf.mesh[1].linear_dims + # Drop dimensions which are not meshed over, i.e. value of 1 + momentum_mesh = [mesh for mesh in momentum_mesh if mesh != 1] + + for idx in range(nk): + unraveled_idx = np.unravel_index(idx, momentum_mesh) + unraveled_inv_idx = _invert_momentum(unraveled_idx, momentum_mesh) + inv_idx = np.ravel_multi_index(unraveled_inv_idx, momentum_mesh) + + positive_half = gf.data[slice(None), idx] + negative_half = gf.data[slice(None), inv_idx] + + if idx == inv_idx: + # Give same id to both halfs for identification of k = -k + yield positive_half, positive_half + else: + yield positive_half, negative_half + +def _check_momentum_symmetry(gf, atol=1e-08): + """Check if momentum symmetry of Green's function is even or odd + + Parameters + ---------- + gf : Gf, + Green's function with a MeshProduct containing and a + MeshBrillouinZone in second position. + atol : float, + Absolute tolerance used as parameter `atol` in `np.allclose`. + + Returns + ------- + +1 if the Green's function is even in momentum space, -1 if odd, + and None if undefined. + """ + signs= [] + for positive_half, negative_half in _split_momentum(gf): + # Check if k = -k, if not equal to 0.0 the gf must be even + if id(positive_half) == id(negative_half): + if not np.allclose(0.0, positive_half): + signs.append(+1) + continue + + if np.allclose(positive_half, negative_half, atol=atol): + signs.append(+1) + elif np.allclose(-1*positive_half, negative_half, atol=atol): + signs.append(-1) + else: + return None + + return _overall_sign(signs) + +def _symmetrize_momentum(gf, symmetry='even'): + r"""Symmetrize the data of a Green's function in momentum space + + Parameters + ---------- + gf : Gf, + Green's function with a MeshProduct containing and a + MeshBrillouinZone in second position. + symmetry : str, ['even', 'odd'], optional + What momentum symmetry shall be enforced: + + 'even' : no sign change :math:`\mathbf{k}\rightarrow\mathbf{k}` + 'odd' : sign change :math:`\mathbf{k}\rightarrow\mathbf{k}` + """ + for positive_half, negative_half in _split_momentum(gf): + # Check if k = -k, i.e. needs different symmetry treatment + if id(positive_half) == id(negative_half): + if symmetry == "odd": + positive_half *= 0.0 + continue + + avg = _average_halfs(positive_half, negative_half) + + # Use slice access so that the data in the Green's function get changed + positive_half[:] = avg + if symmetry == "even": + negative_half[:] = avg + else: + negative_half[:] = -1 * avg + +# -- Orbitals +# ============================================================================ +def _split_orbital_triangle(gf): + """Split Green's function data in upper and lower triangle without diagonal + + Parameters + ---------- + gf : Gf, + One-particle Green's function with a MeshProduct with two meshes. + + Yields + ------ + upper_triangle : np.array + lower_triangle : np.array + """ + target_shape = gf.target_shape + nparticle = len(target_shape) + if nparticle != 2: + raise ValueError("The Green's function must be a one-particle one.") + + norb = target_shape[0] + mesh_slice = (slice(None),) * gf.mesh.rank + + upper_triangle_slice = np.triu_indices(norb, k=1) + lower_triangle_slice = np.tril_indices(norb, k=-1) + combined_slice = upper_triangle_slice + lower_triangle_slice + + for upper_1, upper_2, lower_1, lower_2 in zip(*combined_slice): + upper_triangle = gf.data[mesh_slice + (upper_1, upper_2)] + lower_triangle = gf.data[mesh_slice + (lower_1, lower_2)] + + yield upper_triangle, lower_triangle + +def _split_orbital_diagonal(gf): + """Extract the diagonal part of the Green's function data + + Parameters + ---------- + gf : Gf, + One-particle Green's function with a MeshProduct with two meshes. + + Yields + ------ + diagonal : np.array + """ + target_shape = gf.target_shape + nparticle = len(target_shape) + if nparticle != 2: + raise ValueError("The Green's function must be a one-particle one.") + + norb = target_shape[0] + mesh_slice = (slice(None),) * gf.mesh.rank + + for orb in range(norb): + yield gf.data[mesh_slice + (orb,)*nparticle] + +def _check_orbital_symmetry(gf, atol=1e-08): + """Check if orbital symmetry of Green's function is even or odd + + Parameters + ---------- + gf : Gf, + One-particle Green's function with a MeshProduct with two meshes. + atol : float, + Absolute tolerance used as parameter `atol` in `np.allclose`. + + Returns + ------- + +1 if the Green's function is even in orbital space, -1 if odd, + and None if undefined. + """ + signs = [] + for upper_triangle, lower_triangle in _split_orbital_triangle(gf): + if np.allclose(upper_triangle, lower_triangle, atol=atol): + signs.append(+1) + elif np.allclose(upper_triangle, -1*lower_triangle, atol=atol): + signs.append(-1) + else: + return None + + for diagonal in _split_orbital_diagonal(gf): + if not np.allclose(diagonal, 0.0, atol=atol): + signs.append(+1) + + return _overall_sign(signs) + +def _symmetrize_orbital(gf, symmetry="even"): + r"""Symmetrize the data of a Green's function in orbital space + + Parameters + --------- + gf : Gf, + One-particle Green's function with a MeshProduct with two meshes. + """ + for upper_triangle, lower_triangle in _split_orbital_triangle(gf): + avg = _average_halfs(upper_triangle, lower_triangle) + + # Use slice access so that the data in the Green's function get changed + upper_triangle[:] = avg + if symmetry == "even": + lower_triangle[:] = avg + else: + lower_triangle[:] = -1 * avg + + if symmetry == "odd": + for diagonal in _split_orbital_diagonal(gf): + diagonal *= 0.0 + diff --git a/test/python/CMakeLists.txt b/test/python/CMakeLists.txt index 45101375e..b574f0cb0 100644 --- a/test/python/CMakeLists.txt +++ b/test/python/CMakeLists.txt @@ -16,5 +16,6 @@ add_python_test(1d_hubbard_hf_spin_rot_inv) add_python_test(1d_hubbard_hf_rpa_2site_AFM) add_python_test(compare_general_rpa_to_matrix_rpa) add_python_test(interaction_tensor_charge_spin_factorization) +add_python_test(symmetrize_gf) add_subdirectory(eliashberg) diff --git a/test/python/symmetrize_gf.py b/test/python/symmetrize_gf.py new file mode 100644 index 000000000..55893a340 --- /dev/null +++ b/test/python/symmetrize_gf.py @@ -0,0 +1,119 @@ +# ---------------------------------------------------------------------- + +""" Symmetrize a randomly filled Green's function in frequency, momentum, + and orbital and test if it was done proberly. +""" +# ---------------------------------------------------------------------- + +import itertools + +# ---------------------------------------------------------------------- + +import numpy as np + +# ---------------------------------------------------------------------- + +from pytriqs.gf import Gf, MeshImFreq, MeshBrillouinZone, MeshProduct +from pytriqs.lattice import BrillouinZone, BravaisLattice +from triqs_tprf.ParameterCollection import * + +# ---------------------------------------------------------------------- + +from triqs_tprf.symmetries import enforce_symmetry, check_symmetry, _invert_momentum + +# ---------------------------------------------------------------------- + +p = ParameterCollection(beta = 10, + nw = 10, + nk = 4, + norb = 2,) + +wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nw) + +cell = np.eye(3) +bl = BravaisLattice(cell) +bz = BrillouinZone(bl) +kmesh = MeshBrillouinZone(bz, p.nk * np.eye(3, dtype=np.int32)) + +gf = Gf(mesh=MeshProduct(wmesh, kmesh), target_shape=2*(p.norb,)) +gf.data[:] = np.random.rand(*gf.data.shape) + +# -- Eexception handling +try: + enforce_symmetry(gf, "something", "odd") +except ValueError as error: + if not str(error) == "No symmetrize function for this variable exists.": + raise Exception("Wrong exception was raised: \n %s"%error) +else: + raise Exception("Function call should have failed.") + +try: + enforce_symmetry(gf, "frequency", "weird") +except ValueError as error: + if not str(error) == "Symmetry can only be 'even' or 'odd'.": + raise Exception("Wrong exception was raised: \n %s"%error) +else: + raise Exception("Function call should have failed.") + +# -- Frequency +even_freq_gf = enforce_symmetry(gf, "frequency", "even") +np.testing.assert_equal(+1, check_symmetry(even_freq_gf)['frequency']) + +odd_freq_gf = enforce_symmetry(gf, "frequency", "odd") +np.testing.assert_equal(-1, check_symmetry(odd_freq_gf)['frequency']) + +# -- Momentum +momentum_mesh = [16, 32, 5] +momenta = [ [0, 0, 0], + [1, 4, 0], + [8, 16, 3], + ] +inv_momenta = [ [0, 0, 0], + [15, 28, 0], + [8, 16, 2], + ] +for momentum, inv_momentum in zip(momenta, inv_momenta): + inv_momentum_test = _invert_momentum(momentum, momentum_mesh) + if not np.equal(inv_momentum, inv_momentum_test).all: + raise Exception("The function '_invert_momentum' does not behave as" + " expected.") + +even_momentum_gf = enforce_symmetry(gf, "momentum", "even") +np.testing.assert_equal(+1, check_symmetry(even_momentum_gf)["momentum"]) + +odd_momentum_gf = enforce_symmetry(gf, "momentum", "odd") +np.testing.assert_equal(-1, check_symmetry(odd_momentum_gf)["momentum"]) + +# -- Orbital + +even_orbital_gf = enforce_symmetry(gf, "orbital", "even") +np.testing.assert_equal(+1, check_symmetry(even_orbital_gf)["orbital"]) + +odd_orbital_gf = enforce_symmetry(gf, "orbital", "odd") +np.testing.assert_equal(-1, check_symmetry(odd_orbital_gf)["orbital"]) + +# -- Combination +variables = ["frequency", "momentum", "orbital"] +avail_symmetries = ["even", "odd", None] +for symmetries in itertools.product(avail_symmetries, repeat=len(variables)): + + # Remove the corresponding variable to None that it does not get symmetrized + variables_copy = list(variables) + symmetries_copy = list(symmetries) + while None in symmetries_copy: + idx = symmetries_copy.index(None) + del symmetries_copy[idx] + del variables_copy[idx] + + symmetrized_gf = enforce_symmetry(gf, variables_copy, symmetries_copy) + + translate_symmetries = {"even" : +1, "odd" : -1, None : None} + expected_symmetries = {variable : translate_symmetries[symmetry] \ + for (variable, symmetry) in zip(variables, symmetries)} + + produced_symmetries = check_symmetry(symmetrized_gf) + + if not expected_symmetries == produced_symmetries: + raise AssertionError("Incorrect symmetries were produced") + +print("It's all good honey") From e4e120ac6615bea93390a90e7856122b70ec6aca Mon Sep 17 00:00:00 2001 From: Stefan Date: Tue, 3 Sep 2019 15:53:19 +0200 Subject: [PATCH 048/121] fix remove structured binding declarations due #11 --- c++/triqs_tprf/lattice/eliashberg.cpp | 19 +++++++++++++++---- c++/triqs_tprf/lattice/fourier.hpp | 17 +++++++++++++---- 2 files changed, 28 insertions(+), 8 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index 38e433fc3..231718088 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -34,7 +34,11 @@ namespace triqs_tprf { g_wk_t eliashberg_g_delta_g_product(g_wk_vt g_wk, g_wk_vt delta_wk) { - auto [wmesh, kmesh] = delta_wk.mesh(); + // Get rid of structured binding declarations in this file due to issue #11 + //auto [wmesh, kmesh] = delta_wk.mesh(); + auto wmesh = std::get<0>(delta_wk.mesh()); + auto kmesh = std::get<1>(delta_wk.mesh()); + auto wmesh_gf = std::get<0>(g_wk.mesh()); if (wmesh.size() > wmesh_gf.size()) @@ -80,7 +84,10 @@ g_wk_t eliashberg_g_delta_g_product(g_wk_vt g_wk, g_wk_vt delta_wk) { g_wk_t eliashberg_product(chi_wk_vt Gamma_pp, g_wk_vt g_wk, g_wk_vt delta_wk) { - auto [wmesh, kmesh] = delta_wk.mesh(); + //auto [wmesh, kmesh] = delta_wk.mesh(); + auto wmesh = std::get<0>(delta_wk.mesh()); + auto kmesh = std::get<1>(delta_wk.mesh()); + auto gamma_wmesh = std::get<0>(Gamma_pp.mesh()); if (2*wmesh.size() > gamma_wmesh.size()) @@ -107,7 +114,9 @@ g_wk_t eliashberg_product(chi_wk_vt Gamma_pp, g_wk_vt g_wk, std::tuple split_into_dynamic_wk_and_constant_k(chi_wk_vt Gamma_pp) { auto _ = all_t{}; - auto [wmesh, kmesh] = Gamma_pp.mesh(); + //auto [wmesh, kmesh] = Gamma_pp.mesh(); + auto wmesh = std::get<0>(Gamma_pp.mesh()); + auto kmesh = std::get<1>(Gamma_pp.mesh()); // Fit infinite frequency value auto Gamma_pp_dyn_wk = make_gf(Gamma_pp); @@ -154,7 +163,9 @@ e_r_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, g_tr_t F_tr g_tr_t eliashberg_dynamic_gamma_f_product(chi_tr_vt Gamma_pp_dyn_tr, g_tr_vt F_tr) { - auto [tmesh, rmesh] = F_tr.mesh(); + //auto [tmesh, rmesh] = F_tr.mesh(); + auto tmesh = std::get<0>(F_tr.mesh()); + auto rmesh = std::get<1>(F_tr.mesh()); auto delta_tr_out = make_gf(F_tr); delta_tr_out *= 0.; diff --git a/c++/triqs_tprf/lattice/fourier.hpp b/c++/triqs_tprf/lattice/fourier.hpp index fbecefaba..6844c5d2e 100644 --- a/c++/triqs_tprf/lattice/fourier.hpp +++ b/c++/triqs_tprf/lattice/fourier.hpp @@ -37,7 +37,10 @@ template auto fourier_wr_to_tr_general_target(Gf_type g_wr, int n_tau = -1) { auto _ = all_t{}; - auto [wmesh, rmesh] = g_wr.mesh(); + // Get rid of structured binding declarations in this file due to issue #11 + //auto [wmesh, rmesh] = g_wr.mesh(); + auto wmesh = std::get<0>(g_wr.mesh()); + auto rmesh = std::get<1>(g_wr.mesh()); auto tmesh = make_adjoint_mesh(wmesh, n_tau); auto g_tr = make_gf>({tmesh, rmesh}, g_wr.target()); @@ -68,7 +71,9 @@ template auto fourier_tr_to_wr_general_target(Gf_type g_tr, int n_w = -1) { auto _ = all_t{}; - auto [tmesh, rmesh] = g_tr.mesh(); + //auto [tmesh, rmesh] = g_tr.mesh(); + auto tmesh = std::get<0>(g_tr.mesh()); + auto rmesh = std::get<1>(g_tr.mesh()); auto wmesh = make_adjoint_mesh(tmesh, n_w); auto g_wr = make_gf>({wmesh, rmesh}, g_tr.target()); @@ -100,7 +105,9 @@ auto fourier_wk_to_wr_general_target(Gf_type g_wk) { auto _ = all_t{}; - auto [wmesh, kmesh] = g_wk.mesh(); + //auto [wmesh, kmesh] = g_wk.mesh(); + auto wmesh = std::get<0>(g_wk.mesh()); + auto kmesh = std::get<1>(g_wk.mesh()); auto rmesh = make_adjoint_mesh(kmesh); //auto g_wr = gf, Target>{{wmesh, rmesh}, g_wk.target_shape()}; @@ -133,7 +140,9 @@ auto fourier_wr_to_wk_general_target(Gf_type g_wr) { auto _ = all_t{}; - auto [wmesh, rmesh] = g_wr.mesh(); + //auto [wmesh, rmesh] = g_wr.mesh(); + auto wmesh = std::get<0>(g_wr.mesh()); + auto rmesh = std::get<1>(g_wr.mesh()); auto kmesh = make_adjoint_mesh(rmesh); auto g_wk = make_gf>({wmesh, kmesh}, g_wr.target()); From 12b12647e00ed604c53fb574f6458302cbb41b0a Mon Sep 17 00:00:00 2001 From: Stefan Date: Tue, 3 Sep 2019 17:53:28 +0200 Subject: [PATCH 049/121] [sym] fix bug in frequency and momentum The negative/positive half of the frequency were not mirrored before, resulting in a incorrect enforcing and detecting of frequency symmetry. In the momentum symmetry check numerical zero elements could trigger a +1 for even symmetry, even through they don't matter in a symmetry check. This is now fixed. --- python/triqs_tprf/symmetries.py | 17 ++++++++++++----- 1 file changed, 12 insertions(+), 5 deletions(-) diff --git a/python/triqs_tprf/symmetries.py b/python/triqs_tprf/symmetries.py index acb141610..4feec0cbf 100644 --- a/python/triqs_tprf/symmetries.py +++ b/python/triqs_tprf/symmetries.py @@ -134,9 +134,9 @@ def _check_frequency_symmetry(gf, atol=1e-08): """ negative_half, positive_half = _split_frequency(gf) - if np.allclose(negative_half, positive_half, atol=atol): + if np.allclose(negative_half[::-1], positive_half, atol=atol): return +1 - elif np.allclose(negative_half, -1*positive_half, atol=atol): + elif np.allclose(negative_half[::-1], -1*positive_half, atol=atol): return -1 return None @@ -155,14 +155,14 @@ def _symmetrize_frequency(gf, symmetry='even'): 'odd' : sign change :math:`\nu_n\rightarrow\nu_{-n}` """ negative_half, positive_half = _split_frequency(gf) - avg = _average_halfs(negative_half, positive_half) + avg = _average_halfs(negative_half[::-1], positive_half) # Use slice access so that the data in the Green's function get changed positive_half[:] = avg if symmetry == "even": - negative_half[:] = avg + negative_half[:] = avg[::-1] else: - negative_half[:] = -1* avg + negative_half[:] = -1* avg[::-1] # -- Momentum # ============================================================================ @@ -241,6 +241,13 @@ def _check_momentum_symmetry(gf, atol=1e-08): """ signs= [] for positive_half, negative_half in _split_momentum(gf): + + # If the k-point and its inverse are numercial zero the symmetry does + # not matter + if np.allclose(positive_half, 0.0, atol=atol) and \ + np.allclose(negative_half, 0.0, atol=atol): + continue + # Check if k = -k, if not equal to 0.0 the gf must be even if id(positive_half) == id(negative_half): if not np.allclose(0.0, positive_half): From 16fb4e5db698c865f347f210102c6e06b87a1d78 Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 4 Sep 2019 13:31:08 +0200 Subject: [PATCH 050/121] [sym] allow for general iterator to be used as input --- python/triqs_tprf/symmetries.py | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/python/triqs_tprf/symmetries.py b/python/triqs_tprf/symmetries.py index 4feec0cbf..3a5843723 100644 --- a/python/triqs_tprf/symmetries.py +++ b/python/triqs_tprf/symmetries.py @@ -8,10 +8,10 @@ def enforce_symmetry(gf, variables, symmetries): gf : Gf, One-particle fermionic Green's function with a MeshProduct containing a MeshImFreq on first and a MeshBrillouinZone in second position. - variables : str or list of str, + variables : str or iterator of str, Tells what variable(s) shall be symmetrized, e.g. "momentum" or ["frequency", "momentum"] - symmetries : str or list of str, + symmetries : str or iterator of str, Gives the symmetry for the respective variable, e.g. "even" or ["odd", "even"] @@ -19,9 +19,9 @@ def enforce_symmetry(gf, variables, symmetries): ------- gf : Gf """ - if type(variables) != list: + if type(variables) == str: variables = [variables] - if type(symmetries) != list: + if type(symmetries) == str: symmetries = [symmetries] if len(variables) != len(symmetries): raise ValueError("Variables and symmetries must be of equal length.") From a658495d904c5a715f3707515b1d749a08508573 Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 4 Sep 2019 13:52:05 +0200 Subject: [PATCH 051/121] [sym] add symmetrizing option in eliashberg solver --- python/triqs_tprf/eliashberg.py | 13 ++- test/python/eliashberg/CMakeLists.txt | 1 + test/python/eliashberg/symmetrize_delta.py | 128 +++++++++++++++++++++ 3 files changed, 140 insertions(+), 2 deletions(-) create mode 100644 test/python/eliashberg/symmetrize_delta.py diff --git a/python/triqs_tprf/eliashberg.py b/python/triqs_tprf/eliashberg.py index 166b9946d..7a1e81252 100644 --- a/python/triqs_tprf/eliashberg.py +++ b/python/triqs_tprf/eliashberg.py @@ -122,8 +122,8 @@ def preprocess_gamma_for_fft(Gamma_pp_wk, Gamma_pp_const_k=None): return Gamma_pp_dyn_tr, Gamma_pp_const_r -def solve_eliashberg(Gamma_pp_wk, g_wk, initial_delta=None, Gamma_pp_const_k=None, tol=1e-10, - product='FFT', solver='PM'): +def solve_eliashberg(Gamma_pp_wk, g_wk, initial_delta=None, Gamma_pp_const_k=None, + tol=1e-10, product='FFT', solver='PM', symmetrize_fct=lambda x : x): r""" Solve the linearized Eliashberg equation @@ -165,6 +165,14 @@ def solve_eliashberg(Gamma_pp_wk, g_wk, initial_delta=None, Gamma_pp_const_k=Non 'PM' : Use the Power Method implemented in :func:`power_method_LR`. 'IRAM' : Use the Implicitly Restarted Arnoldi Method implemented in :func:`implicitly_restarted_arnoldi_method`. + symmetrize_fct : function, optional + A function that takes one parameter: A Green's function + :math:`G(i\nu_n, \mathbf{k})`. The mesh attribute of the + Gf must be a MeshProduct with the components + (MeshImFreq, MeshBrillouinZone). + This function is applied after every iteration of the + eigenvalue solver and can be used to enforce a specific + symmetry. Returns ------- @@ -210,6 +218,7 @@ def from_wk_to_x(delta_wk): def matvec(delta_x): delta_wk = from_x_to_wk(delta_x) delta_out_wk = eli_prod(delta_wk) + delta_out_wk = symmetrize_fct(delta_out_wk) delta_out_x = from_wk_to_x(delta_out_wk) return delta_out_x diff --git a/test/python/eliashberg/CMakeLists.txt b/test/python/eliashberg/CMakeLists.txt index 7a1970577..2f3066194 100644 --- a/test/python/eliashberg/CMakeLists.txt +++ b/test/python/eliashberg/CMakeLists.txt @@ -8,3 +8,4 @@ add_python_test(eigenvalue_solver ${PREFIX}) add_python_test(previous_implementation ${PREFIX}) add_python_test(previous_implementation_two_band ${PREFIX}) add_python_test(fft_product_constant_vs_full ${PREFIX}) +add_python_test(symmetrize_delta ${PREFIX}) diff --git a/test/python/eliashberg/symmetrize_delta.py b/test/python/eliashberg/symmetrize_delta.py new file mode 100644 index 000000000..1492c9c23 --- /dev/null +++ b/test/python/eliashberg/symmetrize_delta.py @@ -0,0 +1,128 @@ + +# ---------------------------------------------------------------------- + +""" Test the symmetrizing feature of the solve_eliashberg function +""" +# ---------------------------------------------------------------------- + +import itertools +import functools + +# ---------------------------------------------------------------------- + +import numpy as np + +# ---------------------------------------------------------------------- + +from pytriqs.gf import MeshImFreq, Idx + +from triqs_tprf.ParameterCollection import ParameterCollection +from triqs_tprf.tight_binding import TBLattice +from triqs_tprf.lattice import lattice_dyson_g0_wk +from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk +from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors +from triqs_tprf.lattice import solve_rpa_PH +from triqs_tprf.lattice import gamma_PP_singlet +from triqs_tprf.eliashberg import solve_eliashberg + +# ---------------------------------------------------------------------- + +import matplotlib.pyplot as plt + +# ---------------------------------------------------------------------- + +from triqs_tprf.symmetries import enforce_symmetry, check_symmetry + +# ---------------------------------------------------------------------- + +p = ParameterCollection( + dim = 2, + norbs = 2, + t1 = 1.0, + t2 = 0.5, + t12 = 0.1, + t21 = 0.1, + mu = 0.1, + beta = 1, + U = 1.0, + Up = 0.8, + J = 0.1, + Jp = 0.1, + nk = 4, + nw = 50, + plot=False + ) + +# -- Setup model, RPA susceptibilities, spin/charge interaction and gamma +full_units = [(1, 0, 0), (0, 1, 0), (0, 0, 1)] +all_nn_hoppings = list(itertools.product([-1, 0, 1], repeat=p.dim)) +non_diagonal_hoppings = [ele for ele in all_nn_hoppings if sum(np.abs(ele)) == 1] + +# -- Create hopping matrix for two-band model +t = -np.array([[p.t1, p.t12], [p.t21, p.t2]]) + +H = TBLattice( + units = full_units[:p.dim], + hopping = {hop : t for hop in non_diagonal_hoppings}, + orbital_positions = [(0,0,0)]*p.norbs, + ) + +e_k = H.on_mesh_brillouin_zone(n_k=[p.nk]*p.dim + [1]*(3-p.dim)) + +wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nw) +g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh) + +chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw) + +U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norbs, p.U, p.Up, + p.J, p.Jp) + +chi_s = solve_rpa_PH(chi0_wk, U_s) +chi_c = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation + +gamma = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) + +# -- Test symmetrizing function on eliashberg +variables=["frequency", "momentum", "orbital"] + +# Use all combinations +symmetry_set = list(itertools.product(["even", "odd"], repeat=3)) + +translate_symmetries = {"even" : +1, "odd" : -1, None : None} + +for symmetries in symmetry_set: + symmetrize = functools.partial(enforce_symmetry, + variables=variables, + symmetries=symmetries) + + E, eigen_modes = solve_eliashberg(gamma, g0_wk, product='FFT', solver='IRAM', + symmetrize_fct=symmetrize) + + expected_symmetries = {variable : translate_symmetries[symmetry] \ + for (variable, symmetry) in zip(variables, symmetries)} + + for delta in eigen_modes: + produced_symmetries = check_symmetry(delta) + if not expected_symmetries == produced_symmetries: + raise AssertionError("Incorrect symmetries were produced.") + + if p.plot: + fig, axes = plt.subplots(3, 3) + + vmax = np.max(np.abs(delta[Idx(0),:].data)) + + for orb1, orb2 in itertools.product(range(p.norbs), repeat=2): + shape = (p.nk, p.nk, p.norbs, p.norbs) + data = delta[Idx(0), :].data.reshape(shape) + plt.sca(axes[orb1,orb2]) + plt.imshow(data[:,:,orb1,orb2].real, cmap="RdBu_r", + vmax=vmax, vmin=-vmax) + plt.colorbar() + + plt.sca(axes[-1,-1]) + for orb1, orb2 in itertools.product(range(p.norbs), repeat=2): + plt.plot(delta.data[:, 10, orb1, orb2].real) + plt.plot(delta.data[:, 10, orb1, orb2].imag) + + plt.show() + From ffe0c590750b57103cff270e988f218acbd7e3db Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 21 Oct 2019 11:46:32 +0200 Subject: [PATCH 052/121] [bse] remove tail_corr_nwf to reduce memory usage The sum over the fermionic Matsubara frequency i\nu for \chi(i\omega, i\nu, q) can directly be calculated with the function `imtime_bubble_chi0_wk`. This saves memory, because the \chi(i\omega, i\nu, q) object does not need to be allocated for the generally rather big number of i\nu points used for the tail correction. Still, \chi(i\omega, i\nu, q) needs to be allocated for the number of i\nu used for \Gamma(i\omega, i\nu, i\nu) where memory can be a restriction. --- python/triqs_tprf/bse.py | 28 ++++++---------------------- 1 file changed, 6 insertions(+), 22 deletions(-) diff --git a/python/triqs_tprf/bse.py b/python/triqs_tprf/bse.py index ae2050ddf..411fa28c4 100644 --- a/python/triqs_tprf/bse.py +++ b/python/triqs_tprf/bse.py @@ -38,8 +38,9 @@ from triqs_tprf.lattice import chi0r_from_gr_PH from triqs_tprf.lattice import chi0r_from_gr_PH_nompi from triqs_tprf.lattice import chi0q_from_chi0r -from triqs_tprf.lattice import chi0q_sum_nu, chi0q_sum_nu_tail_corr_PH +from triqs_tprf.lattice import chi0q_sum_nu from triqs_tprf.lattice import chiq_sum_nu_from_chi0q_and_gamma_PH +from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk # ---------------------------------------------------------------------- def solve_local_bse(chi0_wnn, chi_wnn): @@ -207,7 +208,7 @@ def get_chi0_wnk(g_wk, nw=1, nwf=None): return chi0_wnk # ---------------------------------------------------------------------- -def solve_lattice_bse(g_wk, gamma_wnn, tail_corr_nwf=None): +def solve_lattice_bse(g_wk, gamma_wnn): r""" Compute the generalized lattice susceptibility :math:`\chi_{abcd}(\omega, \mathbf{k})` using the Bethe-Salpeter @@ -219,8 +220,6 @@ def solve_lattice_bse(g_wk, gamma_wnn, tail_corr_nwf=None): g_wk : Single-particle Green's function :math:`G_{ab}(\omega, \mathbf{k})`. gamma_wnn : Local particle-hole vertex function :math:`\Gamma_{abcd}(\omega, \nu, \nu')` - tail_corr_nwf : Number of fermionic freqiencies to use in the - tail correction of the sum over fermionic frequencies. Returns ------- @@ -247,31 +246,16 @@ def solve_lattice_bse(g_wk, gamma_wnn, tail_corr_nwf=None): print 'nw =', nw print 'nwf =', nwf print 'nwf_g =', nwf_g - print 'tail_corr_nwf =', tail_corr_nwf print - if tail_corr_nwf is None: - tail_corr_nwf = nwf - - mpi.report('--> chi0_wnk_tail_corr') - chi0_wnk_tail_corr = get_chi0_wnk(g_wk, nw=nw, nwf=tail_corr_nwf) - - mpi.report('--> trace chi0_wnk_tail_corr (WARNING! NO TAIL FIT. FIXME!)') - chi0_wk_tail_corr = chi0q_sum_nu_tail_corr_PH(chi0_wnk_tail_corr) - #chi0_wk_tail_corr = chi0q_sum_nu(chi0_wnk_tail_corr) + mpi.report('--> chi0_wk_tail_corr') + chi0_wk_tail_corr = imtime_bubble_chi0_wk(g_wk, nw=nw) mpi.barrier() mpi.report('B1 ' + str(chi0_wk_tail_corr[Idx(0), Idx(0,0,0)][0,0,0,0])) mpi.barrier() - mpi.report('--> chi0_wnk_tail_corr to chi0_wnk') - if tail_corr_nwf != nwf: - mpi.report('--> fixed_fermionic_window_python_wnk') - chi0_wnk = fixed_fermionic_window_python_wnk(chi0_wnk_tail_corr, nwf=nwf) - else: - chi0_wnk = chi0_wnk_tail_corr.copy() - - del chi0_wnk_tail_corr + chi0_wnk = get_chi0_wnk(g_wk, nw=nw, nwf=nwf) mpi.barrier() mpi.report('C ' + str(chi0_wnk[Idx(0), Idx(0), Idx(0,0,0)][0,0,0,0])) From e9eaa07407b60883fa0f8181ebc46e5a04cd0fd1 Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 11 Nov 2019 14:54:56 +0100 Subject: [PATCH 053/121] incorporate triqs mpi changes --- c++/triqs_tprf/lattice/eliashberg.cpp | 2 +- c++/triqs_tprf/lattice/fourier.hpp | 8 ++++---- c++/triqs_tprf/lattice/rpa.cpp | 2 +- python/triqs_tprf/lattice_desc.py | 2 +- 4 files changed, 7 insertions(+), 7 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index 231718088..c480e2bd0 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -318,7 +318,7 @@ chi_wk_t gamma_PP_spin_charge(chi_wk_vt chi_c, chi_wk_vt chi_s, \ Gamma_pp_wk[w, k] = Gamma_pp_arr; } - Gamma_pp_wk = mpi_all_reduce(Gamma_pp_wk); + Gamma_pp_wk = mpi::all_reduce(Gamma_pp_wk); return Gamma_pp_wk; } diff --git a/c++/triqs_tprf/lattice/fourier.hpp b/c++/triqs_tprf/lattice/fourier.hpp index 6844c5d2e..9c16b68a1 100644 --- a/c++/triqs_tprf/lattice/fourier.hpp +++ b/c++/triqs_tprf/lattice/fourier.hpp @@ -63,7 +63,7 @@ auto fourier_wr_to_tr_general_target(Gf_type g_wr, int n_tau = -1) { g_tr[_, r] = g_t; } - g_tr = mpi_all_reduce(g_tr); + g_tr = mpi::all_reduce(g_tr); return g_tr; } @@ -96,7 +96,7 @@ auto fourier_tr_to_wr_general_target(Gf_type g_tr, int n_w = -1) { g_wr[_, r] = g_w; } - g_wr = mpi_all_reduce(g_wr); + g_wr = mpi::all_reduce(g_wr); return g_wr; } @@ -131,7 +131,7 @@ auto fourier_wk_to_wr_general_target(Gf_type g_wk) { g_wr[w, _] = g_r; } - g_wr = mpi_all_reduce(g_wr); + g_wr = mpi::all_reduce(g_wr); return g_wr; } @@ -165,7 +165,7 @@ auto fourier_wr_to_wk_general_target(Gf_type g_wr) { g_wk[w, _] = g_k; } - g_wk = mpi_all_reduce(g_wk); + g_wk = mpi::all_reduce(g_wk); return g_wk; } diff --git a/c++/triqs_tprf/lattice/rpa.cpp b/c++/triqs_tprf/lattice/rpa.cpp index b33a51df0..3de723f76 100644 --- a/c++/triqs_tprf/lattice/rpa.cpp +++ b/c++/triqs_tprf/lattice/rpa.cpp @@ -61,7 +61,7 @@ chi_wk_t solve_rpa_PH(chi_wk_vt chi0_wk, chi_wk[w, k] = chi_arr; // assign back using the array_view } - chi_wk = mpi_all_reduce(chi_wk); + chi_wk = mpi::all_reduce(chi_wk); return chi_wk; } diff --git a/python/triqs_tprf/lattice_desc.py b/python/triqs_tprf/lattice_desc.py index cd040f2f9..2e67749c1 100644 --- a/python/triqs_tprf/lattice_desc.py +++ b/python/triqs_tprf/lattice_desc.py @@ -502,7 +502,7 @@ module.add_function ("std::tuple triqs_tprf::dynamic_and_constant_to_tr (triqs_tprf::chi_wk_vt Gamma_pp_dyn_wk, triqs_tprf::chi_k_vt Gamma_pp_const_k)", doc = r"""""") -module.add_function ("triqs_tprf::e_k_t triqs_tprf::eliashberg_constant_gamma_f_product (triqs_tprf::chi_r_vt Gamma_pp_const_r, triqs_tprf::g_tr_t F_tr)", doc = r"""""") +module.add_function ("triqs_tprf::e_r_t triqs_tprf::eliashberg_constant_gamma_f_product (triqs_tprf::chi_r_vt Gamma_pp_const_r, triqs_tprf::g_tr_t F_tr)", doc = r"""""") module.add_function ("triqs_tprf::chi_wk_t triqs_tprf::gamma_PP_singlet (triqs_tprf::chi_wk_vt chi_c, triqs_tprf::chi_wk_vt chi_s, array_view,4> U_c, array_view,4> U_s)", doc = r"""Gamma particle-particle singlet From db851d306a4e094978a8aa3a6397d1101a248551 Mon Sep 17 00:00:00 2001 From: Stefan Date: Thu, 14 Nov 2019 17:15:31 +0100 Subject: [PATCH 054/121] [doc] rewrite eliashberg theory --- doc/theory/eliashberg.rst | 523 ++++++++++++++++++++++++++------------ doc/theory/notation.rst | 1 + 2 files changed, 357 insertions(+), 167 deletions(-) diff --git a/doc/theory/eliashberg.rst b/doc/theory/eliashberg.rst index c6ae1af94..10500b53d 100644 --- a/doc/theory/eliashberg.rst +++ b/doc/theory/eliashberg.rst @@ -3,242 +3,431 @@ Linearized Eliashberg Equation ================================ -.. note:: - References: +The linearized Eliashberg equation is a generalization of the +Bardeen-Cooper-Schrieffer (BCS) gap equation to frequency dependent gaps. +It can be used to determine the critical temperature :math:`T_\mathrm{c}`, +at which a transition to a superconducting state occurs, +and the symmetry of the corresponding gap function :math:`\Delta`. +It is given by - - [A.A. Abrikosov, L.P. Gor’kov, et.al., Pergamon, Oxford (1965)] - - [Takimoto, et. al., PRB 69, 104504 (2004)] - - [Yanase, et. al., Physics Reports 387, 1-149 (2003)] - - -.. note:: - All indices on this page only represent orbital degrees of freedom. - Spin is not treated explicitly and therefore only spin-independent Hamiltonians can be used for calculations. - - - - -We asssume a homogenous system with some arbitrary effective pairing interaction :math:`\Gamma`, which leads to the formation of Cooper pairs. +.. math:: + \Delta(K) = \frac{T^2_{\mathrm{c}}}{2 N_{\mathbf{k}}^2}\sum_{K', K''} + \Gamma^{PP}(Q=0, K, K') + \chi^{(0),{PP}}(Q=0, K', K'') + \Delta(K'')\,, + :label: linearized_eliashberg_1 + +where :math:`Q/K` is a combination of bosonic/fermionic Matsubara +frequency and momentum, +:math:`N_{\mathbf{k}}` is the number of momentum points, +:math:`\Gamma^{PP}` is the irreducible particle-particle vertex, +:math:`\chi^{(0),{PP}}` is the bare particle-particle susceptibility, +as defined in :eq:`bare_pp_sus_def`, +and :math:`\Delta` is the gap. + +Note, that the bosonic Matsubara frequency and momentum is set to zero. +This is because we are interested in Cooper-pairs which have a zero +transfered momentum-frequency in a scattering process. + +Normal state and superconducting state +-------------------------------------- + +The linearized Eliashberg equation can be seen from two perspectives. +On one hand we are in the normal state and want to find the transition +to the superconducting one, +and on the other we are in the superconducting state using the limit of +small gaps :math:`\Delta \ll 1`. + +Normal state +^^^^^^^^^^^^ + +Generally speaking a transition from the normal state to a superconducting +one occurs when the particle-particle susceptibility diverges. +This is the case when the product of irreducible vertex and +bare susceptibility becomes unity -Anomalous Green's Functions ---------------------------- +.. math:: + \Gamma^{PP} \cdot \chi^{(0),{PP}} = 1\,. -.. note:: - Explain what happens with all spin quantum numbers in the single-particle Green's function. Do we work with a particular combination of spins? :math:`G_{a\bar{b}} = G_{\alpha \uparrow \bar{b} \downarrow}`? +For values smaller than :math:`1` we are still in the normal state, +but we can calculate the corresponding eigenvectors :math:`\Delta`. +This corresponds to an eigenvalue equation of Eq. :eq:`linearized_eliashberg_1`, +which we can write with the definiton of :math:`\chi^{(0),{PP}}` +in :eq:`bare_pp_sus_def` as, -With the arise of Cooper pairs we need in addition to the normal single-particle Green's function +.. math:: + \lambda\Delta(K) = -\frac{1}{2 N_{\mathbf{k}}\beta}\sum_{K'} + \Gamma^{PP}(Q=0, K, K') + G(K')G(-K') + \Delta(K')\,. + :label: linearized_eliashberg_2 + +The eigenvalue :math:`\lambda` is therefore an indicator of how strong +a superconducting instability is. +These calculations are valid for :math:`\lambda \leq 1` +and yield gaps which have not actually manifested yet. +At :math:`\lambda=1` the normal state breaks down and the superconducting +state with the corresponding gap emerges. + +Superconducting state +^^^^^^^^^^^^^^^^^^^^^ + +For a calculation in the superconducting state we must extend the basis +to accommodate Cooper-pairs. +In addition to the normal single-particle Green's function .. math:: - G_{a\bar{b}}(\tau - \tau') + G_{a\bar{b}}(\tau, \mathbf{r}) \equiv - - \langle \mathcal{T} c_{a}(\tau) c^\dagger_{\bar{b}}(\tau') \rangle - = - - \langle \mathcal{T} a(\tau) \bar{b}(\tau') \rangle\,, + - \langle \mathcal{T} c_{a}(\tau, \mathbf{r}) + c^\dagger_{\bar{b}}(0, \mathbf{0}) \rangle \,, and its backwards propagating counterpart .. math:: - \bar{G}_{\bar{a}b}(\tau - \tau') + \overline{G}_{\bar{a}b}(\tau, \mathbf{r}) \equiv - - \langle \mathcal{T} c^\dagger_{\bar{a}}(\tau) c_{b}(\tau') \rangle - = - - \langle \mathcal{T} \bar{a}(\tau) b(\tau') \rangle\,, + - \langle \mathcal{T} c^\dagger_{\bar{a}}(\tau, \mathbf{r}) + c_{b}(0, \mathbf{0}) \rangle\,, -the single-particle anomalous Green's functions :math:`F` and :math:`\bar{F}` to describe a superconducting state. +we have to introduce the single-particle anomalous Green's functions +:math:`F` and :math:`\overline{F}`. These are defined as .. math:: - F_{ab}(\tau - \tau') + F_{ab}(\tau, \mathbf{r}) \equiv - \langle \mathcal{T} c_{a}(\tau) c_{b}(\tau') \rangle - = - \langle \mathcal{T} a(\tau) b(\tau') \rangle + \langle \mathcal{T} c_{a}(\tau, \mathbf{r}) + c_{b}(0, \mathbf{0}) \rangle \,, +and + .. math:: - \bar{F}_{\bar{a}\bar{b}}(\tau - \tau') + \overline{F}_{\bar{a}\bar{b}}(\tau, \mathbf{r}) \equiv - \langle \mathcal{T} c^\dagger_{a}(\tau) c^\dagger_{\bar{b}}(\tau') \rangle - = - \langle \mathcal{T} \bar{a}(\tau) \bar{b}(\tau') \rangle\,. + \langle \mathcal{T} c^\dagger_{\bar{a}}(\tau, \mathbf{r}) + c^\dagger_{\bar{b}}(0, \mathbf{0}) \rangle\,. -Fourier transforming to Matsubara frequency space then gives that +Fourier transforming to Matsubara frequency and momentum space then gives that .. math:: - \bar{G}_{\bar{a}b}(\mathbf{k}, i\nu_n) = [ G_{b\bar{a}}(-\mathbf{k}, -i\nu_n) ]^{*} - \\ - \bar{F}_{\bar{a}\bar{b}}(\mathbf{k}, i\nu_n) = [ F_{ba}(-\mathbf{k}, -i\nu_n) ]^{*} - -Dyson-Gorkov Equations ----------------------- + \overline{G}_{\bar{a}b}(i\nu_n, \mathbf{k}) = + -G_{b\bar{a}}(-i\nu_n, -\mathbf{k})\,, + :label: g_bar_to_g -The former properties of a superconductor are given by the Dyson-Gorkov equations +and .. math:: - \mathbf{G}(\mathbf{k}, i\nu_n) + \overline{F}_{\bar{a}\bar{b}}(i\nu_n, \mathbf{k}) = - \mathbf{G}^{(0)}(\mathbf{k}, i\nu_n) - + \mathbf{G}^{(0)}(\mathbf{k}, i\nu_n) - \ast \mathbf{\Sigma}(\mathbf{k}, i\nu_n) - \ast \mathbf{G}(\mathbf{k}, i\nu_n) - -.. math:: - \mathbf{G} \equiv - \left[ \begin{array}{cc} - G_{a\bar{b}} & F_{ab} \\ - \bar{F}_{\bar{a}\bar{b}} & \bar{G}_{\bar{a}b} \\ - \end{array} \right] - \quad - \mathbf{G}^{(0)} - \equiv - \left[ \begin{array}{cc} - G^{(0)}_{a\bar{b}} & 0 \\ - 0 & \bar{G}^{(0)}_{\bar{a}b} \\ - \end{array} \right] - \quad - \mathbf{\Sigma} - \equiv - \left[ \begin{array}{cc} - \Sigma_{a\bar{b}} & \Delta_{ab} \\ - \bar{\Delta}_{\bar{a}\bar{b}} & \bar{\Sigma}_{\bar{a}b} \\ - \end{array} \right] + [F_{ab}(-i\nu_n, \mathbf{k}) ]^{*}\,. + :label: f_bar_to_f -In component form this becomes, +All four Green's functions are coupled and given by .. math:: - G(a\bar{b}) = G^{(0)}(a\bar{b}) + G^{(0)}(a\bar{c})\Sigma(\bar{c}d)G(d\bar{b}) + - G^{(0)}(a\bar{c})\bar{\Delta}(\bar{c}\bar{d})\bar{F}(\bar{d}\bar{b}) + \left( \begin{array}{cc} + G & F \\ + \overline{F} & \overline{G}\\ + \end{array} \right) + = + \left( \begin{array}{cc} + \left(G^{(0)}\right)^{-1} - \Sigma & \Delta \\ + \overline{\Delta} & \left(\overline{G}^{(0)}\right)^{-1} - \overline{\Sigma} \\ + \end{array} \right)^{-1}\,, -.. math:: - \bar{G}(\bar{a}b) = \bar{G}^{(0)}(\bar{a}b) + \bar{G}^{(0)}(\bar{a}c)\bar{\Sigma}(c\bar{d})\bar{G}(\bar{d}b) + - \bar{G}^{(0)}(\bar{a}c)\Delta(cd)F(db) +where :math:`\Sigma` and :math:`\overline{\Sigma}` are the normal self-energies +and :math:`\Delta` and :math:`\overline{\Delta}` the anomalous ones, +which correspond to the gap function. -.. math:: - F(ab) = G^{(0)}(a\bar{c}) \Sigma(\bar{c}d) F(db)+ - G^{(0)}(a\bar{c}) \bar{\Delta}(\bar{c}\bar{d}) \bar{G}(\bar{d}b) +The anomalous self-energy is given by .. math:: - \bar{F}(\bar{a}\bar{b}) = \bar{G}^{(0)}(\bar{a}c) \bar{\Sigma}(c\bar{d}) \bar{F}(\bar{d}\bar{b})+ - \bar{G}^{(0)}(\bar{a}c) \Delta(cd) G(d\bar{b}) - -Here :math:`\Sigma` is the normal self-energy and :math:`\Delta` and :math:`\bar{\Delta}` the anomalous self-energies, which are equal in the absence of a magnetic field and will be treated as from now on. - -Anomalous self-energy and particle-particle vertex --------------------------------------------------- + \Delta(K) + = + -\frac{1}{N_{\mathbf{k}} \beta} \sum_{K'} \Gamma^{PP}(Q=0, K, K') F(K')\,. + :label: anomalous_self_energy -.. note:: - Define :math:`\Gamma`. It should be the particle-particle vertex :math:`\Gamma^{(pp)}` related to the generalized susceptibility :math:`\chi` through the Bethe-Salpeter equation in the particle-particle channel. This would give the definition of the four orbital(spin) indices and their order. - -The anomalous self-energy can be expressed with the effective pairing interaction :math:`\Gamma` and the anomalous Green's function :math:`F` as +with .. math:: - \Delta_{\bar{a}\bar{b}}(\mathbf{k},i\nu) = -\frac{1}{N_k \beta}\sum_{\mathbf{q}} \sum_{i\nu'} - \Gamma_{A\bar{a}\bar{b}B}(\mathbf{k}-\mathbf{q}, i\nu - i\nu') F_{AB}(\mathbf{q}, i\nu')\,. - :label: anom_self_energy - -Linearization in :math:`\Delta` -------------------------------- - -Around the transition point to the superconducting state the anomalous self-energy :math:`\Delta` is approximately zero, and, because we are only interested in the transition point, we linearize :math:`F` in the Dyson-Gorkov equations with respect to :math:`\Delta`. This yields + F(K) + = + \frac{\Delta(K)} + {\left(\left(G^{(0)}(K)\right)^{-1}-\Sigma(K)\right) + \left(\left(G^{(0)}(K)\right)^{-1}-\Sigma(K)\right) + - + \overline{\Delta}(K) \Delta(K)}\,. + :label: f_explicit + +With this we could calculate the gap for the superconducting state +below :math:`T_\mathrm{c}`, +but note, that this is not that trivial, +because the self-energy :math:`\Sigma` is also coupled to :math:`\Delta`. +In the limit of :math:`\Delta \ll 1`, +i.e. linearizing Eq. :eq:`f_explicit`, +we also decouple the self-energy and +Eq. :eq:`anomalous_self_energy` becomes the the linearized Eliashberg equation. + +Relation to the BCS gap equation +---------------------------- + +In BCS theory the particle-particle pairing vertex is considered to be +constant in a specific frequency range, which corresponds to gaps with +the same dependence. +For this case the summation over fermionic Matsubara frequencies in +Eq. :eq:`linearized_eliashberg_2` can be done analytically .. math:: - F & = g \Sigma F + g \Delta \bar{G} \\ - G & = g + g \Sigma G + g \Delta \bar{F} + \lambda\Delta(\mathbf{k}) = -\frac{1}{2 N_{\mathbf{k}}}\sum_{\mathbf{k'}} + \Gamma^{PP}(\mathbf{q}=\mathbf{0}, \mathbf{k}, \mathbf{k'}) + \frac{\tan(\epsilon(\mathbf{k'})\beta/2)}{2\epsilon(\mathbf{k'})} + \Delta(\mathbf{k'})\,. + :label: linearized_eliashberg_3 + +Here we assumed a non-interacting Gree'ns function with dispersion relation +:math:`\epsilon`. +Eq. :eq:`linearized_eliashberg_3` corresponds to the linearized BCS gap +equation. +The BCS gap equation can be obtained from Eq. :eq:`linearized_eliashberg_3` +by substituting :math:`\epsilon` with +:math:`\sqrt{\epsilon(\mathbf{k})^2 + |\Delta(\mathbf{k})|^2}`. +This is equivalent to using Eq. :eq:`anomalous_self_energy` +with a non-linearized anomalous Green's function :eq:`f_explicit`. + +Spin diagonalization +-------------------- + +All objects above were formulated with combined spin and orbital indices. +For :math:`SU(2)` symmetric systems we can drop the spin dependency +by diagonalizing everything in spin. +This diagonalization splits the superconducting gap :math:`\Delta` +in two channels, +singlet .. math:: - F & = (g^{-1} - \Sigma)^{-1} \Delta \bar{G} \\ - \bar{G} & = (\bar{g}^{-1} - \Sigma)^{-1} + \bar{\Delta} F + \Delta^{\mathrm{s}} + = + \Delta_{\uparrow\downarrow} + - + \Delta_{\downarrow\uparrow}\,, -.. math:: - F = (g^{-1} - \Sigma)^{-1} \Delta (\bar{g}^{-1} - \bar{\Sigma})^{-1} + \mathcal{O}(\Delta^2) - :label: lin_anom_gf - -We then insert :eq:`lin_anom_gf` into :eq:`anom_self_energy` and obtain the linearized Eliashberg equation +and triplet .. math:: - \Delta_{\bar{a}\bar{b}}(\mathbf{k},i\nu) = -\frac{1}{N_k \beta}\sum_{\mathbf{q}} \sum_{i\nu'} - \Gamma_{A\bar{a}\bar{b}B}(\mathbf{k}-\mathbf{q}, i\nu - i\nu') - \\ \times - \big({G^{(0)}}^{-1}(\mathbf{q}, i\nu') - \Sigma(\mathbf{q}, i\nu') \big)^{-1}_{A\bar{c}} - \Delta_{\bar{c}\bar{d}}(\mathbf{q}, i\nu') - \big({G^{(0)}}^{-1}_{}(-\mathbf{q}, -i\nu') - \Sigma_{}(-\mathbf{q}, -i\nu') \big)^{-1}_{B\bar{d}}\,. + \Delta^{\mathrm{t}} + = + \Delta_{\uparrow\downarrow} + + + \Delta_{\downarrow\uparrow}\,. -To make use of this equations it is usually interpreted as an eigenvalue equation +We can then express Eq. :eq:`linearized_eliashberg_2` in either of those two +channels. +Doing this for the singlet channel, +while suppressing frequency, momentum and orbital indices, yields .. math:: - \lambda \Delta = \Lambda \Delta\,, - -where the eigenvalue :math:`\lambda` is seen as a measurement for the strength of superconducting ordering and a phase transition occurs when it reaches unity. + \lambda + \Delta^{\mathrm{s}} + &= + \lambda + \left(\Delta_{\uparrow\downarrow} - \Delta_{\downarrow\uparrow}\right) + \\ + &= + -\left[\Gamma^{PP}_{\uparrow\uparrow\downarrow\downarrow} + \; + G_{\uparrow\uparrow}G_{\downarrow\downarrow} + \Delta_{\uparrow\downarrow} + + + \Gamma^{PP}_{\uparrow\downarrow\downarrow\uparrow} + \; + G_{\downarrow\downarrow}G_{\uparrow\uparrow} + \Delta_{\downarrow\uparrow} + \right] + + + \\ + &\quad\quad + \left[ + \Gamma^{PP}_{\downarrow\downarrow\uparrow\uparrow} + \; + G_{\downarrow\downarrow}G_{\uparrow\uparrow} + \Delta_{\downarrow\uparrow} + - + \Gamma^{PP}_{\downarrow\uparrow\uparrow\downarrow} + \; + G_{\uparrow\uparrow} + G_{\downarrow\downarrow} + \Delta_{\uparrow\downarrow} + \right] + \\ + &= + -\Gamma^{PP}_{\uparrow\uparrow\downarrow\downarrow} + \; + GG + \left( + \Delta_{\uparrow\downarrow} + - + \Delta_{\downarrow\uparrow} + \right) + + + \Gamma^{PP}_{\uparrow\downarrow\downarrow\uparrow} + \; + GG + \left( + \Delta_{\uparrow\downarrow} + - + \Delta_{\downarrow\uparrow} + \right) + \\ + &= + -\left(\Gamma^{PP}_{\uparrow\uparrow\downarrow\downarrow} + -\Gamma^{PP}_{\uparrow\downarrow\downarrow\uparrow} + \; + \right) + GG + \Delta^{\mathrm{s}} + \\ + &= + -\Gamma^{\mathrm{s}} + GG + \Delta^{\mathrm{s}}\,. + +This is analog for the triplet channel and we obtain for the spin diagonalized +linearized Eliashberg equation -RPA Approach ------------- +.. math:: + \lambda\Delta^{\mathrm{s/t}}(K) = -\frac{1}{2 N_{\mathbf{k}}\beta}\sum_{K'} + \Gamma^{\mathrm{s/t}}(Q=0, K, K') + G(K')G(-K') + \Delta^{\mathrm{s/t}}(K')\,. + :label: linearized_eliashberg_4 -.. note:: - Explain what happens with momenta +Random phase approximation for the irreducible particle-particle vertex +----------------------------------------------------------------------- -The linearized Eliashberg equation can be studied in the RPA limit. -In this case the normal self-energy is set to zero and the effective pairing interaction :math:`\Gamma` for a singlet Cooper pairs is given by +To obtain the irreducible particle-particle vertex in the RPA +one substitutes all vertices with the bare one in the parquet equation. +In the spin diagonalized form this yields for the singlet .. math:: - \Gamma^{(\mathrm{singlet})}(a\bar{b}c\bar{d}) = - \frac{3}{2} U^{(\mathrm{s})}(a\bar{b}A\bar{B}) \chi^{(\mathrm{s})}(\bar{B}A\bar{C}D) - U^{(\mathrm{s})}(D\bar{C}c\bar{d}) \\ - -\frac{1}{2} U^{(\mathrm{c})}(a\bar{b}A\bar{B}) \chi^{(\mathrm{c})}(\bar{B}A\bar{C}D) - U^{(\mathrm{c})}(D\bar{C}c\bar{d}) \\ - + \frac{1}{2}\big(U^{(\mathrm{s})}(a\bar{b}c\bar{d})+ - U^{(\mathrm{c})}(a\bar{b}c\bar{d})\big)\,, + \Gamma^{\mathrm{s}}_{a\bar{b}c\bar{d}}(Q=0, K, K') + \equiv & + \frac{3}{2} + \left[ + \Phi^{\mathrm{m}}_{a\bar{b}c\bar{d}}(K-K') + + + \Phi^{\mathrm{m}}_{c\bar{b}a\bar{d}}(K+K') + \right] + \\&- + \frac{1}{2} + \left[ + \Phi^{\mathrm{d}}_{a\bar{b}c\bar{d}}(K-K') + + + \Phi^{\mathrm{d}}_{c\bar{b}a\bar{d}}(K+K') + \right] + + + U^{\mathrm{s}}_{a\bar{b}c\bar{d}}\,, + :label: singlet_gamma + +and for the triplet -and for a triplet by +.. math:: + \Gamma^{\mathrm{t}}_{a\bar{b}c\bar{d}}(Q=0, K, K') + \equiv & + -\frac{1}{2} + \left[ + \Phi^{\mathrm{m}}_{a\bar{b}c\bar{d}}(K-K') + - + \Phi^{\mathrm{m}}_{c\bar{b}a\bar{d}}(K+K') + \right] + \\&- + \frac{1}{2} + \left[ + \Phi^{\mathrm{d}}_{a\bar{b}c\bar{d}}(K-K') + - + \Phi^{\mathrm{d}}_{c\bar{b}a\bar{d}}(K+K') + \right] + + + U^{\mathrm{s}}_{a\bar{b}c\bar{d}}\,, + :label: triplet_gamma + +with .. math:: - \Gamma^{(\mathrm{triplet})}(a\bar{b}c\bar{d}) = - -\frac{1}{2} U^{(\mathrm{s})}(a\bar{b}A\bar{B}) \chi^{(\mathrm{s})}(\bar{B}A\bar{C}D) - U^{(\mathrm{s})}(D\bar{C}c\bar{d}) \\ - -\frac{1}{2} U^{(\mathrm{c})}(a\bar{b}A\bar{B}) \chi^{(\mathrm{c})}(\bar{B}A\bar{C}D) - U^{(\mathrm{c})}(D\bar{C}c\bar{d}) \\ - + \frac{1}{2}\big(U^{(\mathrm{s})}(a\bar{b}c\bar{d})+ - U^{(\mathrm{c})}(a\bar{b}c\bar{d})\big)\,. + \Phi^{\mathrm{d/m}}_{a\bar{b}c\bar{d}}(Q) + \equiv + U^{\mathrm{d/m}}\chi^{\mathrm{d/m}}(Q)U^{\mathrm{d/m}}\,. -Here :math:`\chi^{(\mathrm{s})}` is the spin-susceptibility tensor defined by +Note, that the superscripts :math:`\mathrm{d}` and :math:`\mathrm{m}` +indicate the density and magnetic channel. +The bare vertex in its respective channel is given by .. math:: - \chi^{(\mathrm{s})}(\bar{a}b\bar{c}d) = \big(\mathbb{1} - \chi^{(0)}(\bar{a}b\bar{A}B) - U^{(\mathrm{s})}(B\bar{A}C\bar{D})\big)^{-1} \chi^{(0)}(\bar{D}C\bar{c}d)\,, - -and :math:`\chi^{(\mathrm{c})}` is the charge-susceptibility tensor defined by + U^{\mathrm{d/m}}_{a\bar{b}c\bar{d}} = + \begin{cases} + U/U, & \mathrm{if}\;a=\bar{b}=c=\bar{d} \\ + -U'+2J/U', & \mathrm{if}\;a=\bar{d}\neq \bar{b}=c \\ + 2U'-J/J, & \mathrm{if}\;a=\bar{b}\neq c=\bar{d} \\ + J/J, & \mathrm{if}\;a=c\neq \bar{b}=\bar{d} \\ + 0, & \mathrm{else} + \end{cases}\,. + +For an implementation prespective we must note, +that in both singlet :eq:`singlet_gamma` and +triplet :eq:`triplet_gamma` a density and magnetic +:math:`\Phi` term appears twice. +Once without an index flip and a dependence on :math:`K-K'`, +:math:`\Phi_{a\overline{b}c\overline{d}}(K-K')`, +and another time with an index flip and a dependence on :math:`K+K'`, +:math:`\Phi_{c\overline{b}a\overline{d}}(K+K')`. +Inside the linearized Eliashberg equation :eq:`linearized_eliashberg_4` +the :math:`\Phi_{c\overline{b}a\overline{d}}(K+K')` term +picks up a sign which depends on the frequency, momentum and orbital +symmetry of the gap :math:`\Delta`. +For a singlet gap this yields a plus and for a triplet a minus. +Therefore the terms just add up and we lose the factor :math:`1/2` in front of +the square brackets in Eq. :eq:`singlet_gamma` and :eq:`triplet_gamma`. + +Also note, that the RPA particle-particle vertices in +Eq. :eq:`singlet_gamma` and :eq:`triplet_gamma` only depend on the difference +between the two fermionic Matsubara frequencies and momenta. +We can therefore write the linearized Eliashberg equation +:eq:`linearized_eliashberg_4` as .. math:: - \chi^{(\mathrm{c})}(\bar{a}b\bar{c}d) = \big(\mathbb{1} + \chi^{(0)}(\bar{a}b\bar{A}B) - U^{(\mathrm{c})}(B\bar{A}C\bar{D})\big)^{-1} \chi^{(0)}(\bar{D}C\bar{c}d)\,, + \lambda\Delta^{\mathrm{s/t}}(K) = -\frac{1}{2 N_{\mathbf{k}}\beta}\sum_{K'} + \Gamma^{\mathrm{s/t}}(K-K') + G(K')G(-K') + \Delta^{\mathrm{s/t}}(K')\,. + :label: linearized_eliashberg_5 + +This allows us to get rid of the summation by using the convolution theorem -here :math:`\chi^{(0)}` is the non-interacting particle-hole bubble. +.. math:: + \lambda + \mathcal{F}\left[\Delta^{\mathrm{s/t}}(K)\right]= -\frac{1}{2} + \mathcal{F}\left[\Gamma^{\mathrm{s/t}}(K-K')\right] + \mathcal{F}\left[ + G(K')G(-K') + \Delta^{\mathrm{s/t}}(K') + \right]\,, + :label: linearized_eliashberg_5 -The spin and charge interaction tensors are given by +making the calculation computationaly more efficient. -.. math:: - U^{(\mathrm{s})}(a\bar{a}b\bar{b}) = - \begin{cases} - U, & \mathrm{if}\;a=\bar{a}=b=\bar{b} \\ - U', & \mathrm{if}\;a=\bar{b}\neq \bar{a}=b \\ - J, & \mathrm{if}\;a=\bar{a}\neq b=\bar{b} \\ - J', & \mathrm{if}\;a=b\neq \bar{a}=\bar{b} \\ - 0, & \mathrm{else} - \end{cases} +.. rubric:: References +.. [#abrikosov] A.A. Abrikosov, L.P. Gor’kov, et.al., Pergamon, Oxford (1965) -.. math:: - U^{(\mathrm{c})}(a\bar{a}b\bar{b}) = - \begin{cases} - U, & \mathrm{if}\;a=\bar{a}=b=\bar{b} \\ - -U'+2J, & \mathrm{if}\;a=\bar{b}\neq \bar{a}=b \\ - 2U'-J, & \mathrm{if}\;a=\bar{a}\neq b=\bar{b} \\ - J', & \mathrm{if}\;a=b\neq \bar{a}=\bar{b} \\ - 0, & \mathrm{else} - \end{cases} +.. [#yanase] Yanase, et. al., Physics Reports 387, 1-149 (2003) -where :math:`U`, :math:`U'`, :math:`J` and :math:`J'` are the usual Kanamori interaction parameters. +.. [#takimoto] Takimoto, et. al., PRB 69, 104504 (2004) +.. [#bickers] Bickers, N. E. Self-Consistent Many-Body Theory for Condensed Matter Systems. Theoretical Methods for Strongly Correlated Electrons, 237–296. 6, (2006) +.. [#rohringer] Rohringer, G., New routes towards a theoretical treatment of nonlocal electronic correlations, (2013) +.. [#nourafkan] R. Nourafkan, G. Kotliar, and A. M. Tremblay, Physical Review Letters 117, 1, (Supplementary), (2016) diff --git a/doc/theory/notation.rst b/doc/theory/notation.rst index 1d82b4982..f2dd81472 100644 --- a/doc/theory/notation.rst +++ b/doc/theory/notation.rst @@ -278,6 +278,7 @@ Crossed-Particle-particle channel (:math:`PPx`) \chi^{(0), pp}_{\bar{a}b\bar{c}d}(\omega, \nu, \nu') = - \beta \delta_{\nu, \nu'} G_{d\bar{a}}(\nu) G_{b\bar{c}}(\omega - \nu) + :label: bare_pp_sus_def .. math:: \chi^{pp}_{\bar{a}b\bar{c}d}(\omega, \nu, \nu') From 37164d414a77b03f0da476398b2c22767f8887c7 Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 20 Nov 2019 12:07:40 +0100 Subject: [PATCH 055/121] work around issue TRIQS/triqs#755 --- c++/triqs_tprf/lattice/eliashberg.cpp | 38 ++++++++++++++++++++++----- c++/triqs_tprf/lattice/eliashberg.hpp | 6 +++-- python/triqs_tprf/eliashberg.py | 13 +++++++-- python/triqs_tprf/lattice_desc.py | 9 ++++--- 4 files changed, 53 insertions(+), 13 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index c480e2bd0..93b8ed8c7 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -111,7 +111,7 @@ g_wk_t eliashberg_product(chi_wk_vt Gamma_pp, g_wk_vt g_wk, return delta_wk_out; } -std::tuple split_into_dynamic_wk_and_constant_k(chi_wk_vt Gamma_pp) { +chi_wk_t get_dynamic_wk(chi_wk_vt Gamma_pp) { auto _ = all_t{}; //auto [wmesh, kmesh] = Gamma_pp.mesh(); @@ -121,7 +121,7 @@ std::tuple split_into_dynamic_wk_and_constant_k(chi_wk_vt G // Fit infinite frequency value auto Gamma_pp_dyn_wk = make_gf(Gamma_pp); - chi_k_vt Gamma_pp_const_k = make_gf(kmesh, Gamma_pp.target()); + auto Gamma_pp_const_k = make_gf(kmesh, Gamma_pp.target()); for (const auto k : kmesh) { auto Gamma_w = Gamma_pp[_, k]; @@ -131,18 +131,44 @@ std::tuple split_into_dynamic_wk_and_constant_k(chi_wk_vt G for( const auto w : wmesh ) Gamma_pp_dyn_wk[w, k] = Gamma_pp[w, k] - Gamma_pp_const_k[k]; } - return {Gamma_pp_dyn_wk, Gamma_pp_const_k}; + return Gamma_pp_dyn_wk; } -std::tuple dynamic_and_constant_to_tr(chi_wk_vt Gamma_pp_dyn_wk, - chi_k_vt Gamma_pp_const_k) { +chi_k_t get_constant_k(chi_wk_vt Gamma_pp) { + + auto _ = all_t{}; + //auto [wmesh, kmesh] = Gamma_pp.mesh(); + auto wmesh = std::get<0>(Gamma_pp.mesh()); + auto kmesh = std::get<1>(Gamma_pp.mesh()); + + // Fit infinite frequency value + auto Gamma_pp_dyn_wk = make_gf(Gamma_pp); + + auto Gamma_pp_const_k = make_gf(kmesh, Gamma_pp.target()); + + for (const auto k : kmesh) { + auto Gamma_w = Gamma_pp[_, k]; + auto tail = std::get<0>(fit_tail(Gamma_w)); + for (auto [a, b, c, d] : Gamma_pp.target_indices()) + Gamma_pp_const_k[k](a, b, c, d) = tail(0, a, b, c, d); + } + + return Gamma_pp_const_k; +} + +chi_tr_t dynamic_to_tr(chi_wk_vt Gamma_pp_dyn_wk) { auto Gamma_pp_dyn_wr = fourier_wk_to_wr_general_target(Gamma_pp_dyn_wk); auto Gamma_pp_dyn_tr = fourier_wr_to_tr_general_target(Gamma_pp_dyn_wr); + return Gamma_pp_dyn_tr; +} + +chi_r_t constant_to_r(chi_k_vt Gamma_pp_const_k) { + auto Gamma_pp_const_r = make_gf_from_fourier<0>(Gamma_pp_const_k); - return {Gamma_pp_dyn_tr, Gamma_pp_const_r}; + return Gamma_pp_const_r; } e_r_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, g_tr_t F_tr) { diff --git a/c++/triqs_tprf/lattice/eliashberg.hpp b/c++/triqs_tprf/lattice/eliashberg.hpp index 10a3867fe..de02554e6 100644 --- a/c++/triqs_tprf/lattice/eliashberg.hpp +++ b/c++/triqs_tprf/lattice/eliashberg.hpp @@ -93,8 +93,10 @@ namespace triqs_tprf { g_wk_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const_r, g_wk_vt g_wk, g_wk_vt delta_wk); g_wk_t eliashberg_product_fft_constant(chi_r_vt Gamma_pp_const_r, g_wk_vt g_wk, g_wk_vt delta_wk); g_wk_t eliashberg_g_delta_g_product(g_wk_vt g_wk, g_wk_vt delta_wk); - std::tuple split_into_dynamic_wk_and_constant_k(chi_wk_vt Gamma_pp); - std::tuple dynamic_and_constant_to_tr(chi_wk_vt Gamma_pp_dyn_wk, chi_k_vt Gamma_pp_const_k); + chi_wk_t get_dynamic_wk(chi_wk_vt Gamma_pp); + chi_k_t get_constant_k(chi_wk_vt Gamma_pp); + chi_tr_t dynamic_to_tr(chi_wk_vt Gamma_pp_dyn_wk); + chi_r_t constant_to_r(chi_k_vt Gamma_pp_const_k); e_r_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, g_tr_t F_tr); /** Gamma particle-particle singlet diff --git a/python/triqs_tprf/eliashberg.py b/python/triqs_tprf/eliashberg.py index 7a1e81252..93c751c50 100644 --- a/python/triqs_tprf/eliashberg.py +++ b/python/triqs_tprf/eliashberg.py @@ -32,10 +32,20 @@ from pytriqs.gf import Gf from lattice import eliashberg_product from lattice import eliashberg_product_fft, eliashberg_product_fft_constant -from lattice import split_into_dynamic_wk_and_constant_k, dynamic_and_constant_to_tr +from lattice import get_dynamic_wk, get_constant_k, dynamic_to_tr, constant_to_r # ---------------------------------------------------------------------- +def split_into_dynamic_wk_and_constant_k(Gamma_pp_wk): + Gamma_pp_dyn_wk = get_dynamic_wk(Gamma_pp_wk) + Gamma_pp_const_k = get_constant_k(Gamma_pp_wk) + return Gamma_pp_dyn_wk, Gamma_pp_const_k + +def dynamic_and_constant_to_tr(Gamma_pp_dyn_wk, Gamma_pp_const_k): + Gamma_pp_dyn_tr = dynamic_to_tr(Gamma_pp_dyn_wk) + Gamma_pp_const_r = constant_to_r(Gamma_pp_const_k) + return Gamma_pp_dyn_tr, Gamma_pp_const_r + def semi_random_initial_delta(g_wk, nr_factor=0.5, seed=None): r"""Create a delta based on the GF with random elements @@ -115,7 +125,6 @@ def preprocess_gamma_for_fft(Gamma_pp_wk, Gamma_pp_const_k=None): elif (const_type == Gf): Gamma_pp_const_k_fit[:] = Gamma_pp_const_k.data Gamma_pp_dyn_wk_fit.data[:] = Gamma_pp_wk.data - Gamma_pp_const_k.data - # -- FFT dynamic and constant term to (tau, real) or (real) Gamma_pp_dyn_tr, Gamma_pp_const_r = dynamic_and_constant_to_tr(Gamma_pp_dyn_wk_fit, Gamma_pp_const_k_fit) diff --git a/python/triqs_tprf/lattice_desc.py b/python/triqs_tprf/lattice_desc.py index 2e67749c1..be50f308a 100644 --- a/python/triqs_tprf/lattice_desc.py +++ b/python/triqs_tprf/lattice_desc.py @@ -14,7 +14,6 @@ # Add here anything to add in the C++ code at the start, e.g. namespace using module.add_preamble(""" #include -#include #include #include @@ -498,9 +497,13 @@ module.add_function ("triqs_tprf::g_wk_t triqs_tprf::eliashberg_g_delta_g_product (triqs_tprf::g_wk_vt g_wk, triqs_tprf::g_wk_vt delta_wk)", doc = r"""""") -module.add_function ("std::tuple triqs_tprf::split_into_dynamic_wk_and_constant_k (triqs_tprf::chi_wk_vt Gamma_pp)", doc = r"""""") +module.add_function ("triqs_tprf::chi_wk_t triqs_tprf::get_dynamic_wk (triqs_tprf::chi_wk_vt Gamma_pp)", doc = r"""""") -module.add_function ("std::tuple triqs_tprf::dynamic_and_constant_to_tr (triqs_tprf::chi_wk_vt Gamma_pp_dyn_wk, triqs_tprf::chi_k_vt Gamma_pp_const_k)", doc = r"""""") +module.add_function ("triqs_tprf::chi_k_t triqs_tprf::get_constant_k (triqs_tprf::chi_wk_vt Gamma_pp)", doc = r"""""") + +module.add_function ("triqs_tprf::chi_tr_t triqs_tprf::dynamic_to_tr (triqs_tprf::chi_wk_vt Gamma_pp_dyn_wk)", doc = r"""""") + +module.add_function ("triqs_tprf::chi_r_t triqs_tprf::constant_to_r (triqs_tprf::chi_k_vt Gamma_pp_const_k)", doc = r"""""") module.add_function ("triqs_tprf::e_r_t triqs_tprf::eliashberg_constant_gamma_f_product (triqs_tprf::chi_r_vt Gamma_pp_const_r, triqs_tprf::g_tr_t F_tr)", doc = r"""""") From f5da4cf6bcefea99055d8f80a1aa96da2a2f0681 Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 10 Aug 2020 15:06:50 +0200 Subject: [PATCH 056/121] [doc] update eliashberg theory --- doc/theory/eliashberg.rst | 361 +++++++++++++++++++++++++------------- 1 file changed, 236 insertions(+), 125 deletions(-) diff --git a/doc/theory/eliashberg.rst b/doc/theory/eliashberg.rst index 10500b53d..f87362ffd 100644 --- a/doc/theory/eliashberg.rst +++ b/doc/theory/eliashberg.rst @@ -3,7 +3,7 @@ Linearized Eliashberg Equation ================================ -The linearized Eliashberg equation is a generalization of the +The linearized Eliashberg equation is a generalization of the linearized Bardeen-Cooper-Schrieffer (BCS) gap equation to frequency dependent gaps. It can be used to determine the critical temperature :math:`T_\mathrm{c}`, at which a transition to a superconducting state occurs, @@ -11,26 +11,25 @@ and the symmetry of the corresponding gap function :math:`\Delta`. It is given by .. math:: - \Delta(K) = \frac{T^2_{\mathrm{c}}}{2 N_{\mathbf{k}}^2}\sum_{K', K''} - \Gamma^{PP}(Q=0, K, K') - \chi^{(0),{PP}}(Q=0, K', K'') - \Delta(K'')\,, + \Delta_{\bar{a}\bar{b}}(K)= -\frac{1}{2 N_{\mathbf{k}}\beta}\sum_{K'} + \Gamma^{PP}_{c\bar{a}d\bar{b}}(Q=0, K, K') + G_{c\bar{e}}(K')G_{d\bar{f}}(-K') + \Delta_{\bar{e}\bar{f}}(K')\,. :label: linearized_eliashberg_1 where :math:`Q/K` is a combination of bosonic/fermionic Matsubara frequency and momentum, :math:`N_{\mathbf{k}}` is the number of momentum points, -:math:`\Gamma^{PP}` is the irreducible particle-particle vertex, -:math:`\chi^{(0),{PP}}` is the bare particle-particle susceptibility, -as defined in :eq:`bare_pp_sus_def`, -and :math:`\Delta` is the gap. +:math:`\Gamma^{PP}` is the irreducible particle-particle vertex +and :math:`G` is the one-particle Green's function. -Note, that the bosonic Matsubara frequency and momentum is set to zero. +Note, that the bosonic Matsubara frequency and momentum in the particle-particle vertex +is set to zero. This is because we are interested in Cooper-pairs which have a zero transfered momentum-frequency in a scattering process. -Normal state and superconducting state --------------------------------------- +Deriving the linearized Eliashberg equation: Normal state and superconducting state +----------------------------------------------------------------------------------- The linearized Eliashberg equation can be seen from two perspectives. On one hand we are in the normal state and want to find the transition @@ -43,62 +42,71 @@ Normal state Generally speaking a transition from the normal state to a superconducting one occurs when the particle-particle susceptibility diverges. -This is the case when the product of irreducible vertex and -bare susceptibility becomes unity .. math:: - \Gamma^{PP} \cdot \chi^{(0),{PP}} = 1\,. + \mathbf{\chi}^{PP} = [\mathbf{1}-\mathbf{\Gamma}^{PP} \mathbf{\chi}^{(0),{PP}}]^{-1} + \mathbf{\chi}^{(0),{PP}} -For values smaller than :math:`1` we are still in the normal state, +This is the case when the largest eigenvalue of +:math:`\mathbf{\Gamma}^{PP} \mathbf{\chi}^{(0),{PP}}` becomes unity. +For a largest eigenvalues that is smaller than :math:`1` we are still in the +normal state, but we can calculate the corresponding eigenvectors :math:`\Delta`. -This corresponds to an eigenvalue equation of Eq. :eq:`linearized_eliashberg_1`, -which we can write with the definiton of :math:`\chi^{(0),{PP}}` -in :eq:`bare_pp_sus_def` as, +This corresponds to the following eigenvalue equation .. math:: - \lambda\Delta(K) = -\frac{1}{2 N_{\mathbf{k}}\beta}\sum_{K'} - \Gamma^{PP}(Q=0, K, K') - G(K')G(-K') - \Delta(K')\,. + \lambda\Delta_{\bar{a}\bar{b}}(K)= \frac{T^2_{\mathrm{c}}}{2 N_{\mathbf{k}}^2}\sum_{K', K''} + \Gamma^{PP}_{c\bar{a}d\bar{b}}(Q=0, K, K') + \chi^{(0),{PP}}_{\bar{e}d\bar{f}c}(Q=0, K', K'') + \Delta_{\bar{e}\bar{f}}(K')\,, :label: linearized_eliashberg_2 -The eigenvalue :math:`\lambda` is therefore an indicator of how strong -a superconducting instability is. -These calculations are valid for :math:`\lambda \leq 1` -and yield gaps which have not actually manifested yet. +which we can write like Eq. :eq:`linearized_eliashberg_1` with the definiton +of :math:`\chi^{(0),{PP}}` :eq:`bare_pp_sus_def`, + +.. math:: + \lambda\Delta_{\bar{a}\bar{b}}(K)= -\frac{1}{2 N_{\mathbf{k}}\beta}\sum_{K'} + \Gamma^{PP}_{c\bar{a}d\bar{b}}(Q=0, K, K') + G_{c\bar{e}}(K')G_{d\bar{f}}(-K') + \Delta_{\bar{e}\bar{f}}(K')\,. + +This equation is valid for :math:`\lambda \leq 1` +and yields eigenvectors, which are superconducting gaps that have not manifested yet. At :math:`\lambda=1` the normal state breaks down and the superconducting state with the corresponding gap emerges. +The size of eigenvalues is therefore an indicator of how likely the associated gap is +to manifest. Superconducting state ^^^^^^^^^^^^^^^^^^^^^ For a calculation in the superconducting state we must extend the basis to accommodate Cooper-pairs. -In addition to the normal single-particle Green's function +In addition to the normal one-particle Green's function .. math:: G_{a\bar{b}}(\tau, \mathbf{r}) \equiv - - \langle \mathcal{T} c_{a}(\tau, \mathbf{r}) - c^\dagger_{\bar{b}}(0, \mathbf{0}) \rangle \,, + - \langle \mathcal{T} c_{a\uparrow}(\tau, \mathbf{r}) + c^\dagger_{\bar{b}\uparrow}(0, \mathbf{0}) \rangle \,, and its backwards propagating counterpart .. math:: \overline{G}_{\bar{a}b}(\tau, \mathbf{r}) \equiv - - \langle \mathcal{T} c^\dagger_{\bar{a}}(\tau, \mathbf{r}) - c_{b}(0, \mathbf{0}) \rangle\,, + - \langle \mathcal{T} c^\dagger_{\bar{a}\downarrow}(\tau, \mathbf{r}) + c_{b\downarrow}(0, \mathbf{0}) \rangle\,, -we have to introduce the single-particle anomalous Green's functions +we have to introduce the one-particle anomalous Green's functions :math:`F` and :math:`\overline{F}`. These are defined as .. math:: F_{ab}(\tau, \mathbf{r}) \equiv - \langle \mathcal{T} c_{a}(\tau, \mathbf{r}) - c_{b}(0, \mathbf{0}) \rangle + \langle \mathcal{T} c_{a\uparrow}(\tau, \mathbf{r}) + c_{b\downarrow}(0, \mathbf{0}) \rangle \,, and @@ -106,8 +114,8 @@ and .. math:: \overline{F}_{\bar{a}\bar{b}}(\tau, \mathbf{r}) \equiv - \langle \mathcal{T} c^\dagger_{\bar{a}}(\tau, \mathbf{r}) - c^\dagger_{\bar{b}}(0, \mathbf{0}) \rangle\,. + \langle \mathcal{T} c^\dagger_{\bar{a}\downarrow}(\tau, \mathbf{r}) + c^\dagger_{\bar{b}\uparrow}(0, \mathbf{0}) \rangle\,. Fourier transforming to Matsubara frequency and momentum space then gives that @@ -121,90 +129,170 @@ and .. math:: \overline{F}_{\bar{a}\bar{b}}(i\nu_n, \mathbf{k}) = - [F_{ab}(-i\nu_n, \mathbf{k}) ]^{*}\,. + [F_{ab}(i\nu_n, \mathbf{k}) ]^{\dagger}\,. :label: f_bar_to_f All four Green's functions are coupled and given by .. math:: \left( \begin{array}{cc} - G & F \\ - \overline{F} & \overline{G}\\ + \mathbf{G} & \mathbf{F} \\ + \overline{\mathbf{F}} & \overline{\mathbf{G}}\\ \end{array} \right) = \left( \begin{array}{cc} - \left(G^{(0)}\right)^{-1} - \Sigma & \Delta \\ - \overline{\Delta} & \left(\overline{G}^{(0)}\right)^{-1} - \overline{\Sigma} \\ + \left(\mathbf{G}^{(0)}\right)^{-1} - \mathbf{\Sigma} & \mathbf{\Delta} \\ + \overline{\mathbf{\Delta}} & \left(\overline{\mathbf{G}}^{(0)}\right)^{-1} - \overline{\mathbf{\Sigma}} \\ \end{array} \right)^{-1}\,, -where :math:`\Sigma` and :math:`\overline{\Sigma}` are the normal self-energies -and :math:`\Delta` and :math:`\overline{\Delta}` the anomalous ones, -which correspond to the gap function. - -The anomalous self-energy is given by +where :math:`\Sigma/\overline{\Sigma}` are the normal self-energies +and :math:`\Delta/\overline{\Delta}` the anomalous ones. +The anomalous self-energies are equivalent to the superconducting gap and are given by .. math:: - \Delta(K) + \Delta_{\bar{a}\bar{b}}(K) = - -\frac{1}{N_{\mathbf{k}} \beta} \sum_{K'} \Gamma^{PP}(Q=0, K, K') F(K')\,. + \frac{1}{2N_{\mathbf{k}} \beta} \sum_{K'} + \Gamma^{PP}_{c\bar{a}d\bar{b}}(Q=0, K, K') + F_{cd}(K')\,, :label: anomalous_self_energy -with - .. math:: - F(K) + \overline{\Delta}_{{a}{b}}(K) = - \frac{\Delta(K)} - {\left(\left(G^{(0)}(K)\right)^{-1}-\Sigma(K)\right) - \left(\left(G^{(0)}(K)\right)^{-1}-\Sigma(K)\right) - - - \overline{\Delta}(K) \Delta(K)}\,. - :label: f_explicit - -With this we could calculate the gap for the superconducting state -below :math:`T_\mathrm{c}`, -but note, that this is not that trivial, -because the self-energy :math:`\Sigma` is also coupled to :math:`\Delta`. -In the limit of :math:`\Delta \ll 1`, -i.e. linearizing Eq. :eq:`f_explicit`, -we also decouple the self-energy and -Eq. :eq:`anomalous_self_energy` becomes the the linearized Eliashberg equation. + \frac{1}{2N_{\mathbf{k}} \beta} \sum_{K'} + \Gamma^{PP}_{a\bar{c}b\bar{d}}(Q=0, K, K') + \overline{F}_{\bar{c}\bar{d}}(K')\,. + :label: anomalous_self_energy_2 + +With either of those equations we could calculate the gap for the superconducting state +below :math:`T_\mathrm{c}`. +But note, that this is not trivial, due to the coupling of the Green's functions and +self-energies. +In the limit close to :math:`T_\mathrm{c}` the superconducting gap is very small and +we can approximate the anomalous Green's function with + +.. math:: + \mathbf{F} = - + \left[\left(\mathbf{G}^{(0)}\right)^{-1} - \mathbf{\Sigma}\right]^{-1} + \mathbf{\Delta} + \left[\left(\mathbf{\overline{G}}^{(0)}\right)^{-1} - \mathbf{\overline{\Sigma}}\right]^{-1} + :label: approx_anomalous_gf + +Plugging this linearized version of the anomalouse Green's function in +Eq. :eq:`anomalous_self_energy` with the help of relation +Eq. :eq:`g_bar_to_g` yields the linearized Eliashberg equation +Eq. :eq:`linearized_eliashberg_1`. Relation to the BCS gap equation ----------------------------- +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -In BCS theory the particle-particle pairing vertex is considered to be +In BCS theory the particle-particle vertex is considered to be constant in a specific frequency range, which corresponds to gaps with the same dependence. -For this case the summation over fermionic Matsubara frequencies in -Eq. :eq:`linearized_eliashberg_2` can be done analytically +For this case the summation over fermionic Matsubara frequencies in the linearized +Eliashberg equation Eq. :eq:`linearized_eliashberg_1` can be done analytically. +For a one-band case and a non-interacting Green's function with dispersion relation +:math:`\epsilon`, this yields .. math:: - \lambda\Delta(\mathbf{k}) = -\frac{1}{2 N_{\mathbf{k}}}\sum_{\mathbf{k'}} + \Delta(\mathbf{k}) = -\frac{1}{2 N_{\mathbf{k}}}\sum_{\mathbf{k'}} \Gamma^{PP}(\mathbf{q}=\mathbf{0}, \mathbf{k}, \mathbf{k'}) \frac{\tan(\epsilon(\mathbf{k'})\beta/2)}{2\epsilon(\mathbf{k'})} - \Delta(\mathbf{k'})\,. + \Delta(\mathbf{k'})\,, :label: linearized_eliashberg_3 -Here we assumed a non-interacting Gree'ns function with dispersion relation -:math:`\epsilon`. -Eq. :eq:`linearized_eliashberg_3` corresponds to the linearized BCS gap -equation. -The BCS gap equation can be obtained from Eq. :eq:`linearized_eliashberg_3` +which corresponds to the linearized BCS gap equation. +The non-linear BCS gap equation can be obtained from Eq. :eq:`linearized_eliashberg_3` by substituting :math:`\epsilon` with :math:`\sqrt{\epsilon(\mathbf{k})^2 + |\Delta(\mathbf{k})|^2}`. -This is equivalent to using Eq. :eq:`anomalous_self_energy` -with a non-linearized anomalous Green's function :eq:`f_explicit`. + + +Details for applications +------------------------ + +SPOT Condition +^^^^^^^^^^^^^^ + +In the general case the superconducting gap function :math:`\Delta` is dependent on +momentum :math:`\mathbf{k}`, fermionic Matsubara frequency :math:`i\nu_n`, +orbital-indices :math:`a,b` and spin-indices :math:`\alpha,\beta` + +.. math:: + \Delta \equiv \Delta_{a\alpha;b\beta}(i\nu, \mathbf{k})\,. + +Because the Pauli principle dictates :math:`\Delta` to be odd under particle exchange, +the symmetry combinations of those four degrees of freedom are constrained. +This is formalized as the so called :math:`SPOT` condition + +.. math:: + \hat{S}\hat{P}\hat{O}\hat{T} \Delta_{a\alpha;b\beta}(i\nu, \mathbf{k}) + = + - \Delta_{b\beta;a\alpha}(-i\nu, -\mathbf{k})\,, + +with the operators :math:`\hat{S}`, :math:`\hat{P}`, :math:`\hat{O}`, :math:`\hat{T}`, +that denote permutation of electrons in spin space (:math:`\hat{S}`), +real space (parity) (:math:`\hat{P}`), +orbital space (:math:`\hat{O}`), and time (frequency) (:math:`\hat{T}`). +While :math:`\Delta` has to be odd under the combined action of the symmetry operations +:math:`\hat{S}\hat{P}\hat{O}\hat{T}`, +it can be either even (:math:`+`) or odd (:math:`-`) under each separate operation, +i.e. + +.. math:: + \hat{S}\Delta_{a\alpha;b\beta}(i\nu, \mathbf{k}) + &= + \pm \Delta_{a\beta;b\alpha}(i\nu, \mathbf{k})\,,\\ + \hat{P}\Delta_{a\alpha;b\beta}(i\nu, \mathbf{k}) + &= + \pm \Delta_{a\alpha;b\beta}(i\nu, -\mathbf{k})\,,\\ + \hat{O}\Delta_{a\alpha;b\beta}(i\nu, \mathbf{k}) + &= + \pm \Delta_{b\alpha;a\beta}(i\nu, \mathbf{k})\,,\\ + \hat{T}\Delta_{a\alpha;b\beta}(i\nu, \mathbf{k}) + &= + \pm \Delta_{a\alpha;b\beta}(-i\nu, \mathbf{k})\,. + +A gap function can therefore be classified as even (:math:`+`) or odd (:math:`-`) +under these four degrees of freedom. We list all eight possible combinations +in the table below: + +.. table:: + :align: center + :widths: grid + + +-----------------+-----------------+-----------------+-----------------+ + | S | P | O | T | + +=================+=================+=================+=================+ + | :math:`-` | :math:`+` | :math:`+` | :math:`+` | + +-----------------+-----------------+-----------------+-----------------+ + | :math:`-` | :math:`-` | :math:`-` | :math:`+` | + +-----------------+-----------------+-----------------+-----------------+ + | :math:`-` | :math:`-` | :math:`+` | :math:`-` | + +-----------------+-----------------+-----------------+-----------------+ + | :math:`-` | :math:`+` | :math:`-` | :math:`-` | + +-----------------+-----------------+-----------------+-----------------+ + | :math:`+` | :math:`-` | :math:`-` | :math:`-` | + +-----------------+-----------------+-----------------+-----------------+ + | :math:`+` | :math:`+` | :math:`+` | :math:`-` | + +-----------------+-----------------+-----------------+-----------------+ + | :math:`+` | :math:`+` | :math:`-` | :math:`+` | + +-----------------+-----------------+-----------------+-----------------+ + | :math:`+` | :math:`-` | :math:`+` | :math:`+` | + +-----------------+-----------------+-----------------+-----------------+ + +Because all other combinations are unphysical it is possible to restrict the gap to the +allowed symmetries while solving the linearized Eliashberg equation. + Spin diagonalization --------------------- +^^^^^^^^^^^^^^^^^^^^ -All objects above were formulated with combined spin and orbital indices. For :math:`SU(2)` symmetric systems we can drop the spin dependency by diagonalizing everything in spin. This diagonalization splits the superconducting gap :math:`\Delta` in two channels, -singlet +the singlet channel .. math:: \Delta^{\mathrm{s}} @@ -213,7 +301,7 @@ singlet - \Delta_{\downarrow\uparrow}\,, -and triplet +and triplet channel .. math:: \Delta^{\mathrm{t}} @@ -293,22 +381,25 @@ while suppressing frequency, momentum and orbital indices, yields GG \Delta^{\mathrm{s}}\,. -This is analog for the triplet channel and we obtain for the spin diagonalized +This is analog for the triplet channel and we obtain the spin diagonalized linearized Eliashberg equation .. math:: - \lambda\Delta^{\mathrm{s/t}}(K) = -\frac{1}{2 N_{\mathbf{k}}\beta}\sum_{K'} - \Gamma^{\mathrm{s/t}}(Q=0, K, K') - G(K')G(-K') - \Delta^{\mathrm{s/t}}(K')\,. + \lambda\Delta^{\mathrm{s/t}}_{\bar{a}\bar{b}}(K)= -\frac{1}{2 N_{\mathbf{k}}\beta}\sum_{K'} + \Gamma^{\mathrm{s/t}}_{c\bar{a}d\bar{b}}(Q=0, K, K') + G_{c\bar{e}}(K')G_{d\bar{f}}(-K') + \Delta^{\mathrm{s/t}}_{\bar{e}\bar{f}}(K')\,, :label: linearized_eliashberg_4 -Random phase approximation for the irreducible particle-particle vertex ------------------------------------------------------------------------ +with all indices being only orbital ones. -To obtain the irreducible particle-particle vertex in the RPA +Random phase approximation for the spin diagonalized irreducible particle-particle vertex +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +To obtain the spin diagonalized irreducible particle-particle vertex in the +random phase approximation (RPA) one substitutes all vertices with the bare one in the parquet equation. -In the spin diagonalized form this yields for the singlet +This yields for the singlet channel .. math:: \Gamma^{\mathrm{s}}_{a\bar{b}c\bar{d}}(Q=0, K, K') @@ -330,7 +421,7 @@ In the spin diagonalized form this yields for the singlet U^{\mathrm{s}}_{a\bar{b}c\bar{d}}\,, :label: singlet_gamma -and for the triplet +and for the triplet channel .. math:: \Gamma^{\mathrm{t}}_{a\bar{b}c\bar{d}}(Q=0, K, K') @@ -355,13 +446,16 @@ and for the triplet with .. math:: - \Phi^{\mathrm{d/m}}_{a\bar{b}c\bar{d}}(Q) + \Phi^{\mathrm{d/m}}_{a\bar{b}c\bar{d}} \equiv - U^{\mathrm{d/m}}\chi^{\mathrm{d/m}}(Q)U^{\mathrm{d/m}}\,. + U_{a\bar{b}e\bar{f}}^{\mathrm{d/m}} + \chi_{\bar{f}e\bar{g}h}^{\mathrm{d/m}}(Q) + U^{\mathrm{d/m}}_{h\bar{g}c\bar{d}} + \,. Note, that the superscripts :math:`\mathrm{d}` and :math:`\mathrm{m}` indicate the density and magnetic channel. -The bare vertex in its respective channel is given by +Here :math:`U^{\mathrm{d/m}}` is the bare local Kanamori interaction given by .. math:: U^{\mathrm{d/m}}_{a\bar{b}c\bar{d}} = @@ -371,10 +465,11 @@ The bare vertex in its respective channel is given by 2U'-J/J, & \mathrm{if}\;a=\bar{b}\neq c=\bar{d} \\ J/J, & \mathrm{if}\;a=c\neq \bar{b}=\bar{d} \\ 0, & \mathrm{else} - \end{cases}\,. + \end{cases}\,, + +with the Hubbard interaction :math:`U` and the Hund's :math:`J`. -For an implementation prespective we must note, -that in both singlet :eq:`singlet_gamma` and +Note, that in both singlet :eq:`singlet_gamma` and triplet :eq:`triplet_gamma` a density and magnetic :math:`\Phi` term appears twice. Once without an index flip and a dependence on :math:`K-K'`, @@ -385,32 +480,54 @@ Inside the linearized Eliashberg equation :eq:`linearized_eliashberg_4` the :math:`\Phi_{c\overline{b}a\overline{d}}(K+K')` term picks up a sign which depends on the frequency, momentum and orbital symmetry of the gap :math:`\Delta`. -For a singlet gap this yields a plus and for a triplet a minus. -Therefore the terms just add up and we lose the factor :math:`1/2` in front of -the square brackets in Eq. :eq:`singlet_gamma` and :eq:`triplet_gamma`. +For all allowed singlet combinations it is positive and for all allowed triplet ones +negative. Therefore Eq. :eq:`singlet_gamma` and Eq. :eq:`triplet_gamma` become + +.. math:: + \Gamma^{\text{s}}_{a\overline{b}c\overline{d}}(Q=0, K, K') \equiv + \Lambda^{\text{s}}_{a\overline{b}c\overline{d}} + + + 3 + \Phi^{\text{m}}_{a\overline{b}c\overline{d}}(K-K') + - + \Phi^{\text{d}}_{a\overline{b}c\overline{d}}(K-K') + \,, + :label: singlet_gamma_2 + +.. math:: + \Gamma^{\text{t}}_{a\overline{b}c\overline{d}}(Q=0, K, K') \equiv + \Lambda^{\text{t}}_{a\overline{b}c\overline{d}} + - + \Phi^{\text{m}}_{a\overline{b}c\overline{d}}(K-K') + - + \Phi^{\text{d}}_{a\overline{b}c\overline{d}}(K-K') + \,. + :label: triplet_gamma_2 +Note, that this simplification is only allowed, if the solutions of :math:`\Delta` +are restricted to the allowed symmetries, otherwise unphysical solution can occur. Also note, that the RPA particle-particle vertices in -Eq. :eq:`singlet_gamma` and :eq:`triplet_gamma` only depend on the difference +Eq. :eq:`singlet_gamma_2` and :eq:`triplet_gamma_2` only depend on the difference between the two fermionic Matsubara frequencies and momenta. We can therefore write the linearized Eliashberg equation :eq:`linearized_eliashberg_4` as .. math:: - \lambda\Delta^{\mathrm{s/t}}(K) = -\frac{1}{2 N_{\mathbf{k}}\beta}\sum_{K'} - \Gamma^{\mathrm{s/t}}(K-K') - G(K')G(-K') - \Delta^{\mathrm{s/t}}(K')\,. + \lambda\Delta^{\mathrm{s/t}}_{\bar{a}\bar{b}}(K)= -\frac{1}{2 N_{\mathbf{k}}\beta}\sum_{K'} + \Gamma^{\mathrm{s/t}}_{c\bar{a}d\bar{b}}(K-K') + G_{c\bar{e}}(K')G_{d\bar{f}}(-K') + \Delta^{\mathrm{s/t}}_{\bar{e}\bar{f}}(K')\,. :label: linearized_eliashberg_5 This allows us to get rid of the summation by using the convolution theorem .. math:: \lambda - \mathcal{F}\left[\Delta^{\mathrm{s/t}}(K)\right]= -\frac{1}{2} - \mathcal{F}\left[\Gamma^{\mathrm{s/t}}(K-K')\right] + \mathcal{F}\left[\Delta_{\bar{a}\bar{b}}^{\mathrm{s/t}}(K)\right]= -\frac{1}{2} + \mathcal{F}\left[\Gamma_{c\bar{a}d\bar{b}}^{\mathrm{s/t}}(K-K')\right] \mathcal{F}\left[ - G(K')G(-K') - \Delta^{\mathrm{s/t}}(K') + G_{c\bar{e}}(K')G_{d\bar{f}}(-K') + \Delta_{\bar{e}\bar{f}}^{\mathrm{s/t}}(K') \right]\,, :label: linearized_eliashberg_5 @@ -418,16 +535,10 @@ making the calculation computationaly more efficient. .. rubric:: References -.. [#abrikosov] A.A. Abrikosov, L.P. Gor’kov, et.al., Pergamon, Oxford (1965) - -.. [#yanase] Yanase, et. al., Physics Reports 387, 1-149 (2003) - -.. [#takimoto] Takimoto, et. al., PRB 69, 104504 (2004) - -.. [#bickers] Bickers, N. E. Self-Consistent Many-Body Theory for Condensed Matter Systems. Theoretical Methods for Strongly Correlated Electrons, 237–296. 6, (2006) - -.. [#rohringer] Rohringer, G., New routes towards a theoretical treatment of nonlocal electronic correlations, (2013) - -.. [#nourafkan] R. Nourafkan, G. Kotliar, and A. M. Tremblay, Physical Review Letters 117, 1, (Supplementary), (2016) - - +.. [#abrikosov] A. A. Abrikosov, L. P. Gor’kov, and I. E. Dzyaloshinski, Pergamon, Oxford (1965) +.. [#yanase] Y. Yanase, T. Jujo, T. Nomura, et. al., Physics Reports 387, 1-149 (2003) +.. [#takimoto] T. Takimoto, T. Hotta, and K. Ueda, PRB 69, 104504 (2004) +.. [#bickers] N. E. Bickers, Self-Consistent Many-Body Theory for Condensed Matter Systems. Theoretical Methods for Strongly Correlated Electrons, 237–296. 6 (2006) +.. [#rohringer] G. Rohringer, New routes towards a theoretical treatment of nonlocal electronic correlations (2013) +.. [#nourafkan] R. Nourafkan, G. Kotliar, and A. M. Tremblay, Physical Review Letters 117, 1, (Supplementary) (2016) +.. [#linder] J. Linder and A. V. Balatsky, Reviews of Modern Physics 91, 45005 (2019) From d9807750679221c086350bdce352e54429d40687 Mon Sep 17 00:00:00 2001 From: Stefan Date: Tue, 11 Aug 2020 09:16:21 +0200 Subject: [PATCH 057/121] [eli] remove old print outs --- python/triqs_tprf/eliashberg.py | 2 -- 1 file changed, 2 deletions(-) diff --git a/python/triqs_tprf/eliashberg.py b/python/triqs_tprf/eliashberg.py index 93c751c50..07d400e3e 100644 --- a/python/triqs_tprf/eliashberg.py +++ b/python/triqs_tprf/eliashberg.py @@ -319,7 +319,6 @@ def power_method(init, offset=0.0, tol=tol, max_it=max_it): it = 1 while True: norm, new_v_k = iteration(v_k, offset) - print(norm) # -- Convergence criterion add = np.max(np.abs(v_k + new_v_k)) @@ -380,7 +379,6 @@ def allclose_by_scalar_multiplication(delta_1, delta_2, atol=1e-10): try: division_of_deltas = np.divide(delta_1_arr, delta_2_arr) except ValueError: # Arrays do not contain the same # of zeroes and are therefore not equal - print('FUUUCK') return False # Check if elements share common scalar factor From 6932661619fe8b4503690f60166d6f0574ca45a9 Mon Sep 17 00:00:00 2001 From: Stefan Date: Tue, 11 Aug 2020 09:43:59 +0200 Subject: [PATCH 058/121] [eli] reorder functions + add docstrings --- python/triqs_tprf/eliashberg.py | 235 +++++++++++++++++++------------- 1 file changed, 137 insertions(+), 98 deletions(-) diff --git a/python/triqs_tprf/eliashberg.py b/python/triqs_tprf/eliashberg.py index 07d400e3e..00e90cd63 100644 --- a/python/triqs_tprf/eliashberg.py +++ b/python/triqs_tprf/eliashberg.py @@ -36,104 +36,8 @@ # ---------------------------------------------------------------------- -def split_into_dynamic_wk_and_constant_k(Gamma_pp_wk): - Gamma_pp_dyn_wk = get_dynamic_wk(Gamma_pp_wk) - Gamma_pp_const_k = get_constant_k(Gamma_pp_wk) - return Gamma_pp_dyn_wk, Gamma_pp_const_k - -def dynamic_and_constant_to_tr(Gamma_pp_dyn_wk, Gamma_pp_const_k): - Gamma_pp_dyn_tr = dynamic_to_tr(Gamma_pp_dyn_wk) - Gamma_pp_const_r = constant_to_r(Gamma_pp_const_k) - return Gamma_pp_dyn_tr, Gamma_pp_const_r - -def semi_random_initial_delta(g_wk, nr_factor=0.5, seed=None): - - r"""Create a delta based on the GF with random elements - - Returns an anomalous self-energy that can be used as an inital input for the iterative - solvers. The momentum space is random, while the Matsubara space is only partialy - randomized to ensure working tail fits for the Fourier transformations. - - Parameters - ---------- - g_wk : Gf, - Green's function :math:`G(i\nu_n, \mathbf{k})`. The mesh attribute of the Gf must - be a MeshProduct with the components (MeshImFreq, MeshBrillouinZone). - nr_factor : float, optional - Percentage of :math:`\omega` points which shall not be randomized. This is needed - to assure a working tail fit for the Fourier transformations. The default is 0.5, - meaning that 50% of the :math:`\omega` points will not be randomized. - seed : int, optional - Set a np.random.seed to enforce predictable results. - - Returns - ------- - delta : Gf, - An initial anomalous self-energy :math:`\Delta(i\nu_n, \mathbf{k})` to start - an iterative solver, given as a Gf with MeshProduct with the components - (MeshImFreq, MeshBrillouinZone). - """ - - np.random.seed(seed) - - delta = g_wk.copy() - shape = delta.data.shape - delta.data[:] = delta.data.real # Pure real delta is sufficient w/o magnetic field - random_data = np.random.random(shape[1:]) - freq_data = np.mean(np.abs(delta.data), axis=tuple(range(len(shape))[1:])) - not_randomized = int(nr_factor*shape[0] / 2.) - start, stop = not_randomized, shape[0]-not_randomized - freq_data[start:stop] *= np.random.random(stop-start) - - delta.data[:] = np.tensordot(freq_data, random_data, axes=0) - - return delta - -def preprocess_gamma_for_fft(Gamma_pp_wk, Gamma_pp_const_k=None): - r""" Prepare Gamma to be used with the FFT implementation - - Parameters - ---------- - Gamma_pp_wk : Gf, - Pairing vertex :math:`\Gamma(i\omega_n, \mathbf{k})`. The mesh attribute of - the Gf must be a MeshProduct with the components (MeshImFreq, MeshBrillouinZone). - Gamma_pp_const_k : float or np.ndarray or Gf - Part of the pairing vertex that is constant in Matsubara frequency space - :math:`\Gamma(\mathbf{k})`. If given as a Gf its mesh attribute needs to - be a MeshBrillouinZone. - - Returns - ------- - Gamma_pp_dyn_tr : Gf, - The dynamic part of Gamma, which converges to zero for - :math:`\omega_n \rightarrow \infty`, but now in :math:`\tau`-space. - Its mesh attribute is MeshProduct with the components - (MeshImTime, MeshCyclicLattice). - Gamma_pp_const_r : Gf, - The constant part of Gamma with mesh attribute MeshCyclicLattice. - """ - - # -- Determine the dynamic and constant part via a tail fit - # -- (This is done even if the constant term is given to get the specific Gf types) - Gamma_pp_dyn_wk_fit, Gamma_pp_const_k_fit = split_into_dynamic_wk_and_constant_k(Gamma_pp_wk) - - # -- Use a constant term if explicitly given - const_type = type(Gamma_pp_const_k) - if (const_type == float) or (const_type == np.ndarray): - Gamma_pp_const_k_fit.data[:] = Gamma_pp_const_k - Gamma_pp_dyn_wk_fit.data[:] = Gamma_pp_wk.data - Gamma_pp_const_k - elif (const_type == Gf): - Gamma_pp_const_k_fit[:] = Gamma_pp_const_k.data - Gamma_pp_dyn_wk_fit.data[:] = Gamma_pp_wk.data - Gamma_pp_const_k.data - # -- FFT dynamic and constant term to (tau, real) or (real) - Gamma_pp_dyn_tr, Gamma_pp_const_r = dynamic_and_constant_to_tr(Gamma_pp_dyn_wk_fit, - Gamma_pp_const_k_fit) - - return Gamma_pp_dyn_tr, Gamma_pp_const_r - def solve_eliashberg(Gamma_pp_wk, g_wk, initial_delta=None, Gamma_pp_const_k=None, tol=1e-10, product='FFT', solver='PM', symmetrize_fct=lambda x : x): - r""" Solve the linearized Eliashberg equation Returns the biggest eigenvalues and corresponding eigenvectors of the linearized Eliashberg @@ -249,8 +153,144 @@ def matvec(delta_x): return es, eigen_modes -def implicitly_restarted_arnoldi_method(matvec, init, tol=1e-10): +def preprocess_gamma_for_fft(Gamma_pp_wk, Gamma_pp_const_k=None): + r""" Prepare Gamma to be used with the FFT implementation + + Parameters + ---------- + Gamma_pp_wk : Gf, + Pairing vertex :math:`\Gamma(i\omega_n, \mathbf{k})`. The mesh attribute of + the Gf must be a MeshProduct with the components (MeshImFreq, MeshBrillouinZone). + Gamma_pp_const_k : float or np.ndarray or Gf + Part of the pairing vertex that is constant in Matsubara frequency space + :math:`\Gamma(\mathbf{k})`. If given as a Gf its mesh attribute needs to + be a MeshBrillouinZone. + + Returns + ------- + Gamma_pp_dyn_tr : Gf, + The dynamic part of Gamma, which converges to zero for + :math:`\omega_n \rightarrow \infty`, but now in :math:`\tau`-space. + Its mesh attribute is MeshProduct with the components + (MeshImTime, MeshCyclicLattice). + Gamma_pp_const_r : Gf, + The constant part of Gamma with mesh attribute MeshCyclicLattice. + """ + + # -- Determine the dynamic and constant part via a tail fit + # -- (This is done even if the constant term is given to get the specific Gf types) + Gamma_pp_dyn_wk_fit, Gamma_pp_const_k_fit = split_into_dynamic_wk_and_constant_k(Gamma_pp_wk) + + # -- Use a constant term if explicitly given + const_type = type(Gamma_pp_const_k) + if (const_type == float) or (const_type == np.ndarray): + Gamma_pp_const_k_fit.data[:] = Gamma_pp_const_k + Gamma_pp_dyn_wk_fit.data[:] = Gamma_pp_wk.data - Gamma_pp_const_k + elif (const_type == Gf): + Gamma_pp_const_k_fit[:] = Gamma_pp_const_k.data + Gamma_pp_dyn_wk_fit.data[:] = Gamma_pp_wk.data - Gamma_pp_const_k.data + # -- FFT dynamic and constant term to (tau, real) or (real) + Gamma_pp_dyn_tr, Gamma_pp_const_r = dynamic_and_constant_to_tr(Gamma_pp_dyn_wk_fit, + Gamma_pp_const_k_fit) + + return Gamma_pp_dyn_tr, Gamma_pp_const_r + +def split_into_dynamic_wk_and_constant_k(Gamma_pp_wk): + r""" Split Gamma by tail fitting constant part in frequency + + Parameters + ---------- + Gamma_pp_wk : Gf, + Pairing vertex :math:`\Gamma(i\omega_n, \mathbf{k})`. The mesh attribute of + the Gf must be a MeshProduct with the components (MeshImFreq, MeshBrillouinZone). + + Returns + ------- + Gamma_pp_dyn_wk : Gf, + The dynamic part of Gamma, which converges to zero for + :math:`\omega_n \rightarrow \infty`. + Its mesh attribute is MeshProduct with the components + (MeshImFreq, MeshBrillouinZone). + Gamma_pp_const_k : Gf, + Part of the pairing vertex that is constant in Matsubara frequency space + :math:`\Gamma(\mathbf{k})`. Returned as a Gf with mesh attribute + MeshBrillouinZone. + """ + Gamma_pp_dyn_wk = get_dynamic_wk(Gamma_pp_wk) + Gamma_pp_const_k = get_constant_k(Gamma_pp_wk) + return Gamma_pp_dyn_wk, Gamma_pp_const_k + +def dynamic_and_constant_to_tr(Gamma_pp_dyn_wk, Gamma_pp_const_k): + r""" Fourier transform Gamma parts to imaginary time and real-space + + Parameters + ---------- + Gamma_pp_dyn_wk : Gf, + The dynamic part of Gamma, which converges to zero for + :math:`\omega_n \rightarrow \infty`. + Its mesh attribute is MeshProduct with the components + (MeshImFreq, MeshBrillouinZone). + Gamma_pp_const_k : Gf, + Part of the pairing vertex that is constant in Matsubara frequency space + :math:`\Gamma(\mathbf{k})`. Its mesh attribute is MeshBrillouinZone. + Returns + ------- + Gamma_pp_dyn_tr : Gf, + The dynamic part of Gamma, which converges to zero for + :math:`\omega_n \rightarrow \infty`, but now in :math:`\tau`-space. + Its mesh attribute is MeshProduct with the components + (MeshImTime, MeshCyclicLattice). + Gamma_pp_const_r : Gf, + The constant part of Gamma with mesh attribute MeshCyclicLattice. + """ + Gamma_pp_dyn_tr = dynamic_to_tr(Gamma_pp_dyn_wk) + Gamma_pp_const_r = constant_to_r(Gamma_pp_const_k) + return Gamma_pp_dyn_tr, Gamma_pp_const_r + +def semi_random_initial_delta(g_wk, nr_factor=0.5, seed=None): + r"""Create a delta based on the GF with random elements + + Returns an anomalous self-energy that can be used as an inital input for the iterative + solvers. The momentum space is random, while the Matsubara space is only partialy + randomized to ensure working tail fits for the Fourier transformations. + + Parameters + ---------- + g_wk : Gf, + Green's function :math:`G(i\nu_n, \mathbf{k})`. The mesh attribute of the Gf must + be a MeshProduct with the components (MeshImFreq, MeshBrillouinZone). + nr_factor : float, optional + Percentage of :math:`\omega` points which shall not be randomized. This is needed + to assure a working tail fit for the Fourier transformations. The default is 0.5, + meaning that 50% of the :math:`\omega` points will not be randomized. + seed : int, optional + Set a np.random.seed to enforce predictable results. + + Returns + ------- + delta : Gf, + An initial anomalous self-energy :math:`\Delta(i\nu_n, \mathbf{k})` to start + an iterative solver, given as a Gf with MeshProduct with the components + (MeshImFreq, MeshBrillouinZone). + """ + + np.random.seed(seed) + + delta = g_wk.copy() + shape = delta.data.shape + delta.data[:] = delta.data.real # Pure real delta is sufficient w/o magnetic field + random_data = np.random.random(shape[1:]) + freq_data = np.mean(np.abs(delta.data), axis=tuple(range(len(shape))[1:])) + not_randomized = int(nr_factor*shape[0] / 2.) + start, stop = not_randomized, shape[0]-not_randomized + freq_data[start:stop] *= np.random.random(stop-start) + + delta.data[:] = np.tensordot(freq_data, random_data, axes=0) + + return delta + +def implicitly_restarted_arnoldi_method(matvec, init, tol=1e-10): """Find the eigenvalue with the largest real value via the Implicitly Restarted Arnoldi Method @@ -285,7 +325,6 @@ def implicitly_restarted_arnoldi_method(matvec, init, tol=1e-10): return list(Es), list(U.T) def power_method_LR(matvec, init, tol=1e-10, max_it=1e5): - """Find the eigenvalue with the largest real value via the power method Parameters From 418cf0ed13e0887be6087b2af85dbd41a5c4def3 Mon Sep 17 00:00:00 2001 From: Stefan Date: Tue, 11 Aug 2020 10:20:47 +0200 Subject: [PATCH 059/121] [eli] update test headers --- test/python/eliashberg/eigenvalue_solver.py | 5 +++-- test/python/eliashberg/fft_product_constant_vs_full.py | 6 +++--- test/python/eliashberg/previous_implementation.py | 1 - test/python/eliashberg/symmetrize_delta.py | 1 - 4 files changed, 6 insertions(+), 7 deletions(-) diff --git a/test/python/eliashberg/eigenvalue_solver.py b/test/python/eliashberg/eigenvalue_solver.py index 7bbefdb49..c8881b2bf 100644 --- a/test/python/eliashberg/eigenvalue_solver.py +++ b/test/python/eliashberg/eigenvalue_solver.py @@ -1,7 +1,8 @@ # ---------------------------------------------------------------------- -""" Compare the summation implementation of the linearized Eliashberg product -and the one using Fourier transformations. +""" Compare the output of the implemented eigenvalue solver: +The Power Method and the Implicitly Restarted Arnoldi Method. + """ # ---------------------------------------------------------------------- diff --git a/test/python/eliashberg/fft_product_constant_vs_full.py b/test/python/eliashberg/fft_product_constant_vs_full.py index 558bc7f80..904acfeec 100644 --- a/test/python/eliashberg/fft_product_constant_vs_full.py +++ b/test/python/eliashberg/fft_product_constant_vs_full.py @@ -2,9 +2,9 @@ """ Compare the implementations of the eliashberg products that use FFT. -One can only handle Gammas that are constant in frequecny space while the -other can also treat dynamic Gammas. -Here we test if bot implementations give the same result for a Gamma that +The function `eliashberg_product_fft_constant` can only handle Gammas that are +constant in frequecny space, while `eliashberg_product_fft` can treat dynamic Gammas. +Here we test if both implementations give the same result for a Gamma that is constant in momentum space. This also tests the function 'split_into_dynamic_wk_and_constant_k', to see if the split is done correctly. diff --git a/test/python/eliashberg/previous_implementation.py b/test/python/eliashberg/previous_implementation.py index 0b7238604..0b0883854 100644 --- a/test/python/eliashberg/previous_implementation.py +++ b/test/python/eliashberg/previous_implementation.py @@ -1,4 +1,3 @@ - # ---------------------------------------------------------------------- """ Goes through the steps of solving the linearized Eliashberg equation for singlet pairing in diff --git a/test/python/eliashberg/symmetrize_delta.py b/test/python/eliashberg/symmetrize_delta.py index 1492c9c23..90e11a950 100644 --- a/test/python/eliashberg/symmetrize_delta.py +++ b/test/python/eliashberg/symmetrize_delta.py @@ -1,4 +1,3 @@ - # ---------------------------------------------------------------------- """ Test the symmetrizing feature of the solve_eliashberg function From 362c727d8902a231fef42e6018273fd02d2dc243 Mon Sep 17 00:00:00 2001 From: Stefan Date: Tue, 11 Aug 2020 10:21:05 +0200 Subject: [PATCH 060/121] [eli] reduce model size to speed up execution --- test/python/eliashberg/eigenvalue_solver.py | 2 +- test/python/eliashberg/product_summation_vs_fft.py | 4 ++-- test/python/eliashberg/symmetrize_delta.py | 2 +- 3 files changed, 4 insertions(+), 4 deletions(-) diff --git a/test/python/eliashberg/eigenvalue_solver.py b/test/python/eliashberg/eigenvalue_solver.py index c8881b2bf..ae380263f 100644 --- a/test/python/eliashberg/eigenvalue_solver.py +++ b/test/python/eliashberg/eigenvalue_solver.py @@ -97,7 +97,7 @@ def run_solve_eliashberg(p): J = 0.1, Jp = 0.1, nk = 4, - nw = 350, + nw = 200, fit_const = False, big_factor = 2, product = 'FFT', diff --git a/test/python/eliashberg/product_summation_vs_fft.py b/test/python/eliashberg/product_summation_vs_fft.py index 0ff7891f7..e5eb657e7 100644 --- a/test/python/eliashberg/product_summation_vs_fft.py +++ b/test/python/eliashberg/product_summation_vs_fft.py @@ -192,8 +192,8 @@ def compare_next_delta(p): Up = 0.8, J = 0.1, Jp = 0.1, - nk = 4, - nw = 200, + nk = 3, + nw = 150, nr_factor = 0.5, fit_const = False, big_factor = 2, diff --git a/test/python/eliashberg/symmetrize_delta.py b/test/python/eliashberg/symmetrize_delta.py index 90e11a950..b51bd51b2 100644 --- a/test/python/eliashberg/symmetrize_delta.py +++ b/test/python/eliashberg/symmetrize_delta.py @@ -47,7 +47,7 @@ Up = 0.8, J = 0.1, Jp = 0.1, - nk = 4, + nk = 3, nw = 50, plot=False ) From 9d4900a628d4ee649f6a1a41cc199e08fdf18bc7 Mon Sep 17 00:00:00 2001 From: Stefan Date: Tue, 11 Aug 2020 14:55:27 +0200 Subject: [PATCH 061/121] [eli] refactor model creation of tests --- python/triqs_tprf/tight_binding.py | 24 +++++++++++++++ test/python/eliashberg/eigenvalue_solver.py | 19 +++--------- .../eliashberg/eliashberg_benchmark.tar.gz | Bin 30029 -> 27763 bytes .../eliashberg_benchmark_two_band.tar.gz | Bin 107519 -> 110627 bytes .../fft_product_constant_vs_full.py | 5 ++-- .../eliashberg/previous_implementation.py | 22 +++++--------- .../previous_implementation_two_band.py | 25 +++++----------- .../eliashberg/product_summation_vs_fft.py | 24 ++++----------- test/python/eliashberg/symmetrize_delta.py | 28 ++++++------------ 9 files changed, 60 insertions(+), 87 deletions(-) diff --git a/python/triqs_tprf/tight_binding.py b/python/triqs_tprf/tight_binding.py index 609adf84a..155e678a2 100644 --- a/python/triqs_tprf/tight_binding.py +++ b/python/triqs_tprf/tight_binding.py @@ -21,6 +21,8 @@ # ################################################################################ +import itertools + import numpy as np from pytriqs.lattice.lattice_tools import BrillouinZone as BrillouinZone @@ -201,3 +203,25 @@ def create_square_lattice(norb, t, tp=0.0, zeeman=0.0, spin=False, **kwargs): square_lattice = TBLattice(units, hopping, orbital_positions) return square_lattice + +# ---------------------------------------------------------------------- +def create_model_for_tests(norb, dim, t=0, t1=0, t2=0, t12=0, t21=0, **kwargs): + full_units = [(1, 0, 0), (0, 1, 0), (0, 0, 1)] + units = full_units[:dim] + + if norb == 1: + t_matrix = -t * np.eye(norb) + elif norb == 2: + t_matrix = -np.array([[t1, t12], [t21, t2]]) + else: + raise NotImplementedError + + all_nn_hoppings = list(itertools.product([-1, 0, 1], repeat=dim)) + non_diagonal_hoppings = [hopping for hopping in all_nn_hoppings if sum(np.abs(hopping)) == 1] + hoppings = {hopping : t_matrix for hopping in non_diagonal_hoppings} + + orbital_positions = [(0, 0, 0)] * norb + + model_for_tests = TBLattice(units, hoppings, orbital_positions) + + return model_for_tests diff --git a/test/python/eliashberg/eigenvalue_solver.py b/test/python/eliashberg/eigenvalue_solver.py index ae380263f..47fec8c69 100644 --- a/test/python/eliashberg/eigenvalue_solver.py +++ b/test/python/eliashberg/eigenvalue_solver.py @@ -18,7 +18,7 @@ from triqs_tprf.ParameterCollection import ParameterCollection from pytriqs.gf import Gf, MeshImFreq, Idx -from triqs_tprf.tight_binding import TBLattice +from triqs_tprf.tight_binding import create_model_for_tests from triqs_tprf.lattice import lattice_dyson_g0_wk, solve_rpa_PH from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk @@ -33,18 +33,7 @@ def run_solve_eliashberg(p): # -- Setup model, RPA susceptibilities and spin/charge interaction - full_units = [(1, 0, 0), (0, 1, 0), (0, 0, 1)] - all_nn_hoppings = list(itertools.product([-1, 0, 1], repeat=p.dim)) - non_diagonal_hoppings = [ele for ele in all_nn_hoppings if sum(np.abs(ele)) == 1] - - t = -p.t * np.eye(p.norbs) - - H = TBLattice( - units = full_units[:p.dim], - hopping = {hop : t for hop in non_diagonal_hoppings}, - orbital_positions = [(0,0,0)]*p.norbs, - ) - + H = create_model_for_tests(**p) e_k = H.on_mesh_brillouin_zone(n_k=[p.nk]*p.dim + [1]*(3-p.dim)) # A bigger w-mesh is needed to construct a Gamma with a twice as big w-mesh than GF @@ -58,7 +47,7 @@ def run_solve_eliashberg(p): chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw) chi0_wk_big = imtime_bubble_chi0_wk(g0_wk_big, nw=int(p.big_factor*p.nw)+1) - U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norbs, p.U, p.Up, p.J,p.Jp) + U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norb, p.U, p.Up, p.J,p.Jp) chi_s = solve_rpa_PH(chi0_wk, U_s) chi_c = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation @@ -88,7 +77,7 @@ def run_solve_eliashberg(p): p = ParameterCollection( dim = 1, - norbs = 1, + norb = 1, t = 1.0, mu = 0.0, beta = 5, diff --git a/test/python/eliashberg/eliashberg_benchmark.tar.gz b/test/python/eliashberg/eliashberg_benchmark.tar.gz index 6ebe387f5d952aa847c5a6f9b4e302246d0c74c0..0a7be411b0a4ba2f475def43d44c4ea46dfbc65c 100644 GIT binary patch literal 27763 zcmZ5`bzIZo+pdU!iim=MAP*-5a5Vl2X!0h~y{%fo*h2*XR+F 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z4LA{+sJeUWdX3@z#1xTzz&+5)sE;YsJGIL@A1K<(c%DybP@1=WlF8E{-93U`{1<02 z=Ca@f!hoVL9o@hmmyZ@iOHdv@v0Opm?=M-ZEI!8MNsFN=C0xM zdOoRhlcm|dEog=tBsbd(e?dqNJ)#dobRP49nW*OlmbrkW=h1C4YyQVe3lWTs-Oio9 zyp<8Q5}$Q#Z4+~<3zqkl%Kh(Xke$>QAs_gSX)cq>2GH9D*B-xWvkhL-lltNb)nmW| z$FapWk*SO~XHpKeB$_!$RLIw=+#dRLy?=d3dcpx8@x|d{{=8I)dUqrj*Ny9u6u6yn zDDKGTe^wm$JH}ta0n|5By&;IlQJZdv%NcCz4pmB{9%DQdD*l0qS7vQ84?_gAkRfl4Ml5tT zX69~rvmBCsij5+B&P*xG>UpVuJA(d*d;IlPVuQ}|n{&aX*JVlF6W98I;W$>Q3B?l7 z9-3^u?;#58eCHTS?RN(w7+aGUL>iE*7hp40d=Wu;Ho7{24jmc$G#S^5RapeLRalQz zt_U7eGl@S^xus32~05=c>}2?5E-KGZ7a@c-~55K4hN3VJ;} Jqs4UQ{{adhqr3nB diff --git a/test/python/eliashberg/gamma_creation.py b/test/python/eliashberg/gamma_creation.py index 9701feb37..b38a21cd9 100644 --- a/test/python/eliashberg/gamma_creation.py +++ b/test/python/eliashberg/gamma_creation.py @@ -27,7 +27,7 @@ def test_gamma_PP_singlet_mesh_type(chi_c, chi_s, U_c, U_s): assert type(gamma_singlet.mesh[1]) == MeshBrillouinZone def test_gamma_PP_singlet_value(chi_c, chi_s, U_c, U_s): - gamma = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, -0.5, 1.5) + gamma = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, -1, 3) gamma_singlet = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) np.testing.assert_equal(gamma.data, gamma_singlet.data) @@ -38,7 +38,7 @@ def test_gamma_PP_triplet_mesh_type(chi_c, chi_s, U_c, U_s): assert type(gamma_triplet.mesh[1]) == MeshBrillouinZone def test_gamma_PP_triplet_value(chi_c, chi_s, U_c, U_s): - gamma = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, -0.5, -0.5) + gamma = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, -1, -1) gamma_triplet = gamma_PP_triplet(chi_c, chi_s, U_c, U_s) np.testing.assert_equal(gamma.data, gamma_triplet.data) diff --git a/test/python/eliashberg/previous_implementation_two_band.py b/test/python/eliashberg/previous_implementation_two_band.py index 63113010b..dd964ba77 100644 --- a/test/python/eliashberg/previous_implementation_two_band.py +++ b/test/python/eliashberg/previous_implementation_two_band.py @@ -72,9 +72,9 @@ def test_solve_eliashberg(g0_wk, gamma, expected_E, expected_eigen_mode): mu = 0.0, beta = 1, U = 1.0, - Up = 0.0, - J = 0.0, - Jp = 0.0, + Up = 0.8, + J = 0.1, + Jp = 0.1, nk = 2, nw = 100, version_info = version.info, From 3e2a42a4ee66b9e2559620955a94becface4e1b2 Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 17 Aug 2020 10:38:11 +0200 Subject: [PATCH 071/121] [eli] update c++ functions docstrings --- c++/triqs_tprf/lattice/eliashberg.hpp | 207 +++++++++++++++++--------- 1 file changed, 139 insertions(+), 68 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.hpp b/c++/triqs_tprf/lattice/eliashberg.hpp index c685ad040..7b056dbba 100644 --- a/c++/triqs_tprf/lattice/eliashberg.hpp +++ b/c++/triqs_tprf/lattice/eliashberg.hpp @@ -25,22 +25,27 @@ namespace triqs_tprf { - /** Linearized Eliashberg product + /** Linearized Eliashberg product via summation - Computes the product + Computes the linearized Eliashberg product in the singlet/triplet channel given by .. math:: - \Delta^{(out)}_{\bar{a}\bar{b}}(\mathbf{k},i\nu) = -\frac{1}{N_k \beta}\sum_{\mathbf{k}'} \sum_{i\nu'} - \Gamma_{A\bar{a}B\bar{b}}(\mathbf{k}-\mathbf{k}', i\nu - i\nu') - \\ \times - G_{A\bar{c}}(\mathbf{k}', i\nu') - \Delta_{\bar{c}\bar{d}}(\mathbf{k}', i\nu') - G_{B\bar{d}}(-\mathbf{k}', -i\nu') - - @param chi_pp particle-particle vertex :math:`\Gamma^{(pp)}_{a\bar{b}c\bar{d}}(\mathbf{k}, i\nu_n)` - @param g_kw single particle Green's function :math:`G_{a\bar{b}}(\mathbf{k}, i\nu_n)` - @param delta_kw pairing self-energy :math:`\Delta_{\bar{a}\bar{b}}(\mathbf{k}, i\nu_n)` - @return Gives the result of the product :math:`\Delta^{(out)} \sim \Gamma^{(pp)}GG \Delta` + \Delta^{\mathrm{s/t}, \mathrm{out}}_{\bar{a}\bar{b}}(i\nu,\mathbf{k}) + = + -\frac{1}{2N_\mathbf{k} \beta}\sum_{i\nu'}\sum_{\mathbf{k}'} + \Gamma^{\mathrm{s/t}}_{c\bar{a}d\bar{b}}(i\nu - i\nu',\mathbf{k}-\mathbf{k}') + \\ + \times + G_{c\bar{e}}(i\nu',\mathbf{k}') + G_{d\bar{f}}(-i\nu',-\mathbf{k}') + \Delta^{\mathrm{s/t}, \mathrm{in}}_{\bar{e}\bar{f}}(i\nu',\mathbf{k}')\,, + + by summation. + + @param Gamma_pp particle-particle vertex :math:`\Gamma^{\mathrm{s/t}}_{a\bar{b}c\bar{d}}(i\nu_n,\mathbf{k})` + @param g_wk single particle Green's function :math:`G_{a\bar{b}}(i\nu_n,\mathbf{k})` + @param delta_wk superconducting gap :math:`\Delta^{\mathrm{s/t}, \mathrm{in}}_{\bar{a}\bar{b}}(i\nu_n,\mathbf{k})` + @return Gives the result of the product :math:`\Delta^{\mathrm{s/t}, \mathrm{out}}` */ @@ -48,45 +53,93 @@ namespace triqs_tprf { /** Linearized Eliashberg product via FFT - Computes the product + Computes the linearized Eliashberg product in the singlet/triplet channel given by .. math:: - \Delta^{(out)}_{\bar{a}\bar{b}}(\mathbf{k},i\nu) = -\frac{1}{N_k \beta}\sum_{\mathbf{k}'} \sum_{i\nu'} - \Gamma_{A\bar{a}B\bar{b}}(\mathbf{k}-\mathbf{k}', i\nu - i\nu') - \\ \times - G_{A\bar{c}}(\mathbf{k}', i\nu') - \Delta_{\bar{c}\bar{d}}(\mathbf{k}', i\nu') - G_{B\bar{d}}(-\mathbf{k}', -i\nu')\,, + \Delta^{\mathrm{s/t}, \mathrm{out}}_{\bar{a}\bar{b}}(i\nu,\mathbf{k}) + = + -\frac{1}{2N_\mathbf{k} \beta}\sum_{i\nu'}\sum_{\mathbf{k}'} + \Gamma^{\mathrm{s/t}}_{c\bar{a}d\bar{b}}(i\nu - i\nu',\mathbf{k}-\mathbf{k}') + \\ + \times + G_{c\bar{e}}(i\nu',\mathbf{k}') + G_{d\bar{f}}(-i\nu',-\mathbf{k}') + \Delta^{\mathrm{s/t}, \mathrm{in}}_{\bar{e}\bar{f}}(i\nu',\mathbf{k}')\,, by taking advantage of the convolution theorem. We therefore first calculate .. math:: - \Delta^{(out)}_{\bar{a}\bar{b}}(\mathbf{r}, \tau) = - -\Gamma_{A\bar{a}B\bar{b}}(\mathbf{r}, \tau) F_{AB}(\mathbf{r}, \tau) \,, + F^{\mathrm{s/t}}_{ab}(i\nu,\mathbf{k}) + = + G_{a\bar{c}}(i\nu,\mathbf{k}) + G_{b\bar{d}}(-i\nu,-\mathbf{k}) + \Delta^{\mathrm{s/t}, \mathrm{in}}_{\bar{c}\bar{d}}(i\nu,\mathbf{k})\,, - where + which we then Fourier transform to imaginary time and real-space .. math:: - F_{AB}(\mathbf{r}, \tau) = - \mathcal{F}\big(G_{A\bar{c}}(\mathbf{k}', i\nu') - \Delta_{\bar{c}\bar{d}}(\mathbf{k}', i\nu') - G_{B\bar{d}}(-\mathbf{k}', -i\nu')\big)\,. + F^{\mathrm{s/t}}_{ab}(\tau,\mathbf{r}) + = + \mathcal{F}^2 + \big( + F^{\mathrm{s/t}}_{ab}(i\nu,\mathbf{k}) + \big)\,. + + We then calculate first the dynamic gap + + .. math:: + \Delta^{\mathrm{s/t}, \mathrm{dynamic}}_{\bar{a}\bar{b}}(\tau,\mathbf{r}) + = + -\frac{1}{2} + \Gamma^{\mathrm{s/t}, \mathrm{dynamic}}_{c\bar{a}d\bar{b}}(\tau, \mathbf{r}) + F^{\mathrm{s/t}}_{cd}(\tau, \mathbf{r})\,, + + and then the static gap + + .. math:: + \Delta^{\mathrm{s/t}, \mathrm{static}}_{\bar{a}\bar{b}}(\mathbf{r}) + = + -\frac{1}{2} + \Gamma^{\mathrm{s/t}, \mathrm{static}}_{c\bar{a}d\bar{b}}(\mathbf{r}) + F^{\mathrm{s/t}}_{cd}(\tau=0, \mathbf{r})\,. - Then we Fourier transform + We then Fourier transform the dynamic gap to imaginary frequencies .. math:: - \Delta^{(out)}_{\bar{a}\bar{b}}(\mathbf{k},i\nu) = - \mathcal{F}\big(\Delta^{(out)}_{\bar{a}\bar{b}}(\mathbf{r}, \tau)\big)\,, + \Delta^{\mathrm{s/t}, \mathrm{dynamic}}_{\bar{a}\bar{b}}(i\nu_n,\mathbf{r}) + = + \mathcal{F} + \big( + \Delta^{\mathrm{s/t}, \mathrm{dynamic}}_{\bar{a}\bar{b}}(\tau,\mathbf{r}) + \big)\,, + + and then add both component together + + .. math:: + \Delta^{\mathrm{s/t}, \mathrm{out}}_{\bar{a}\bar{b}}(i\nu_n,\mathbf{r}) + = + \Delta^{\mathrm{s/t}, \mathrm{dynamic}}_{\bar{a}\bar{b}}(i\nu_n,\mathbf{r}) + + + \Delta^{\mathrm{s/t}, \mathrm{static}}_{\bar{a}\bar{b}}(\mathbf{r})\,, + + and then finally Fourier transform to :math:`\mathbf{k}`-space + + .. math:: + \Delta^{\mathrm{s/t}, \mathrm{out}}_{\bar{a}\bar{b}}(i\nu_n,\mathbf{k}) + = + \mathcal{F} + \big( + \Delta^{\mathrm{s/t}, \mathrm{out}}_{\bar{a}\bar{b}}(i\nu_n,\mathbf{r}) + \big)\,. - to get the same result, but with far less computational effort. - @param chi_rt dynamic part of the particle-particle vertex :math:`\Gamma^{(pp)}_{a\bar{b}c\bar{d}}(\mathbf{r}, \tau)` - @param chi_r constant part of the particle-particle vertex :math:`\Gamma^{(pp)}_{a\bar{b}c\bar{d}}(\mathbf{r})` - @param g_kw single particle Green's function :math:`G_{a\bar{b}}(\mathbf{k}, i\nu_n)` - @param delta_kw pairing self-energy :math:`\Delta_{\bar{a}\bar{b}}(\mathbf{k}, i\nu_n)` - @return Gives the result of the product :math:`\Delta^{(out)} \sim \Gamma^{(pp)}GG \Delta` + @param Gamma_pp_dyn_tr dynamic part of the particle-particle vertex :math:`\Gamma^{\mathrm{s/t}, \mathrm{dynamic}}_{c\bar{a}d\bar{b}}(\tau, \mathbf{r})` + @param Gamma_pp_const_r static part of the particle-particle vertex :math:`\Gamma^{\mathrm{s/t}, \mathrm{static}}_{c\bar{a}d\bar{b}}(\mathbf{r})` + @param g_wk one-particle Green's function :math:`G_{a\bar{b}}(i\nu_n,\mathbf{k})` + @param delta_wk superconducting gap :math:`\Delta^{\mathrm{s/t}, \mathrm{in}}_{\bar{a}\bar{b}}(i\nu_n,\mathbf{k})` + @return Gives the result of the product :math:`\Delta^{\mathrm{s/t}, \mathrm{out}}` */ @@ -99,47 +152,65 @@ namespace triqs_tprf { chi_r_t constant_to_r(chi_k_vt Gamma_pp_const_k); e_r_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, g_tr_t F_tr); - /** Gamma particle-particle singlet + /** The particle-particle vertex in the singlet channel - Computes the particle-particle vertex for singlet pairing in the RPA limit + Computes the singlet channel particle-particle vertex in the + random phase approximation given by - .. math:: - \Gamma^{(\mathrm{singlet})}(a\bar{b}c\bar{d}) = - \frac{3}{2} U^{(\mathrm{s})}(a\bar{b}A\bar{B}) \chi^{(\mathrm{s})}(\bar{B}A\bar{C}D) - U^{(\mathrm{s})}(D\bar{C}c\bar{d}) \\ - -\frac{1}{2} U^{(\mathrm{c})}(a\bar{b}A\bar{B}) \chi^{(\mathrm{c})}(\bar{B}A\bar{C}D) - U^{(\mathrm{c})}(D\bar{C}c\bar{d}) \\ - + \frac{1}{2}\big(U^{(\mathrm{s})}(a\bar{b}c\bar{d})+ - U^{(\mathrm{c})}(a\bar{b}c\bar{d})\big) - - @param chi_c charge susceptibility :math:`\chi^{(\mathrm{c})}_{\bar{a}b\bar{c}d}(\mathbf{k}, i\omega_n)` - @param chi_s spin susceptibility :math:`\chi^{(\mathrm{s})}_{\bar{a}b\bar{c}d}(\mathbf{k}, i\omega_n)` - @param U_c charge interaction :math:`U^{(\mathrm{c})}_{a\bar{b}c\bar{d}}` - @param U_s spin interaction :math:`U^{(\mathrm{s})}_{a\bar{b}c\bar{d}}` - @return :math:`\Gamma^{(\mathrm{singlet})}_{a\bar{b}c\bar{d}}(\mathbf{k}, i\omega_n)` + .. math:: + \Gamma^{\mathrm{singlet}}(i\omega_n,\mathbf{q}) = + 3 \mathbf{U}^{\mathrm{s}} + \mathbf{\chi}^{\mathrm{s}}(i\omega_n,\mathbf{q}) + \mathbf{U}^{\mathrm{s}} + -\mathbf{U}^{\mathrm{c}} + \mathbf{\chi}^{\mathrm{c}}(i\omega_n,\mathbf{q}) + \mathbf{U}^{\mathrm{c}} + + \frac{1}{2}\big(\mathbf{U}^{\mathrm{s}}+ + \mathbf{U}^{\mathrm{c}}\big)\,, + + where all products are particle-hole products. + Note, that this is a special case, where the particle-particle vertex only + depends on one bosonic frequency and momentum. It can therefore only be used + in the linearized Eliashberg equation, if symmetries are enforced, + as desribed in the theory here: :ref:`eliashberg_rpa`. + + @param chi_c charge susceptibility :math:`\chi^{\mathrm{c}}_{\bar{a}b\bar{c}d}(i\omega_n,\mathbf{q})` + @param chi_s spin susceptibility :math:`\chi^{\mathrm{s}}_{\bar{a}b\bar{c}d}(i\omega_n,\mathbf{q})` + @param U_c charge interaction :math:`U^{\mathrm{c}}_{a\bar{b}c\bar{d}}` + @param U_s spin interaction :math:`U^{\mathrm{s}}_{a\bar{b}c\bar{d}}` + @return The singlet channel particle-particle vertex :math:`\Gamma^{\mathrm{singlet}}(i\omega_n,\mathbf{q})` */ chi_wk_t gamma_PP_singlet(chi_wk_vt chi_c, chi_wk_vt chi_s, array_view, 4> U_c, array_view, 4> U_s); - /** Gamma particle-particle triplet + /** The particle-particle vertex in the triplet channel - Computes the particle-particle vertex for triplet pairing in the RPA limit + Computes the triplet channel particle-particle vertex in the + random phase approximation given by - .. math:: - \Gamma^{(\mathrm{triplet})}(a\bar{b}c\bar{d}) = - -\frac{1}{2} U^{(\mathrm{s})}(a\bar{b}A\bar{B}) \chi^{(\mathrm{s})}(\bar{B}A\bar{C}D) - U^{(\mathrm{s})}(D\bar{C}c\bar{d}) \\ - -\frac{1}{2} U^{(\mathrm{c})}(a\bar{b}A\bar{B}) \chi^{(\mathrm{c})}(\bar{B}A\bar{C}D) - U^{(\mathrm{c})}(D\bar{C}c\bar{d}) \\ - + \frac{1}{2}\big(U^{(\mathrm{s})}(a\bar{b}c\bar{d})+ - U^{(\mathrm{c})}(a\bar{b}c\bar{d})\big) - - @param chi_c charge susceptibility :math:`\chi^{(\mathrm{c})}_{\bar{a}b\bar{c}d}(\mathbf{k}, i\omega_n)` - @param chi_s spin susceptibility :math:`\chi^{(\mathrm{s})}_{\bar{a}b\bar{c}d}(\mathbf{k}, i\omega_n)` - @param U_c charge interaction :math:`U^{(\mathrm{c})}_{a\bar{b}c\bar{d}}` - @param U_s spin interaction :math:`U^{(\mathrm{s})}_{a\bar{b}c\bar{d}}` - @return :math:`\Gamma^{(\mathrm{triplet})}_{a\bar{b}c\bar{d}}(\mathbf{k}, i\omega_n)` + .. math:: + \Gamma^{\mathrm{triplet}}(i\omega_n,\mathbf{q}) = + -\mathbf{U}^{\mathrm{s}} + \mathbf{\chi}^{\mathrm{s}}(i\omega_n,\mathbf{q}) + \mathbf{U}^{\mathrm{s}} + -\mathbf{U}^{\mathrm{c}} + \mathbf{\chi}^{\mathrm{c}}(i\omega_n,\mathbf{q}) + \mathbf{U}^{\mathrm{c}} + + \frac{1}{2}\big(\mathbf{U}^{\mathrm{s}}+ + \mathbf{U}^{\mathrm{c}}\big)\,, + + where all products are particle-hole products. + Note, that this is a special case, where the particle-particle vertex only + depends on one bosonic frequency and momentum. It can therefore only be used + in the linearized Eliashberg equation, if symmetries are enforced, + as desribed in the theory here: :ref:`eliashberg_rpa`. + + @param chi_c charge susceptibility :math:`\chi^{\mathrm{c}}_{\bar{a}b\bar{c}d}(i\omega_n,\mathbf{q})` + @param chi_s spin susceptibility :math:`\chi^{\mathrm{s}}_{\bar{a}b\bar{c}d}(i\omega_n,\mathbf{q})` + @param U_c charge interaction :math:`U^{\mathrm{c}}_{a\bar{b}c\bar{d}}` + @param U_s spin interaction :math:`U^{\mathrm{s}}_{a\bar{b}c\bar{d}}` + @return The triplet channel particle-particle vertex :math:`\Gamma^{\mathrm{triplet}}(i\omega_n,\mathbf{q})` */ From d4a5173b05c8517cf823c5ab6aa74164665fc9de Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 17 Aug 2020 10:59:44 +0200 Subject: [PATCH 072/121] [eli] adjust old notebooks to new 1/2 factor --- .../PHT_Hubbard_Model.ipynb | 552 +++--------------- ...tion on the attractive Hubbard model.ipynb | 34 +- 2 files changed, 82 insertions(+), 504 deletions(-) diff --git a/benchmark/eliashberg/particle_hole_transformation/PHT_Hubbard_Model.ipynb b/benchmark/eliashberg/particle_hole_transformation/PHT_Hubbard_Model.ipynb index 28ccfa21f..8dbdaf46c 100644 --- a/benchmark/eliashberg/particle_hole_transformation/PHT_Hubbard_Model.ipynb +++ b/benchmark/eliashberg/particle_hole_transformation/PHT_Hubbard_Model.ipynb @@ -68,7 +68,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -86,7 +86,7 @@ "zeeman = 0.0" ] }, - "execution_count": 4, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } @@ -126,14 +126,14 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "Starting run with 1 MPI threads at : 2019-05-14 14:36:57.601312\n" + "Starting run with 1 MPI rank(s) at : 2020-08-17 10:44:43.599610\n" ] } ], @@ -147,20 +147,20 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ - "path = [(r'$\\Gamma$', np.array([0.0, 0.0, 0.0])), \n", - " ('X', np.array([0.5, 0.0, 0.0])),\n", - " ('M', np.array([0.5, 0.5, 0.0])), \n", - " (r'$\\Gamma$', np.array([0.0, 0.0, 0.0])), \n", + "path = [(r'$\\Gamma$', 2*np.pi*np.array([0.0, 0.0, 0.0])), \n", + " ('X', 2*np.pi*np.array([0.5, 0.0, 0.0])),\n", + " ('M', 2*np.pi*np.array([0.5, 0.5, 0.0])), \n", + " (r'$\\Gamma$', 2*np.pi*np.array([0.0, 0.0, 0.0])), \n", " ]" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -169,7 +169,7 @@ "Text(0.5,0,'DOS')" ] }, - "execution_count": 8, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, @@ -221,7 +221,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -293,7 +293,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 8, "metadata": {}, "outputs": [], "source": [ @@ -318,7 +318,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 9, "metadata": {}, "outputs": [ { @@ -327,13 +327,13 @@ "Text(0.55,0.18,'$\\\\chi^{(c)}$')" ] }, - "execution_count": 11, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", + "image/png": 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" ] @@ -371,7 +371,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 10, "metadata": {}, "outputs": [], "source": [ @@ -411,7 +411,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 11, "metadata": {}, "outputs": [], "source": [ @@ -433,7 +433,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 12, "metadata": {}, "outputs": [ { @@ -442,13 +442,13 @@ "Text(0.625,0.3,'AFM')" ] }, - "execution_count": 14, + "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -575,7 +575,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ @@ -595,7 +595,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 14, "metadata": {}, "outputs": [ { @@ -604,7 +604,7 @@ "Text(0.125,0.3,'AFM')" ] }, - "execution_count": 16, + "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, @@ -665,7 +665,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 15, "metadata": {}, "outputs": [], "source": [ @@ -679,7 +679,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 16, "metadata": {}, "outputs": [ { @@ -688,7 +688,7 @@ "Text(0.5,0,'DOS')" ] }, - "execution_count": 18, + "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, @@ -719,7 +719,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 17, "metadata": {}, "outputs": [], "source": [ @@ -739,7 +739,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 18, "metadata": {}, "outputs": [ { @@ -748,7 +748,7 @@ "Text(0.08,0.1,'AFM')" ] }, - "execution_count": 20, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, @@ -856,7 +856,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 19, "metadata": {}, "outputs": [], "source": [ @@ -883,7 +883,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 20, "metadata": {}, "outputs": [], "source": [ @@ -906,7 +906,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 21, "metadata": {}, "outputs": [ { @@ -915,13 +915,13 @@ "Text(0.07,0.15,'CDW')" ] }, - "execution_count": 23, + "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -979,7 +979,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 22, "metadata": {}, "outputs": [ { @@ -1025,7 +1025,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 23, "metadata": {}, "outputs": [], "source": [ @@ -1051,10 +1051,10 @@ "### Linearized Eliashberg equation\n", "\n", "We will now use the implementation of the linearized Eliashberg equation to confirm this superconducting phase.\n", - "To do this we need to construct the particle-particle vertex $\\Gamma(\\omega, \\mathbf{k})$ which in the case of the attractive Hubbard model is just a constant \n", + "To do this we need to construct the (singlet) particle-particle vertex $\\Gamma(\\omega, \\mathbf{k})$ which is for the attractive Hubbard model [N. E. Bickers, Self-Consistent Many-Body Theory for Condensed Matter Systems. Theoretical Methods for Strongly Correlated Electrons, 237–296. 6 (2006)]\n", "\n", "$$\n", - "\\Gamma(\\omega, \\mathbf{k}) = -U\\,.\n", + "\\Gamma(\\omega, \\mathbf{k}) = -2U\\,.\n", "$$\n", "\n", "We can then use the `solve_eliashberg` function of the `triqs_tprf.eliashberg` module to solve the linearized eliashberg equation for the specifc $\\Gamma$ to obtain the $\\lambda$ as an indicator for the strength of the superconducting phase.\n", @@ -1074,7 +1074,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 24, "metadata": {}, "outputs": [], "source": [ @@ -1095,7 +1095,7 @@ " wmesh_boson = MeshImFreq(beta=temperature_to_beta(p.T), S='Boson', n_max=p.nw)\n", " gamma_pp = Gf(mesh=MeshProduct(wmesh_boson, g0_wk.mesh[1]),\n", " target_shape=g0_wk.target_shape*2)\n", - " gamma_pp.data[:] = p.U\n", + " gamma_pp.data[:] = 2*p.U\n", " \n", " Es, eigen_modes = solve_eliashberg(gamma_pp, g0_wk, solver='IRAM', tol=1e-5)\n", "\n", @@ -1124,7 +1124,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 25, "metadata": {}, "outputs": [], "source": [ @@ -1143,7 +1143,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 26, "metadata": {}, "outputs": [ { @@ -1152,13 +1152,13 @@ "Text(0.07,0.15,'SC')" ] }, - "execution_count": 28, + "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -1214,7 +1214,7 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 27, "metadata": {}, "outputs": [], "source": [ @@ -1226,7 +1226,7 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 28, "metadata": {}, "outputs": [ { @@ -1235,7 +1235,7 @@ "Text(0.52,0.6,'$|\\\\downarrow \\\\rangle$')" ] }, - "execution_count": 30, + "execution_count": 28, "metadata": {}, "output_type": "execute_result" }, @@ -1273,7 +1273,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 29, "metadata": {}, "outputs": [], "source": [ @@ -1326,7 +1326,7 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 30, "metadata": {}, "outputs": [], "source": [ @@ -1363,7 +1363,7 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 31, "metadata": {}, "outputs": [ { @@ -1372,13 +1372,13 @@ "Text(0.5,1,'Hubbard with $\\\\mathrm{Zeeman}=\\\\xi$')" ] }, - "execution_count": 38, + "execution_count": 31, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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G8hz7cD7bJ3De21k4k6gON5ZnsiS6Pb4C/C+cz/Y8zg+sbTjjPD4MfBfowplTJ+WkrtlkjNmCM2XAfTiT9p7C+T424PxQetJau8y7CCUVHcNS0zFswkpdt6cz+rFP5QxhjPkWsAz4Gk4rYRinyM15nGPNJ3HGRE3KfpmWje9vLsjEOcEXiw3tKioiIpI91tr7cFrIcq609HhYa2cCW3F+IP6xMebvPQ5JREQ8MpFzglrURETEa4kWtdFWc8xpxpjTDBQ8afMyFhER8dZEzglK1ERExGuJQiIFkahZa2/H6ebSg9NtTEREitREzglK1ERExDPxSUIXxxfzPlGz1n4HZxxOJU6RgIsj7CIiIgVqoucEJWoiIuKlV+Gciy7jFFTIdzfiFDt5lzHmAa+DERERT03onKBiIiIiIiIiIjlG86iJ5CZdQRGR0fCNvImkoWOtiIzEs+Osuj6KiIiIiIjkGCVqIiIiIiIiOUaJmoiIiIiISI5RoiYiIiIiIpJjlKiJiIiIiIjkGCVqIiIiIiIiOUaJmoiIiIiISI5RoiYiIiIiIpJjlKiJiIiIiIjkGCVqIiIiIiIiOSbodQAio2GtfSewDrgWuAaYAnzXGPPbafZZDfw5cCtQBjQD/wb8vTEmMsw+vw58ErgOCAB7gX8yxvx7mud5H/BHwEogAuwCvmKMeWyML1NEREREBFCiJvnjz3EStA7gGLA83cbW2rcC/wP0AD8A2oA3A18FbgfuSbHPh4G/B84D3wH6gHcC37bWvsoY88kU+3wF+JN4TP8KlADvBh611n7EGPMP43mxo3GsrYv/2tTKE8+foLsvQnlJgDdc08Bvrp5PU11Fpp624LS1tbF582b27NlDX18fJSUlXH311dx2223U1dV5HZ6IiBSxk50nWd/8IzYe3UBPuIeyYBl3zrmLty1+B7MrZ3sdXt4It7bS8S8P0PWjh4h1duKrrKTiHW+n6kMfJDh/vtfhDcsXi8W8jkFkRNbau3CSoWaclrUNDNOiZq2tjm9XA9xujNkev78MeBq4DXiPMeb7rn3mA/uATuAGY0xr/P5a4DlgEbDaGLPZtc9q4FdAC3CTMeaC67F2AJXA8sRjjVHa/5ibDp7lvh/sJhyJEY4ObBr0+wgGfNz/rmtZvWT6OJ62uBw8eJAHH3yQSCRCNBpN3u/3+wkEAtxzzz0sWbLEwwhFRuTzOoA8px9BkrN2nN7Ol7bdTzgaJhIb6AgU8AUI+oP82c33ccPMGz2MMD/0PL2Btg9+iFh/P4TDAyuCQXyhEHUP/Atlr74r3UN4dpzVGDXJC8aYDcaYg8aY0ZxU3wlMB76fSNLij9GD0zIH8IdD9vk9oBT4B3diFU++7o8v/sGQfRLLX0wkafF9WoF/jD/e744i3jE51tbFfT/YTU9/dFCSBhCOxujpj3LfD3ZzrK1rsp+6oLS1tfHggw/S398/KEkDiEaj9Pf38+CDD9LW1uZRhCIiUqxOdp7kS9vupzfSOyhJA4jEIvRGevnStvs52XnSowjzQ7i11UnSursHJ2kA4TCx7m7aPvghwq2tnsQ3EiVqUoheHf/7RIp1zwJdwGprbeko9/nJkG0mss+E/demVsKR9PlqOBLje5taJ/upC8rmzZuJRFIOVUyKRCJs2bIlSxGJiIg41jf/iHA0nHabcDTMw80PZSmi/NTxLw84LWlpxPr76Xjgm1mKaGw0Rk0K0bL43wNDVxhjwtbaV4BVwELg5VHsc9Ja2wk0WWsrjDFd1tpKoBHoMMakupx1MP536XBBWmvvBe5NsWpxfX09ixcv5g1veMMVK594/sQVLWlDhaMxnthzgj+5O+1QvqK2Z8+eK1rShopGo+zZs4e77747S1GJiIjAxqMbrmhJGyoSi7Dh6AY+cPWHshRV/un60UNXtqQNFQ7T9aP/Yer9f5GdoMZAiZoUopr43/Zh1ifunzrGfSrj23WN8zmGmo8z3u4K58+fp6qqKuVO3X3pD9wJXb0R9u7dO6pti1FfX9+kbiciIjJZesI9o9quO9zFr47/MsPR5K+FnR2jGmAW6+jMeCzjoURNilHi/+xYBpGPZ5+Rtm8Fnklx/7UMJIJXKC8J0DWKZK0s5GfKlCkjblesQqEQ/SN0hwAoKSnJQjQiIiIDyoJldIe7R9yuNFBKbWltFiLKT7GKcnydI7+PvqrKLEQzdkrUpBAlWrOGS3aqh2yXuD0tvs/5NPtcGuVzjNTihjHm28C3h95vrd3IMC1tAG+4poFHdhxL2/0x4IM7FilJS2fhwoUcOHCAdJVv/X4/V199dRajEhERgTvn3MWTrT9N2/3Rj59rp1+XxajyT9/dd1H60E/xhdNc4A4GqXjHb2QvqDFQMREpRPvjf68YH2atDQILgDBwaJT7zMbp9njMGNMFYIzpBI4DVfH1QyVqul8x5m2ifnP1fIKB9A35wYCPu1dpDrB0Vq5cSSAQSLtNIBDg1ltvzVJEIiIijrctfgdBf/r2lIA/wO0Na7IUUX7q+Z13QDD9++gLhaj64PuzFNHYKFGTQvR0/O+VlThgLVABbDLG9I5ynzcO2WYi+0xYU10F97/rWspCfoL+wQmb3welQR8fu6uBWdXqspdOdXU169atIxgM4vNdmfj6/X7uueceTXotIiJZN7tyNmsa7ki5zo+fkD/Ee5b/FvXl9VmOLL9E58ym4yv3EStN8ZsoGMRXXk7dA/+Ss5NeK1GTQvTfwDng3dba5EyQ8QmvEyV9/nnIPt8CeoEPxyesTuxTC9wXX/zGkH0Sy5+Jb5fYZz7wR/HH+9b4X8bwVi+Zznf+9+289YamQcna4ullfPmt87muKXUhEhmsqamJN7/5zSxdupRQKDRoXTAYZN68eR5FJiIixaw/2s+us7uSy0F/EB8+SgOl3DTrZj5y7UdZVrsszSNIQv+aG+n6w98adJ+vqpLK3/otZvzsyZEmu/aUL934DJFcYa19G/C2+OIs4PU4XRd/Eb/vnDHmk0O2/2+gB/g+0Aa8BacM/38D/2vo5NnW2o8AX8cZo/YDoA9n8uwm4G/cj+/a52+ATwDH4o9bArwLqAc+Yoz5h3G81o3Aunnz5nHvvfeOuP13f/UKf/+k08PytvlVfPSuxrE+pcRFo1EeeughOjo6ALj77ru56aabPI5KJK3RFDST4elHkOSkDUef5qs7/gaAylAln7rxz0bsCinDq/jLf6bsB48BUHr3G6n98pcIjL7HjGfHWbWoSb64Fnhf/N/r4/ctdN33TvfGxpj1OAU5ngV+A/gI0I+TVL17aJIW3+fvcZK5vcDvAB8ETgH3pkrS4vv8Cc5caKfi2/9OfP83jydJG49ls6uTt1vOja6cr6Tm9/tZuXJlcnnz5s0jzrUmIiIymWKxGA83r08u3zLrViVpExR86WDydmjBAg8jGRt96pIXjDGfBz4/xn1+BYxppmJjzKPAo2Pc59+Bfx/LPpNp4YxK/D6IxuBMR5jO3giVpemLZMjwFi9ezO7du+nr6+PChQscOHCA5cs1cbiIiGTHC+f2cKi9BYCgL8hts2/zOKI8199PYP9A/bjAvLkeBjM2alETyXMlwQCzasqTy4fOq1VtIkKhEEuXDhT/3Lx5s4fRiIhIsXG3pl0z/VoqQrk5x1e+CDQfxtcXnze1rhZ/Vf6M41eiJlIAGutciZq6P07Y8uXLk5Ugjxw5wvHjxz2OSEREisGxy0d57vS25PLaprUeRlMYgnsHuj0GFuZPt0dQoiZSEBpqBxK1g2e7PYykMFRWVrLA1Yd9y5YtHkYjIiLF4pGWh5O3l0xdwrTy6R5GUxgCrkQttCy/KmUqURMpAI21FcnbLWfVojYZ3EVF9u7dS3t7u4fRiIhIoWvvbefpIz9PLq9tXOdhNIUjuPdA8nbJ4iUeRjJ2StRECsCM6jJCAaer3oXuCBe7wx5HlP/q6+uZNWsW4FTg2rp1q8cRiYhIIfvJK4/TF+0DYFbFLBbULPQ4ogLQ3UOg5TAAMR8EF+bXe6pETaQABPw+muoGWtU0Tm1yrFq1Knl7586d9Pb2ehiNiIgUqr5IHz9+5bHk8prGtcmx0jJ+wQOv4Is40+z4ZszAX1Exwh65RYmaSIGYN22gKpTmU5scjY2NVFc789T19vayc+dOjyMSEZFC9MyxjbT3XgRgSmgKV0+72uOICoN7fFq+taaBEjWRguFO1JpVUGRS+Hy+Qa1qW7du1QTYIiIyqYZOcH3r7NUE/JoPdTK4x6eFXFPv5AslaiIFwp2oHTrXQywW8zCawrFw4UJKS0sBaG9v5+WXX/Y4IhERKSS7zuzkyGVnHFXIH+KW2bd4HFHhcJfmL1miRE1EPDK9uoyykHMF7nJvlPOdKigyGYLBIMuXL08ub9q0SUmwiIhMmvXNDyVvXz/jesqD5Wm2llHr6CLQegyAmN9HcP58b+MZByVqIgXC7/Mxt95Vpl/j1CbNsmXL8Pudw+WJEyc4evSoxxGJiEghaG1vZffZXQD48LGmURNcT5bgywOtab7Zs/GVlngYzfgoURMpIEO7P8rkKC8vZ9GiRcnlzZs3exiNiIgUiodbBlrTltUup66szsNoCkvwRVchEdc5PJ8oURMpIHNdidpBFRSZVCtWrEje3rdvH21tbR5GIyIi+a6tp41njm5MLq9r0gTXkynwkmt82rJlHkYyfkrURArIvPqBRO2V8z1ENZZq0tTW1tLY2Jhc1gTYIiIyEY8feoxwzBlP3lDZyNzqeR5HVFgGFxJZ4mEk46dETaSA1FWVUFUaBKC7P8bpS/0eR1RYVq5cmby9a9cuurvVaikiImPXG+7hJ688nlxe26SxaZPJ19ZO4MRpAGLBIIE5czyOaHyUqIkUEJ/PN6j7owqKTK7Zs2dTW1sLQH9/Pzt27PA4IhERyUc/P/pzLvdfBqCmpIZV9Vd5HFFhCbq6PfqbGvAFgx5GM35K1EQKzDwlahnj8/kGtapt3bqVSCTiYUQiIpJvorEoj7gmuF7dcDt+n36STyb3+LTg4sUeRjIx+laIFBh3otZ8tsvDSArTggULKC935rjp6Ohg7969HkckIiL55LlT2zjReQKA0kApN8282eOICk9w74Hk7ZKl+VlIBJSoiRQc91xqh9v6iERVUGQyBQIBTYAtIiLj9rCrNe2GGTdSGiz1MJoCFIsNKiQSWpyfhURAiZpIwampKGFqRQiAvkiM4xf7PI6o8CxdupRAIADA6dOnaW1t9TYgERHJC80XD/Li+RcA8ONnTeMdHkdUeHxnzuM/dwGAWGkJgYYGjyMaPyVqIgVI49Qyq6ysjMWuPu+aAFtEREbD3Zq2sn4VNaU1HkZTmNytaf65c/AF8jfdyd/IRWRYgys/qoR8JrgnwD548CDnzp3zMBoREcl1Z7vO8ovjzyaX12qC64xwj08L5XEhEVCiJlKQ3BNfHzyrRC0TampqmOOal0WtaiIiks5jhx4lGosCMHfKXBqrGj2OqDC5W9RKl61Is2XuU6ImUoDcLWrHLvTRH4l6GE3hcpfq37NnD52dnR5GIyIiuaqrv4snW59ILt/RqAmuMyIWG1Kaf5GHwUycEjWRAlRZGmTaFKeKVCQGRy6ooEgmzJw5k/r6egDC4TDbt2/3OCIREclFPzvyFJ1h52JebWkdy+vyu6UnV/mPncJ/qcNZqCjHP2OGtwFNkBI1kQLl7v6ocWqZMXQC7G3bthEOhz2MSEREck0kGuGRloeTy2sa1miC6wxxj0/zz5+Hz+fzMJqJ07dEpEANKihyVpUfM2X+/PlUVDhz13V1dbFnzx6PIxIRkVyy5eRmznSdBqA8WM71M2/wOKLCFXDPn7Ykf+dPS1CiJlKg3CX6m1VQJGP8fv+gCpCbN2/WBNgiIpK0vvmh5O2bZt5MSaDEw2gKW9A1Pq1k2XIPI5kcStRECtSc+goSDf4n2vvp6VdBkUxZunQpwWAQgHPnztHS0uJxRCIikgv2tb3M/gv7AAj4AqxuuN3jiApYJELwpebkYnBhfhcSASVqIgWrLBRg5tQyAGJAa5u6P2ZKSUkJS1xdLFSqX0REYHBr2lXTXsWUkikeRlPYAq8cw9cd/61TPYVAfZ23AU0CJWoiBcxdUOTQOSVqmbR/sP9aAAAgAElEQVRixYrkoOVDhw5x+vRpjyMSEREvneo8yZYTAxfu1jVqgutMcpfl9y+Y71kck0mJmkgBGzRO7YzGqWXSlClTmDt3bnJ5y5YtHkYjIiJee7TlEaI4ww4WVC9kZuUsjyMqbO6JrkuWLvUwksmjRE2kgLkrPzarRS3jVq1alby9Z88eLl++7GE0IiLilY6+Dp46/GRyeW2TWtMyzV2av2TJMg8jmTxK1EQKWFNtBf54d7wzHWE6eyMeR1TYpk+fzvTp0wGIRqM899xzHkckIiJe+OnhJ+iJOBdIp5VPZ8nU/C8Vn9P6+wnsP5RcDC5a6GEwk0eJmkgBCwX9NNaVJ5cPnVerWqa5W9W2b99OX1+fh9GIiEi2haNhHmt5JLm8pmFN3k+8nOsCzYfx9Yedhfo6/NXV3gY0SZSoiRS4uSooklVz5syhqqoKgO7ubp5//nmPIxIRkWz65fFfcL7nPAAVwUqum3G9xxEVPvf4tMCC+Z7FMdmUqIkUOHdBkYOa+Drj/H4/K1euTC5v2bJFE2CLiBSJWCzGw66S/LfMvoWgP+hhRMUh4BqfFlpWGOPTQImaSMFzJ2pqUcuOxYsXEwqFAGhra+PAgQMj7CEiIoXgxXMv0NLeAkDQF+S22as9jqg4DKr4uKQwKj6CEjWRgjd7ahmhgNM3vq0rQnt32OOICl8oFGKZ64repk2bPIxGRESy5eGWgda0a6ZfQ2WoMs3WMim6ewi0HAYg5oPgggUeBzR5lKiJFLiA309TXUVyuUWtalmxfPny5ODxI0eOcOLECY8jEhGRTDp2+RjbTm1LLt+hCa6zIrj/EL6IM1+db8YM/BUVI+yRP5SoiRQBdX/MvsrKSha4rupt3rzZw2hERCTTHml5OHl7ydQlTK+Y7mE0xSPg6vYYXFgYZfkTlKiJFAEVFPGGu6jI3r17aW9v9zAaERHJlEu97Tx95GfJZbWmZU/wpYFErZAKiYASNZGiMLREv6oQZkd9fT2zZs0CnEpgW7du9TgiERHJhJ+0/oS+qDNv5syKWSysKayWnVw2qJDI4sKaWFyJmkgRmFFTRlkoAMDl3ijnO1VQJFvcrWo7d+6kt7fXw2hERGSy9UX6+PGhR5PLdzTeoQmus8R3uZNA6zEAYn4/wfnzvQ1okilREykCfp+PufUDg2s1Ti17mpqaqK6uBqC3t5ddu3Z5HJGIiEymZ489w8XeiwBUhaq4eto1HkdUPAIvNydv+xpm4Sst8TCayadETaRIzHWNU1Plx+zx+XxXTIAdjUY9jEhERCZLLBYbVJL/ttmrCfgDHkZUXNzdHoOLFnkYSWYoURMpEioo4p1FixZRWloKQHt7O/v27fM4IhERmQy7z+7i8CVnDq+QP8Qts2/1OKLiEtx7IHm7ZGlhFRIBJWoiRWOeq6DIK+dVUCSbgsGgJsAWESlA65sHWtOum3E95cFyD6MpPu7S/CVLCquQCChREykadVUlVJYGAejuj3HqUr/HERWX5cuX4/c7h9zjx49z9OhRjyMSEZGJOHyplV1ndgLgw8cdjWs9jqi4+NraCZw8A0AsGCQwZ47HEU0+JWoiRcLn8w3q/qhxatlVXl7OQtdEnJoAW0Qkv61vXp+8vax2GXVldR5GU3zc86f5mxrwBYMeRpMZStREiog7UTt0XolatrmLiuzbt48LFy54GI2IiIzXhZ42njm2Ibm8tulO74IpUgHX+LTg4sUeRpI5StREisiggiJnujyMpDjV1tbS0NAAOJXCtmzZ4nFEIiIyHj8+9GPCUWdO0obKBuZVz/M4ouIzaKLrpcs9jCRzlKiJFBH3XGqH2/qIRFVQJNvcrWq7du2ip0ctmyIi+aQ33MNPWh9PLt/RuM7DaIpULDao62NoiVrURCTP1VSUMLUiBEBfJMaJ9j6PIyo+DQ0NTJ06FYD+/n527NjhcUQiIjIWTx99mst9lwCoLqlh1bRVHkdUfHxnzuM/5wwfiJWWEJjd4HFEmaFETaTIqKCIt4ZOgL1161YikYiHEYmIyGhFY1EeaRkoIrK64XYCPk1wnW3u+dP8c+fgCxRmSlOYr0pEhjXXNZ9asya+9sTChQspKysD4PLly+zdu9fjiEREZDS2n3qO4x3HASgNlHLzzJs9jqg4ucenhQpw/rQEJWoiRWZQQRElap4IBAIsXz4w8Hnz5s2agFxEJA+4J7i+YcaNlAZLPYymeLkTtdJlhVlIBJSoiRSdua5E7diFPvojUQ+jKV7Lli0jEHC6y5w6dYrDhw97HJGIiKTTfPEgL55/AQA/fm5vXONxREUqFiPgKiQSXLTIw2AyS4maSJGpLA0ybYpzBTASgyMXVFDEC2VlZSxynVw0AbaISG572DXB9Yr6lUwtnephNMXLf/Qk/ksdzkJlBf4ZM7wNKIOUqIkUoXn17oIi6v7oFXdRkQMHDnDu3DkPoxERkeGc7TrLL4//Irm8ThNce8Zdlt8/by4+n8/DaDJLiZpIEXJ3f2w5q8qPXqmpqaGpqSm5rAmwRURy02OHHiUScyr0zpkyl8aqRo8jKl4BdyGRpUs9jCTzlKiJFKF50wYmvlblR2+tWjUw/87zzz9PV1eXh9GIiMhQXf1dPNn6RHL5jsa1HkYj7tL8JUuXeRhJ5ilREylCc+orSXQUONHeT0+/Cop4ZebMmdTV1QEQDofZvn27xxGJiIjbz448RWe4E4Da0lpW1K3wOKIiFokQfLkluVjIhURAiZpIUSoLBZg51ZnHKwYcblP3R6/4fL5BrWrbtm0jHA57GJGIiCREYhEeaXk4uXx7wxr8Pv189krglWP4uuO/WWqqCcQvdBYqfdNEitTggiJK1Lw0f/58Kiqc7qidnZ288MILHkckIiIAW05s5kzXaQDKAmXcMPNGjyMqbgFXt0f//HkeRpIdStREipS7oEjzGY1T85Lf72fFioGuNJoAW0QkNzzcMjDB9U2zbqYkUOJhNOKe6LqkwAuJgBI1kaI1z52oqUXNc0uXLiUYDAJw9uxZDh065HFEIiLFbV/by+xr2wdAwBfg9gZNcO01d2n+Qi8kAkrURIpWU20F/vjcI2c6wnT2RjyOqLiVlJSwZMmS5PKmTZs8jEZERNY3D7Smraq/iiklUzyMRujvJ7B/4CJmcOFCD4PJDiVqIkUqFPTTWFueXD50Xq1qXluxYkVy4s5Dhw5x5swZjyMSESlOpzpPseXE5uSyJrj2XuBgK77+eLGt+jr81dXeBpQFStREiph7nNohdX/03JQpU5g7d25yefPmzWm2FhGRTHm05RGiOFPXzK9ewKzKWR5HJMGXmpO3AwvmexZHNilREylig8apaeLrnLBy5crk7RdeeIGOjg4PoxERKT4dfR387MiTyeV1jes8jEYS3BUfQ8uWexhJ9ihREylic1WiP+fMmDGD6dOnAxCJRNi2bZvHEYmIFJcnD/+U7rBz8XJa+TSW1BZ+dcF8MKjio2tMdyFToiZSxBpqywgFnDFRbV0R2rs10XIucLeqbd++nf7+fg+jEREpHuFomMcOPZJcXtNwR3LssHiou4dAy2EAYr7iKCQCStREilrA76epriK5rHFquWHu3LlUVVUB0N3dzfPPP+9xRCIixeFXx3/Jue5zAFQEK7h2xnUeRyQAwf2H8EWcMYO+GTPwl5ePsEdhUKImUuTc49TU/TE3aAJsEZHsi8VirG/+UXL5ltm3EvKHPIxIEgKubo/F0poGStREip678uNBFRTJGUuWLCEUcn4gtLW1ceDAgRH2EBGRidh7/kVa2lsACPiC3Db7No8jkoTgoEIihT/RdYISNZEiN69+cIl+tdzkhlAoxNKlAwPYVapfRCSz3K1p10y/hspQlYfRiFsxFhIBJWoiRW9GTRllIedQcLk3yvlOFRTJFe4JsA8fPszJkyc9jkhEpDAd7zjOtlMDVXbXNq71MBpx813uJHD4OAAxv5/gvPneBpRFStREipzf52NOvSa+zkWVlZXMnz8/uaxWNRGRzHi4eX3y9uKpi5leMcPDaMQt8PLARNe+hln4Sks8jCa7lKiJiAqK5DB3qf69e/dy6dIlD6MRESk8l3rbefroz5PLazXBdU5xj08LLlrkYSTZp0RNRAYlas0qKJJTpk2bxsyZMwGIRqNs3brV44hERArLT1p/Ql+kF4CZFTNZWFNcyUCuGzQ+bdlyDyPJPiVqIsJcd9fH8yookmvcrWo7duygt7fXw2hERApHf6SfHx96NLm8pnGtJrjOMe7S/CWLi6eQCChRExGgvqqEytIgAN39MU5d6vc4InGbM2cO1dXVAPT29rJ7926PIxIRKQzPHNvIxd6LAFSFqrh62tUeRyRuvrZ2AifPABALBgnMafI4ouxSoiYi+Hy+Qd0fD53XOLVc4vP5Bk2AvWXLFqLRqIcRiYjkv1gsxsMtDyWXb519G0F/0MOIZCj3+DT/nEZ8weL6fJSoiQiggiK5bvHixZSWlgJw8eJF9u3b53FEIiL5bffZXRy+dBiAkD/ErZrgOucEXhro9hhcvNjDSLyhRE1EAJhbX5G8ffBMl4eRSCrBYFATYIuITKL1zQOtaddNv47yYLmH0Ugqgye6XuZhJN5QoiYiwOAWtcNtfUSjKiiSa5YvX47f7xy2jx07xtGjRz2OSEQkPx2+1MquMzuTy3c0qSR/zonFBnV9DC1Ri5qIFKmaihKmVoQA6IvEON7e53FEMlRFRQULFixILqtVTURkfNwTXC+rXU5dWZ2H0UgqvjPn8Z93Cr3ESksJNDR4HFH2KVETkSR3mX6NU8tN7lL9+/bt48KFCx5GIyKSfy70tLHx2Ibk8jpNcJ2TBhUSmTcHn7/40pbie8UiMixNfJ376urqmD17NuBULNME2CIiY/P4Kz8mHA0D0FDZwLya+d4GJCkFXxwYnxYqwkIioERNRFyUqOWHVatWJW/v2rWLnh61foqIjEZvuIfHX3k8uXxH41oPo5F03C1qpcuWexiJd5SoiUjSHFfXx6MX+whHVFAkFzU0NFBTUwNAX18fO3bs8DgiEZH8sOHoBi73XQKguqSGVdOu8jgiSSkWG1yaf5Fa1ESkyFWVBZk2xZmrKxKFwxd6PY5IUvH5fINa1bZu3UokEvEwIhGR3BeNRQdNcL26YTUBX8DDiGQ4/qMn8V/udBYqK/DPmO5tQB5RoiYig8xztaodUkGRnLVw4ULKysoAuHz5Mi+99JLHEYmI5LYdp7dzvOM4ACX+Em6eeYvHEclwBhUSmT8Pn8/nYTTeCXodgIjklrnTKtjR2gY449Reu3yqxxFJKoFAgOXLl7N7924ANm3axFVXXVW0JzMRkZGsb/5R8vYNM2+kNFjqYTSSTuCl5uTt0JIlAJx793vG/4A+H9O+918TDSvr1KImIoOooEj+WLZsGYGA023n1KlTHDlyxOOIRERyU8vFZl449wIAPnysabzD44gkHXeLWsnSeCGRaHT8//J0eIBa1ERkkDn1lfiAGHCivZ/ecJTSoK7p5KKysjIWLVrEgQPOCW3Tpk3MmzfP46hERHLP+uaBsWkr61YytVS9RXJWJELw5ZbkYnDRwkGrg4sXU3rnOkpuuAFfoLDHGCpRE5FBykIBZk4t49TFHmJA6/kels2s8DosGcbKlSuTidqBAwc4f/489fX1HkclIpI7znWf45fHf5FcXtt0p3fByIgCrxzF1x0fI19TTaCuDoDK3/99ep95hnBzM+HmZrp++CCld9xB2Z13Epw318OIM0eXyUXkCu6CIi0qKJLTampqaGpqSi5v2bLFw2hERHLPY4ceIRJzur7NmTKHpilNI+whXgrsHSjL718wP3m7/PWvY+r9X2TqV/+W8je/GZ/fT8+Pf8zFP/1TLn76z+j+yRNEL3dkP+AMUqImIleY6x6ndkbj1HLdypUrk7d3795NV1eXh9GIiOSO7nA3P33lieTyHY3rPIxGRiPoStRK4oVEBq1vbKTyvb9N7Tf+mepPf5qSm28mfPQond/6Fm0f+hCX/vZv6duxk1g0ms2wM0JdH0XkCu6CImpRy32zZs2irq6OtrY2wuEw27dvZ+3atV6HJSLiuZ8dforOsDMfV21pLSvqVngckYxkUKK2dNmw2/n8fkpuuJ6SG64nermD3l/+gp4NG+nbspW+LVsJNDRQ+7WvZiPkjFGLmohcoam2An+8zPvpjjCdvflZLalY+Hy+Qa1q27ZtIxwOexiRiIj3IrEIj7SsTy7f3rAGv08/fXNafz+BA4eSi8FFi0a1m39KFeVvfCPVH/8YJddfD0D08uWMhJhN+raKyBVCQT+NteXJ5UPn1aqW6+bPn095ufOZdXZ28uKLL3ockYiIt7ae2MLprtMAlAXKuGHmjR5HJCMJHGzF1x+/0Fhfh3/KlBH3iXX30PPzp7n42c9x4aMfo2/nTnyVlZSty/9urur6KCIpzZ1WydE2Z6zToXM9vKqhcoQ9xEuBQIAVK1awc+dOADZv3sw111yjCbBFpGitbxkoyX/TrJspCZR4GI2MhrvbY2DB/LTb9r3wIr0bNtC7bRv09YHfT+jaaym7605KbrwJXyj/05z8fwUikhHzplXyqwNnAU18nS+WLl3Knj17CIfDnDlzhkOHDrFolN1GREQKyb62fexrexmAgC/A6obbPY5IRsM90XVo2fIr1kdOn6Znw0Z6n32W6LlzAAQaGii9cx1l69bhr63NWqzZoERNRFKaqxL9eae0tJTFixezb98+wGlVU6ImIsXoYdcE16vqr6K6pNrDaGS0Ai81J2+XLlk6aN3FzxnC8fObr7ycsl/7NUrvupPQ0sHbFRIlaiKSUkNtGaGAj/5IjLauCO3dYWrKdcjIdStWrEgmai0tLZw5c4YZM2Z4HJWISPac6jzF5hObksvrmvJ/rFJR6O4h0HIYgJgPAgsXDFqdSNKCixZRcsvN+EpKkpNfj0b53XdPbrxZoF9dIpJSwO+nqa6CV846ZY0PnevhujlVHkclI6murmbu3LkcOXIEcCbAfstb3uJxVCIi2fPYoUeI4syhNb96AbMqZ3sckYxGcN8hfBHnc/PNmIG/vDzlduGWFsItLWN+fCVqIlJQ5k6rTCZqLUrU8saqVauSidqePXt49atfTVWVPjsRKXwdfR08dfjJ5PJaTXCdNwKu8WnBRQuvWF+65naguApkKVETkWG5J75WQZH8MX36dKZNm8a5c+eIRCI899xz3HXXXV6HJSKScU8d/indYed8VV82jaW1hTt+qdAEXxqo+BhKMdH1lD/+42yGkxM0j5qIDGvekIIisVjMw2hktHw+H6tWrUouP/fcc/T393sYkYhI5oWjYR499EhyeU3jGk1RkkfcpflLlizxMJLcoURNRIY1o6aMspBzmLjcG+V8Z9jjiGS05s6dS2Wlk2h3d3ezZ88ejyMSEcmsX534Jee6nZLtFcEKrptxvccRyWj5LnUQOHwcgJjfT3D+fG8DyhFK1ERkWH6fjzmuVrVDKtOfN/x+PytWrEgub968WS2iIlKwYrHYoJL8N8+6hZA/5GFEMhaBfQPFQXwNs/GVXDk5+fnffz8d3/p2yv379+8ncupUpsLzjBI1EUnLPU6t5bwStXyyZMkSQiHnh8r58+c5ePDgCHuIiOSnvef30nzRKdMe9AVZ3bDa44hkLNwTXQcXp57/M3b5MrHurpTr2j/7Obp+9FDKdfksbTERa+14L78+Y4y5c5z7ygRYa28F3gDsM8Z83+t4JP+5J75uPqOCIvmkpKSEJUuW8NJLLwFOq9rSAp4YVESK1/rmHyVvXz39aipDqnSbTwaNT0tRSGR0Cq/XyEgtaqeH+ZcYld4zzPq2TAQro3IrYIB3ex2IFAZ3i9qh8yookm9WrFiRHEzf2trKyZMnPY5IRGRyHe84znOntiWXVZI//7hL85csViGRhLQtasaYWanut9ZuBNYBPzDG3Dv5YYlIrqivKqGyNEhnb5ju/hinL/czq/rKvuOSm6qqqpg3bx6tra2AMwH229/+dm+DEhGZRI+0rCcWb01ZXLOY6RUzPI5IxsLXdpHAybMAxIJBAnOaPI4od2iMmoik5fP5Bo9TU0GRvOMu1f/iiy9y6dIlD6MREZk8l/ou8fMjP08ur21Sa1q+cXd79M9pxBfUNM8JWXsnrLXvBH4PuBGYitM9chPwd8aYZ1Js/zHgq8DDxpi3WWt/D/hDYDnQBWwA7jPGHIpvPw/4DM74rBlAK/DPwNeNMbEhj30tsAtoN8ZMtda+BvgUcANQBrwc3/ffhu475HFuBD6K07o4Mx7X88C/A/9ujImO8Lx3Ap8AbgamA18wxnw+vu31wNuA1wBz46/pErAb+DbwXXds1tqpwAXX0701xRjD64wxu4fGMcxrexvwEPC8MebaIesuAjXAdfGY/g/wOmA2sGno+MT4+/uHwG3AtPg+24FvGGPWp3p+yS1z6yt46Xg74CRqty+s9jgiGYtp06YxY8YMzpw5QzQaZdu2bbzmNa/xOiwRkQl74pXH6Yv0AjCjYiYLa1IXopDcFXAlasHFiz2MJPdkPFGz1pYD3wPe6rr7Ek5i83bg7dbazxhj7k/zGN8APoQzNq4XJ2l5F7DWWnsLUAs8xUAyEwKWAV+L3/eZNI/9u8A3cVoXLwKlOAnbN4F11tr3pUrWrLWfAb4AJGZS7ACqcZK2dcBvWGvfboxJOcustfb9wL+4njc6ZJNtQCB+O4yTBNYDvxb/9yZr7W+6YovijA+sAKbE36eLQx5zsme8vQ4nma4BOuNxJllr/cA/4CRpCZeAOuD1wOuttQ8YYz40yXHJJHO3qDWfSV1xSXLbqlWrOHPmDAA7duxg7dq1lKQofywiki/6I/38+NBjyeU7Gtdqgus8FHxp9IVE+rZuo23f/jGv8wG1X/+7ccfolWx0ffwnnCRtP/AOoNIYU4Pz4/7jOAnIF621bxxm/zuB9wEfxEmEqnFaoA7jtOB8EScRfBFY4Xrsv4rv/6l4a1sqFcA/4rQcNRljanGSCBtf/14GJxkAWGvfB/wFTtLxCWCaMWZK/PHejNOa96b4NsM97z8A33E9byXwLdc2T8Vf9xygLP66qoEP4LRGvht4f2JjY8yl+JjCz8XvesIYM2vIv73DxDNeX8f5XG80xlQZYyrcMQGfxXn/TuC0ptbEX0cV8DvAOeCD1tor3mPJLXNdiVprWx/RqAqK5JumpiamTJkCQE9PD7t27fI4IhGRiXn22EYu9DqdiapCVVw97WqPI5Ixi8UGleYPLUlfSCTW3U301Kkr/qVbFz11Km/nWMtoi5q19gbgXuAUcJcxJlluzBhzCfiatbYLp2XpM8BPUjxMDfAxY8y/uu57zlr7EeARnGTqBE6y0B1/7A7g0/Eud9fjJIpfT/HYIWAn8C5jTMQV1+fjXQk/Cnw23uoTjr+mMuCv4/u/wxjztOs19QKPWWtb44/7EWvtF+OPOfR5f2KMeZ9r3z6c5DOxfEXiaoy5DHzTWns6/tr/N/CvQ7fLosvA640xyZY7Y0wzgLV2NnAfTiL+OneSaIzpAv4z/jp+Ctxnrf1Gum6m4q2pFSXUVIRo7+qnLxLjeHsfc2pLvQ5LxsDv97Ny5Uq2bt0KOEVFbrrpJvx+DVUWkfwTi8VY3zIweuLW2bcR9GtsU77xnz6H/3z8Z2RpKYHZs4fdtvqzf56lqHJHps/Q98b/ft+dpA3xPZyJD2611qaa9OIiznixoX7OwIQJX0skaSm2AbgqTYxfTiRpQ3wJpzvhLGCN6/434Ywn2+1O0tyMMS8Ce4By4PZhnvevh7l/NH6K043x6mHes2z5V3eSNsRvAiXAk8O15BljngTOA004Yw8lh82rV0GRfLdo0aJkd8eLFy+yf3/qLiIiIrlu99ndHL7UCkDIH+LW2bd5G5CMi7ssv2/eHHxpLh6WvOpVE/qXjzJ96SExLfzvWWvfM8K2AaABODDk/gPx1qZBjDFd1tpOnG50Lw7zmKfjf2vTPO/GVHcaY05Za/cDK3Ba5RLbJV7TcmttunbURJGOOSnWxYAtafZNjO/6TeA9wDU4RThSNWHMAprTPVYGbU6zLvE+vXaE96km/ncOThEXyVHzplWy56iTl7ec7ebOJTUj7CG5JhQKsWzZMl544QXAmQB7xYoVHkclIjJ27gmur5t+HeXBcg+jkfEK7h34CRvK0PxpsViM/t3PU3LdtSNvnGMynagl2i8TY8tGUpHivnSzs0ZG2CaxPjTM+m5jzIVh1gEcx0nUprvuS7ymsvi/kaR6TZ3DtAACye6VjwCvdd3dgzOmK/GaZuCMjazEO2fTrEu8T5WMLsZU75PkEPc4tYNnh/36So5bvnw5e/fuJRqNcvToUY4dO0ZTk+asEZH8cfhSK7vO7Ewur2lc62E0MhHu8Wmly9IXEhmryKlT9GzYSO8zzxC9cIFpP/j+pD5+NmQ6UUu0X77PGPMfGX6uTEhVOijxmr5ljPm9cT5uqq6Wbh/HSdLacaYNeHRo11Fr7WWc1kQvyxulex2J98kYY/5vNoKRzJrr6vp49GIf4UiMYEDVtfJNRUUFCxYsoKWlBXBa1e655x6PoxIRGb2HmwfGpi2rXU59eb2H0ci4xWIEXBUfg4smXpo/1ttH75bN9Dy9gfDLAx21fBX52R6Q6UTtNE4Z/pUZfp7xKrfWTk0zzirRKuRuOUp0p8zka0r8avozY8wDQ1daaytxkrTxSpTRT9ciONF+bdl4nySLqsqCTJtSyrnLvUSicORCLwunjaZRWXLNypUrk4nayy+/zMWLF5k6NeWUiiIiOeVCzwU2HtuQXF7bqAmu85X/6En8lzudhcoK/DOmp98hjf4DB+h5egN9mzcT6473+gkEKLnuWkrXrqXkhhsnIeLsy3QxkcQYprdba3P10nvK/+HW2pk4c7GBU8ExIfGabrTWzs1QTIl+SO6FAgkAACAASURBVMPVz/61NPsm5mNL934nEtNSa+20Yba5Kc3+o5F4n14fTyylAMytH7gipYIi+auuro7Z8cpasVgsWQlSRCTXPf7KY4SjzvXmhsoG5lUPNwOT5Dp3t0f//HljngMv2t5O1yOPcOFjH6f9zz9L79NPO0la/HHq/vUBqj/1KUpvvRVfKD8rgmY6UUvMC7YU+Ei6Da216Qp+ZNKnrbWBFPd/CqfAySngl677H8WpVBgAvpouAZ3Aa2qP/72iRI21thT4fJp9E1MBDHt53BhzDEiMzXvr0PXW2kbgt0cTaBrfxalMORVnYvBhefjZyxgNmvha49Ty2sqVA43dO3fupKdHibeI5LbeSC+Pv/J4cnmNJrjOa8G9A90eR5o/LSEWidL73HYu/dVf0fYHf0jXd75L5MQJfJWVlL3udUz9y78kuHQpAP4qLwujT46MppfGmK3W2n/Dmez4a9baOcDXjTFHAay11Til7+/FSXx+I5PxpNAPXAt8z1r7cWPMcWvtFJwxYp+Ib/OFxBxqAMaYTmvtx4H/wJnA+1Fr7WeNMbsArLUlwHU4E1K/k9RVH0fyFLAYuN9aexR4yhgTtdZejTMf3BKgD6f8/VCJUvg3WmtfZYx5YZjneBBnEvH7rbWHgQ04rXFrcea1iw6z36gYY45aa78A/F/g4/Fk7C+NMQcArLUVwC3Ab+EkpLdM5PkkO9yJWosStbzW2NhITU0N7e3t9PX1sXPnTlavXj3yjiIiHtlw5Gku9znXo6tLqrlqWrrZlyTXBVyJWsnSkWdp6vzP79Dz7LPE2uPtGT4foauvpuyuuyi5+ea8bTVLJxuv6H/jJBS/DXwS+KS19hJOifpqBrrorU+9e0Z14SRl3wTeaa29GI8p0cL2n6SYw80Y85/xxONvceZVe5O1thvoxhnbldh/uLFvI/kC8BagEXgC6LXW9gFTcJLL9wD/j9SJ2nbgeZyS/nusteeAeAdg7jbGvBS//Xng13GmRHgKp6pkFKf64n6cFsWJTqb9Fzhj6T6Fk4zfG59SoQ/nfUq06O6e4PNIlsypr8SH85/3xKV+esNRSoOaMDkf+Xw+Vq5cyebNTi/lrVu3cssttxAIpOpgICLirWgsysOuCa5vm307AZ+OV3krEiH4srs0/6IRd+l+9FEA/LW1lL3+dZSuW0egvrALyWT8F5YxptcY816cKobfB44yUNq+Fadl5z3AezMdyzDxfQt4PfCz+F19wA7gAzjVKmPD7Pd1nEIZ/wjsw0lypuAUHnkK+GNg1ThjOgncjJOMncT5nDqAHwK3GWP+J82+MeAN8X2P4CRE8+L/SlzbnQRuBb6NU/jDH//7lfhznxtP7ENjMcZ8Gme827eAQ/HnqQRO4HQjfT/wmok+l2RHWSjAzBqngEg0Bq3n1V0uny1atIiyMufzvHTpEi+/rKkMRSQ37Ti9neMdxwAo8Zdw86ybPY5IJiLwylF8Pb3OQk01/trRj4KJXrxI/0svE963n1h/f4YizA2+WCxlHlLQrLXX4hTqaDfGqNSZ5BRr7UZg3bx587j33ntH3L6jp5/NB89RV5VqPvTJ9x+/OMTWlvMA/M7N07l7VV1WnlcyY/fu3Tz//PMAzJ49mw984AMa85Ff9GFNTPH9CMpTn/nl/+GFc3sAuG32an594Zs9jkgmomT9U1R9/msABK69mtrP/PmI+/Tt2kXPz5+mb+dOCDujknwVFZTefjuld95JaIlT3v/iZz9HeP9+pv3wBykfJ3L2DKV33EGgbtS/Xzw7zhZeZ04Ryai50yqTiZoKiuS/ZcuW8cILLxCNRjl58iRHjhxh3jxVUROR3NFysSWZpPnwsabxDo8jkolyV3wMxYt/jKTkuusoue46opc76H32GXo2bCRy5Ag9Tz1Fz1NPEWhqovTOdQPl+QuABpeIyJjMq3cXFFHXx3xXXl7OokUDYwMSY9ZERHLFw80PJW+vqFvJ1FJ1hsp3wZcGxqeVLF2WZssr+adUUf6mN1H7lb9m6l/+JWWvfS2+igoix445VSCPHAGgd/PmvO8aqRY1ERmTproK/D4f0ViM0x1hOnsjVJZqQHc+W7lyJQcPOtW39u/fz/nz56kv8AHaIpIfznWf4xfHn00ur2u607tgZHL09xM4cCi5GFy4cNwPFVy0kKpFC6m89330btlK74YN9L/4IgCXv/o1fOX/n737Do/rvA78/71TMTPovRMECJIAQbBKIiWREklLNlUsW7aKs7HjJI7XcXrZOGXtm5tNvM7Gu9nfb+Nk12Vj2ZJtNYqiCqlOghQJNrE3EI1E7yDqYNrdPwYYDkgQdYABBufzPHyAO3PLAQnO3DPnfc9rw7J5E9YtW7CsmlbriLCSipoQYkrMJgNZCbbAdo00FFnw4uPjycrKCmyXl5eHMRohhLjpreo38OpeALKjc8iOyQ5zRGKmjBW1KO7hla+SEjHExMz4nIrZTNSW+4n7zrdJ+MEPsH3xCxhSUtAHBxn68CN6/m7cJX3nrUVZUVNV9TQyAVuIactNdlDXOQBAVbuTkkzHBEeI+W7VqlU0NDQA/gYj27dvx2azTXCUEELMnkHPIPtq9wa2t2ZvDWM0IlRMF2+un2bMXxry8xtTknE8/TSOp5/Gde4cQx98yNDx4yG/zlyQipoQYsqCF76WhiKRIT09nYTh9sgej4cTJ06EOSIhxGL3wbX36Hf7l4KNtyZQlFgc5ohEKIxqJLJiavPTpsqyejUxf/xHJP7oh7N6ndkiiZoQYspygxuKtMvQx0igKAqrgsbvHz16FM9w+2MhhJhrXt3LnqrXA9v3Z96PQZHb1khgvHCzomZdNrmOjzNlsNvn5DqhJr/xQogpy0yIwmz0jx7uHPDS45Qb+kiQl5cXGO7Y39/P+eEJ2UIIMdeONpXTPNAMQJQxig1pG8MckQiJQSfGKn9XRl2ZnaGPkWTBzFHTNO22RSlVVZ0388w0TasHsoAtqqoeCsH5TMBIT9EcVVXrZ3rO4fNuBG4dqPuBqqqfCsX5xeJgNBjITrRT0+YfklLV5mRdTnSYoxIzZTQaKSoq4pNPPgH8rfrXrFkjC2ALIebc7qCW/BvT7sJitIQxGhEqpsvVKD4fAEpaGgaZCz2uBZOoBWkHvGM9oWnag8BHw5tLVVWtvcN+3wO+Nbz596qqfjvEMc5nbqBl+HsbEBvGWMQClpvsCCRq1R2SqEWK5cuXc/bsWTweD62trdTU1JA/g9bJQggxVZc7L3O58xIABsXAfZn3hzkiESrGoPlpJqmmTWghJmp33SkBmwxN0/4Z+OPhzb9RVfW7IYkq9HTgyvD3IVutT1XVM0A6gKZpXwN+FKpzi8UluKHI1VZpKBIprFYrBQUFXLnif/k5cuSIJGpCiDkVvMB1SdJqYq3ymXKkMAXNTzNPcaHrxWghJmrTommaAvwr8I3hh/5UVdV/DmNI41JV1QusDHccQtzJklsaiui6LkPkIkRxcXEgUausrKStrY2UlJQwRyWEWAxa+ls40ng4sL01+4EwRiNCLbg1v2X53DQSWcgWRTMRTdMMwE/wJ2k68M35nKQJsRCkxkURZfa/hPQO+ejol4YikSI2NpacnJzA9pEjR8IYjRBiMXmj+nV8+Ocw5cXmkeHICHNEIlSUnj6M1/zrdeoGA6YlS8Ic0fwX8RW14aYczwG/BviAr6mq+u8THLMU+DPgYSAb8AAVwEvAv6iqOjDJa/8U+A3gRVVVnx1nv28DfwccV1X17qC4x2wmomna3wN/A/xEVdWvaZr2m8DvAsX45++dAL6rquoHk4lTiOkwKAo5SQ6uNvcC/nlqydHmMEclQmXVqlXU1dUBcPbsWXbs2IHDIQubCyFmT7+7n/euvRvY3pol1bRIYrxUGfheycxAsYSuQYynoRFPRQW+nh5M2dlYNqwPPKf7fCiGhVmbWphRT5KmaWbgV/iTNA/w5UkkaU8Bl4DfAwqHH7YCG4B/BA5rmjbZMUC/GP76uKZp43Va+NIt+0+apmn/DvxfYB3+RDQW2A68q2naE1M9nxBTIeupRa7U1FSSkpIA8Hq9HD9+a7NYIYQIrXdr9zHo8c95TopKZnmCzGGKJMELXZuWFYTknN6ODm78l7+n+0/+hL5/+zcGXniBoaPlgecH33qLjme/hOvcwlxuJpITNSuwC/gC/srUM6qqjpsIaZq2CX+yZAT+K5CrqqodsAP34q9UrQF+OskYPsDfYdEOjJk0aZq2BijCn2S9OMnzjvgC8AzwH4E4VVVjgQLgEP5/23/RNM04xXMKMWnBDUUq52lDkRs3bnDkyBFee+01nn/+eZ5//nleeeUV3n77bY4fP05jY+Mdj62vr+fgwYPs2rWLF154gZ///Oe8/PLLvP/++1y5cgW3O2R9fuadWxfAPn78eET/vEKI8PL4PLxR/UZg+/6s+2Xec4QxXbxZUbMsn3kbBl9vLze+/R3c585hzM4m6lM7btvHsnkzKAquBfphYyQnar8EHgOGgM+rqrprEsf8M/7hoH+qqupfq6paB/7GHqqqHgE+AzQDj2iatnaikw03BHlpePPX7rDbSDXtI1VVmyYRY7B44DdVVf3hyHBMVVWrh8/pxj9s854pnlOISQtO1Ko7/A1F5pOamhr27NlDRUUFHo+H9PR0cnNziY2Npaenh4sXLwbWDAs2ODjIvn37+OCDD6iursZgMJCZmUlubi7R0dE0NTVRXl7Oq6++Sl9fXxh+srmxZMmSwHDHgYEBzp49G+aIhBCR6uPGQ7QPtgFgM9lZl7p+giPEQhPcmt+ybNmMzzf42m587e3YHn+c+O//E9Ff//rt10xMxJiVhfvy5RlfLxwieY7auuGvz6mq+tZEO2uatgLYBPQDPxxrH1VVOzRNewf/vLOHgNOTiOMXwB8AD2malqSqakfQNRXg2aD9pqpaVdXbqnCqqtZrmnYS/89TAhy+7UghQiAp2oLDaqJ/yMOgW6el10167PxYlHRwcJDDhw/j8/nYuHEjRUVFGILGqOu6TktLC62traOOc7lc7N27l97eXlJSUti0aROJiYmj9nG73Vy5coWzZ8/icrnm5OcJB4PBQFFRESdOnACgvLyc9evXy6fcQoiQ0nWd1yt3B7bvSb8Hs2HxzHm+2HGR4qTicIcxq5TOboxN/kRcN5kw5mTP+JxDJ05gSEnB/h9+bdw5aIbkZDw1NTO+XjhEcqJ2FH816euapp1RVfVfJ9j/3uGvVuCapml32m9krlnOnXYIpqpquaZpVfiHJD4F/O9brrkEf9Xv1cmc7xYnxnmuYfhrwjTOKyJIa4+T1NioWTm3oijkJtm51NgD+OepzZdEra6uDo/HQ0pKyqghfCMURSE9PZ309PRRjx89epTe3l6Sk5P59Kc/jdF4++hhs9lMSUkJubm5mEyR/DIKhYWFnDlzBrfbTXt7O5WVlRQWFk58oBBCTNKFjgtUdvvbthsVI/dm3jvBEZHjfPt5fnXlF+TGLmFb9jYKEyKzZX3w+mmGnGyUELx3+trbsaxfP2GjEMVuQ1+go18ieejjV4B9w9//i6Zpvz3B/iP9X01A2jh/RsZ62acQy6+Gv37plsdHtt9WVfXGFM43onec50Y6Oyyej6TEmP7utXP8zUun+WlZFYcr2mjrCW3Tj1HDH+dRQxGn0x9LVNTkk9Senh5qhj9127Rp05hJWrDY2Fjs9qm8FCw8FotlVGImrfqFEKEWvMB1afIaHObx+q9Flj3VrwNwvecaz138KS9XvEjbQFuYowo9Y1CiFqpGIorFgj4wcSN2X1s7ygLtWhzJHwW7gM8DbwI7gB9qmuZUVfWFO+w/krQGWuSH0Av42+lv0TQte3hoohF/hQ2mN+xRiElRgBsDbk5Ud3KiphOAeLuFwvQYlqfHUJgeS3KMddrnD07UrrZOauWKOTEyt6qpqYmuri4SEiYuLtfX16PrOgkJCYGOhwKKioq4dOkSuq5TU1NDc3PzbZVIIYSYjsa+Bo41Hw1sL6YFrpv6m9B1HZPBRIothU5nJ2faznC58zKbM+9lS+ZWrKbpvz/PJ8EdHy3LQ9PN05iTg6emBt/AAIY7fGjq7ezEU1uLuagoJNeca5FcUUNVVSfwWeAg/p/1OU3TvniH3VuGv64IdadEVVUvAWfw3zOPzEnbAaQCPfiTSSFmxX/70nq+saOQHSXp5CY5UFDo7ndxvKqDFw7X8re7zvLtl8/ws4PVlFe209E3NKXz5wYlarWdLny++dFQJDc3F5vNhsfj4Y033uD999/n/PnzNDU13XFeWUeHfwqpJGmjRUdHsyRoYdLy8vJx9hZCiMnbU/U6Ov73jYK4AlLtqWGOaO6k29PZlrMNj8+DxWjlmRXPck/GJoa8Q+yv+4h/O/sDTrXe3vBqwdH1UUMfzSEaPm+9/z70/n76f/RjdI9njMvq9P/7T8HtxrplS0iuOdciuaIGgKqqA5qmPQq8i7+5xi80TXOpqrrnll1HxvPE4k+i3iW0foG/tf+vAd/n5rDH14YTSiFmhc1ipCQnnpKceACcbi9VLb1cbfb/qescoKvfxbGqDo5V+xOVRIc1UHG7Z1nyuOePt1uIs5u5MeDG5dVpuOEiJyH8nwCazWYefvhhDh06REdHBw0NDTQ0+KduKopCcnIyRUVFLF26NHDM0JA/SZ3KcMnFori4mNraWgDOnTvHjh07iImJCW9QQogFrcfVw/vX3w9sb81+MHzBhIGiKNybeR8ur4v3r79HeZOVz+R9hvy4fA41HKKu9zqvXn2F022n2Ja9nby4pROfdB4ytLRj6Oz2b0RZMWZkjH/AJEXt2MHQwUMMffwx7qoqLOv9nUK9dfX0/+KXuI4dw9vYiKmoCOvWhZmoRXRFbYSqqr34W+t/gn/O1kuapn36ln3Oc7M5x3/TNO2OE080TbNrmjbVjgm/BHRg3fDaaZ8fflyGPYo5FWU2sio7ns9tzOE/PVbMP31pHd98aDmfKkknL9mBQVHo7BviaGU7z388uS5JS+bpwtfx8fE89thj7Ny5k9WrV5ORkYHFYkHXddra2igrK+PQoUPhDnNBSElJITXV/0m3z+fj2LFjYY5ICLHQ7avZi8vr/4As1ZZKQVxo5i4tFCNL2qxLXc/yhOVUdF3hcudlViWV8OWir7Az7xHirfFUdVfx4/M/4rXKXXQ5u8Ic9dQFt+VXluRO2PxjshSTidi/+issd9+Nr7kZ59tvA+CpqmJw9268jY1Y1q8n9i/+YsF2K474itoIVVVvaJr2EPARUAq8pmnao6qqfhS02+8DZfgrX2Wapv0FcEBVVa+maQagGHgS+F3gLqB+Ctev0zTtELAF+L9AHP7hlh/M/KcTYvqsZiPFWXEUZcZyvaOf83U3OHC5hYEhL5MdxJib7OBsnf/Tsqq2QR4sjJu9gKchNTU1kGSMJGlnzpyhsbGRqqoqsrOzycvLw2r1VwJHGpGI0YqLiwPLGZw4cYItW7ZgscyPLp9CiIXF7XXzVtAC11uyti7Ym+npGvl546xxPLvi13jh8vO8e+0dzEYzm9I3sznzXgoTCjnRcpxjzcc42XKCS52X2JK1hU0ZmxfMEgajhj0WzHz9tGAGh53YP/8zPNev4zp1Cl9LC7rPhzEpGfO6tZhDsF5bOC2aRA1AVdXO4WRtP1AEvKFp2qdVVf14+PmjmqZ9AX+VawP+JMqlaVov/iGRwf8jpjMR5xf4E7WRVRxfGl4UW4SYpmlfBf59gt18qqoah/fPA8YrH72oquqzYz2hadpvAL+HP5H3AqeA76uqOq/nHuq6zvWOAa4293C1uZeqlj6cnuFfRx3S4qMoTJvc0LZRDUXaBmcj3JBRFIXU1FR27NjBW2+9RWdnJ9evXycvL4+kpCSqq6sDc9XEaDk5OcTExNDb24vT6eT06dPcfXeoey8JIRaDsoYDdA35q0PR5mhKU9aEOaK549N9GBTDqG2L0cL9mffT2NfIh9c/JM2eTn5cPqn2NB5a8mmKEos50nSYix0Xead2H6daT/G7pd/EbJz/yVpwomZduXJ2rpGbiyk3d1bOHU6LKlEDUFW1VdO0HcABoBB4W9O0h1RVPTb8/JuaphUCfwjsxL/+WTzQDVzG3/L/ZVVVG8a8wPheBv5/biZ8Muxx9pwG7rQY3hZgO7B3jOfOALvHePz8WCfSNO37wJ/hr67+CLDgbxjzhqZpf6Cq6r9MMe5Z49N16jr6qRiem1Y9kpjpoCiQmWCnMC2GZenRLEuLITpq8i/+DsvNl5LaThdfff4qWwpieHRV4rxZV+1WBoOBjIwMOjs7AxW07OxsTpw4QVdXFx0dHdJU5BYjC2CPDHvcu3cve/fuxWKxUFpayubNm29bHFwIIUY09Texu3IX++s+YtBz80O90uQ1mAyL55b01iRtZLswYTnPrHiGF6/8ij1Vu3l2xZdId2RgNphZGpdPuiODkqTVvHNtHwVx+ZiN5tuSvvnEUNdE1M92YTp6OvCY6/gJTEuXYpTOwZOijIyPne80TRsJdKmqqrXhjCVSaJr2NfzJxQeqqn4q3PHMFU3TjuBvLPPESFOZoIrac6qqfnWS57kX+BioAu5SVbUr6Fwn8a+5t3Kqv6+apu0HHliyZAlf/erEofQ53Ry52k5i9NgNPN473xSomA0NJ2YGg0J2op3C9BiWpcWwLC0am2V6b5IX6rv58f4qXB7fqMeNCpiMCn+8LZN12XO/Jo6u6xMOozlw4AC1tbUsW7aM++67D4CysjJqampITk7mM5/5zLhrqfX09GAymSJ+LbVg165dY//+/bc9bjAYMBqNPPXUU7Ig9txaXGPFQm9h3ARFgJMtJ/jese/i8Xnw6qMHE5kNZr608j+wIiE0bdvnq9Otp2geaGZlwkp0INWeisPswOPzjEpUD9Tv571r77I8YQWfW/Z5Yi2xo87TM9RDrNX/2HxN1MyHThD9598FtwfFG/TvbTSCyUTsn/0plnXrQnY9X1c3vq5OdLf7zjGt8P9+edtasW7ZgnHyHyyG7XV28Xx8IQSgaVoJ/iStAXhrhqf7xvDXfxhJ0gBUVa3VNO0HwLeB3wTUGV5nRl4/UQ8KZCXYKcmOY1laDPmp0VjNM1+Foq3HOWaSBuDVwevR+Z8fNfKPT+TNeWXtypUrtLe3s2LFClJSUkY95/P5qKys5Nq1awDk5eUFnrvnnntoa2ujvb2dd955h82bN9+2Bpvb7aaiooIzZ87wmc98ZtEkaj09PXdsvuLz+fD5fLz88st84xvfkMqaECKgqb+J7x37LkPesZd/cfvc/PLyC/zB2j8iyRaZIxm6nF28cvVlAA41HMRsMGMymMiMzsJhdpBmTyPTkYnVFMUD2Q/S6ezkZMsJyuoP8Fj+46PONZKkAfMySTPUNRH9599FcY7x7+31gtdLz3//HyR8/59mXFkbOn6CgV/8Am/DBAPdFIXkF381o2uFw0JM1Go0zT+iTVVV+SRxijRN2wgcD3ccYfQfh7/+5A7zAzM1TfuPQBLQARxRVfXsHc61ffjrvjGe24s/UdtOmBM1AHRo6h7EaFBwe3W8Pp2CGVTRRnxwoRmP9/YkLZjHq/P2hU5+a/PcDnPw+XxUVVVRVVWFzWYjMTERi8WCy+Wis7OTwUH/sJuSkhKysrICx1mtVnbu3MmBAwdobW1lz549xMXFERcXh8FgYGBggPb2dnw+H1FRUYuqmcbFixfxesefVuv1eikvL+eRRx6Zo6iEEPPd7spdeHy3r3MVzOvz8nHjIT5b8MQcRTW33r32DgA2k43smBwMGOj39NHj6qGqu3LUvg6zA4fZv+5pedMR1qasIzsmOxxhT0vUz3bBGOuajeLxMPDmW8R87benfR3XyU/o/f73QddRoqIwpKai2GzTPt98tJAStZaJdxGT4Ob2v8vOcAQy1zRNswG/DviAH99ht4eG/wQftx/4DVVVrwc95gCygD5VVZvGOM/IzNnl48TzVeCrYzy19k7HTMefPVoUWDOturWP6+39fHixGYXgeWkxw/PSpvaScLy6g4nWt/bqcLCqd84TtcLCQqKjo2lsbKS9vZ2uri6cTicGgwG73U5mZiaFhYWkpaXddqzdbmfnzp3U1dVRU1NDW1sbjY2NgeQsMzOTnJwcli5ditk8/ydyh0p1dTUTDZf3+XycPXtWEjUhRMD+uo9uG+54Kx8+TredishEze1zYzVaSYhKoMvZRdtAK5sz7yXdnk6KLRWXz0VDXz2DnkGu9dTS5+6jZ6gHHZ3S5NIFlaQBWN7+CMUzQa88rxdXWRnMIFEbeO010HXsTz2F7XNPoETg+/GCSdRUVZVZhyGgquoZYLH+XT6NvzHMW6qq1t3y3ADwX/A3EqkefqwU+FtgG/CBpmlrVVXtH35upP/8jTtca+Tx+HHiyQMemGzw07U0JZqlKdE8vDpjzIYiDZ0D7L/sz93T42xB89ZiiLOP/6LndI9fTZvqfqFkNpvJzc0ldwZdoHJycsjJyQlhVAube5yx/8FcLtcsRyKEWEicnskteeLyRuZrh9lg5nPLPk/tjRrKm8u51HGRvTVvkxOTy5qUNZQml7Imxf8Z7aaMzfS7+7CZ7NT31ZMU5R9GPl/noo1FGZjcv7c+w6VwPLW1GPPysD/1xRmdZz5bMImaECHw9eGv/+fWJ1RVbQW+c8vDZZqmPQwcAu4Bvgb8f1O85njlh1r83UdvtZabiWBIGRSFJcnRLEmO5qGSkcQtqEV/ax8HL7dy8Ip/razUmCi+8+TqO54vymyYVBIWZV4Yby5ifGazeVLJ2mIaDiqEmFiUKWpUl8c7sRgj+7UjL24peXFLOdt2lqPN5VzrqaWu9zoVXRVsSNtITnQOsdZYHGZ/A67cmJsfNC6UJA1At0eh9E/8761ERc3oOorRiCkzc0bnmO8kUROLgqZpxcC9+Nvovz3ZevqX8gAAIABJREFU41RV9Wia9mP8idpWbiZqIxWzOyVUE1XcUFX1p8BPx4h1P3NQaYORxM3BkmQHnyrJYNDlYf+lVj662MzAkJfW3vE/7borP4mPK9rGHf5oVGBLweTWYxPzW35+PhUVFeMOfzQYDJSWls5hVEKI+e7BnG28W/vOuMMfDRhYmxK6LoDzgdvr5uWrL/FA9oNkRWcFqmKlKaX+haybj3Oy9QQVXVe43nuN1cmlrEleQ4YjE6tp7E7OC4HrkW1YX3tn/OGPRiOWrVtndB1Tfj7etrYZnWO+WzjpuRAzM1ETkfGMvAoEVnUeHgLZAERrmpYxxjEj/ckrpnitOeV0e7lQf4PdJ+r4pzcv8q1fneat0w0MDE3ur2jHqnRMxvFfRkxGhUdWSQfASFBcXDzucgUARqORTZs2zVFEQoiF4HPLnpxwH6PByH2Z989BNHPn7dq3uNhxgdYB//QCg2JA13V8ug+bycaW7K382spf556MTSgYON58jF2Vr3K46TAtAy14fVO9XZkfnF95EkwT1IJMJuyPPTqj69ie+Cyeq1dxnRtzqduIIBU1EfE0TYsCvoy/ichPpnGKkbvO6lse/3D4vJ8B/v2W53YG7TNvON1eqlp6A81F6joH8I1UR4a/JEZbWJYWQ2F6LMszxq+EpcRG8bUHC/jx/ircHt+ocZ7B66jN10WvxdTExsbywAMPcODAAbxe75iVtccee0xa8wshRok2R2NUjGNW1AwYMBqMfGnlf4io1vytAy0cbz5GcVIxy4fXhxtZ31NBCVTXUu2pPJ7/WYoTiylvKudK12U+uP4eV7sr2JC6gfy4AhKiEia42vziy8mg7/t/7V9HbciFEvxeEbSO2kxb8xtzc7E9+SQ93/setkcfxbJhPYbkZLjDGqpTWDdt3pBETSwGTwEJwJtjNBEBQNO0e4BTqqq6bnl8O/Anw5vP33LY/8afqP2Npmm7b1nw+veAIW5P4Obchfpurjb3UtHcS/0YiVmCw0Jheszwn1iSY6Y23GJVdjx//dlVPHewmpo2f68VkwG2L4/jkVWJkqRFmOzsbB5//HEuXrxIdXU1brcbRVECSVtTU5MMfRRCjPJG1R5cPv/bq9Xof49xeV1YjBbWpqzjvsz7IypJA3ijeg9Wo5X1qRtwmB2BJG3EyJyzkYStIH4ZeXFLOdN2mmPNR7nec43rPdfYnrOD7bk7wvVjTJv7/o3cePkHRP/lP2K6MNwI22TCumMH9scenXGSBtD1jd8NfD+4ezeDu3ffeWdZR02IeWukicgPx9nnH4FVw/PD6ocfK+XmWmnfVlX1cPABqqoe1jTtfwB/CpzVNO0VwAI8AyQCf6Cqam1IfoIZ+Lf3r4JCIDGLD0rMlqfHkBwzs8m84K+srcyMCyRqj69O5Jn1KRMcJRaq2NhYNm3aFBjieP36dT766CMATp48yZYtWxbNIuBCiPENuAd4s3pPYPvx/CdYlxpZc9FudbHjAjU3atiUsYnC+Jur9Hh1L0bFSENfAw19DWxI24BR8Q8n9+k+jIqR9akbWB6/nGPNxzjafJTipGKA2xK9hcCXk4HrMw8EEjXrQw8R81u/GbLzGxIS7lg9ixSSqImIpmlaEXA/EzcR+TnweeAu/MMWzfjXm3sJ+BdVVQ+OdZCqqn+madpZ4PfxJ4Q+4BPgn1RVfTNUP8dMxNnN/mGMw8lZSuzME7OxOF03h7REW8afxyQiS05ODgkJCXR1deF2uykvL2f79u0THyiEiHh7a96iz90HQLw1ntKUyK+4v1XzJkm2ZEqT12A0GANVMyP+98YXr/ySHlcPWdFZZEVnATfnr+noRFti2J67gw1pG4mzxi2o1vy38kXf/NDON9AX0nMn/p//HdLzzUeSqImIpqrqJfz1pIn2+wnTm7+GqqrPAc9N59i58A9Ph3T97DsadN9M1GyWhfmGIqZHURRWr15NWVkZAMeOHePee+8laoatl4UQC9uQd4jdVTeHoz2Q9WCgghSpDjaUcWPoBjtyHyI3dgkAOnqgmnai5QSdzk62Zj8QSNJG3Dp/Lc7qbyC9UJM0AN1xM1HTBwbCGMnCtHD/5YUQ84ozKFGzmyP7jVjcbsmSJcTGxgIwNDTE8ePHwxyRECLc3qt9hxtD3QDEmGNYn7YhzBHNriHvEO/U7gPgWk8t13pqATAqRoyKEY/Pwzu1e0l3pLMmeQ3gH/J4q4WcmN1Kjw40zMbXL4naVElFTYhFZNDl5fDVNi439tDUPUj/kAcFsFtNZCXYWJkZx+bCZKKmkWgFD32UitriYzAYKCkp4fBh/1TO8vJyNm3ahNlsDnNkQohwcPvc7Kp8NbB9f9ZWTIbIvu3sd/ezKWMTV7srqey+SmN/A6uTS7k77W7SHOl8cP19Bj2DbMvZTprD30wjkpKysehBQx8ZnN1ETXc60QcH77jWp3R9FELMW+fquvnZwWr/EMVbXsNcHhfd/S4uNNxg35lGvrJlKauy46d0/sFRFbXIfuMRYysoKODMmTP09/czMDDAyZMnZU01IRapj65/SPtgOwB2k5170u8Jc0SzLzEqke05n2JFwkrOtp/lYscFjjaVU91dxcrEIg42lLEysYg1Kf4pCQt57tlkBSdq+sBgyM/v6+9n4MWXcJWX4+vuvvOO0vVRCDFfXWq8wQ8/rETXdeLsZtbnJZKT5CAmyoRPh/4hN9c7BviktpOeATf/58NKfv+h5SzPiJ30NaSiJkaqakePHgXg8OHDbNy4EdNEC58KISKK1+fl1auvBLbvzbwPs3FxVNftZjuFCctJtadREFfA6bbTVHVXcrChDAWFBGsCDrN/OKBBMUR8sjZqjprTGdJz+/r7ufFXf423udnf/dFiAZcLJTYWvacnsJ9hAVbSRsi7pxARzuvTeeHjWnRdZ/uqdJ7YkI3RcHt/lbsL4PMbs9l9sp6PLrTw/Me1/O2TqzGMse9Ygueo2aSitmgtW7aMM2fO4HQ66e3t5cyZM2zYENnzUoQQox1qPEhTfyPgXzdtc8a9YY5o7oy00Y+zxlGasobM6Ewquio403aGpv5Gjrcco9/dx13p97A0bumobo+RmLCNHvoY2ora4Ouv421uxrp1K9Ff+236fvwThsrKSPrxj/ANDjJUdpCBX/0K8+rVxPzeN0N67bkSeb8RQohRztV10d3vYsPSRJ68K2fMJG2E0WDgC3flsn5pIp39Q5yrH2cYwS1GDX2U9vyLlslkYtWqVYHtQ4cO4fPdPlleCBGZfLqPVypeCmxvSt9MlGnxdIC9dVHrVHsad6ffw2P5j3Ff5v3YTXbOtp/lxYpfsbfmbTqdnSiKEkjYIo7dhj7yd+Jyo3u94+8/Ba4TJ1FiYoj++u+gREWNWlPNYLNh+/TDxP71XzNUVsbgu++G7LpzSRI1ISLchfoboMCj67Im3nnYo2uzQB8+dhK8Ph2Xx38zrgBWU2QvQCnGt2LFCiwWCwDd3d2cP38+zBEJIebKseajXOu5BoDZYOb+rPvDHNHsG6tzYzCL0cKS2Dy2Zj/AZwueoDS5lCGPk48bD/GLy89zqOEgQ96hBbeg9aQoyi0t+kNXVfO2tmIqKEAZfr8ZWYxJ99789zAXLsO0YgVDH34UsuvOJUnUhIhwdZ0DJEdbSZ3CQtdpcVEkx1ip6+if1P7Bwx6tJgVDJL7ZiEkzm80UFxcHtg8ePBiZnxQLIUbRdZ2Xr9yspm1Muwu72THOEQvbyOvanYYsjiRwI18dZgcrE4t4aMmneTT/cZbGLaWlv4V9tXupHW7lH4n0mKBELYSdHxVFQbHbbm5b/fc5em/PqP2MiYl4GxtDdt25JImaEBGuu99Ferxt4h1vkR5vo6vfNal9gxuJRMn8NAGsXLky0Jq/vb2dy5cvhzkiIcRsO912mqvdFYB/7bCt2Q+EOaLZdaLlBPtq93Kh4wKNfY20DrQC/qUJ4GYCN9I0ZERCVAJrU9ayM+9RtmY/QHFSMSsSVsz9DzBHRlXUQjhPzZCYiK+94+Z2SjIAnpqaUft5GhthgTa1WphRCyEmzen2YpvGnDGbxTiqUjaewVGNRKSaJsBqtbJixYrAsMeysjJWrlwZmUN7hBAAvHzlxcD361LWEWuZfOfghabmRjWvV70W2LaZ7Hh8bjKiM0mOSsZqtFIQvwyDopBqTyPaHI3L6wrM1zMZTGRGZ5IYdbMjYaR2gAxe9FofCF1Fzbg0D/fZc+heH4rRgGX1agaA/hd+gTE9HUNiEoPv7MNbW4s5aO70QiKJmhARzuPVpzUU0aAoeHyTG642quOjKfLeZMT0FBcXc+nSJbxeL83NzVRVVbFs2bJwhyWEmAUXOy5wvuMcAAYMPJizPcwRza7K7krAPw8vISqRWEsMdb11XO+5Rn1vHT7dx5GmwxgNRny6j7zYpZgNZpJtyWQ6MjEZTKTZ00i2pQQ+wIrEJA2YtTlqlnXrcB0+gvvMaSzr12NauhTzunW4T52i64/+eNS+ti9+IWTXnUuSqAkhZmxQ1lATY7DZbBQWFgaGPZaVlUmiJkSEeimomlaSvJqEqIQwRjP7ViSs4Fz7WTqdnaTZU3kwexsOs4PqG9Xo6DT2NdI+2I5H91DVXUnNjWoAKrquYFSMeHUvJoOJb931V9hMU5+esJAEz1HzhbCiZr3vPszFxSiOmxW72D/+Y/p//nOGysvR+/sxZmZif+qLWKSiJoSYr6pbe/n5oZqJdwxS1dI76X2DK2p2maMmgpSUlFBRUYHP56Ouro5r166xZMmScIclhAihyu6rfNJ6MrC9PWdHGKOZG7mxS3h6+TO8VPEiV7uvsjSugLvT76Y0ZQ0Aa1LWAnC+/RzXemqJNkfzeMETXO2qoN/dT3N/E4UJhdhMtogd8jhi9By1EDYTMZkwpqSMfswWRfTXf4for/9OyK4TTpKoCbEItPUM0dYzNPUDJzliMriZiN0qa6iJmxwOBwUFBVy9ehXwV9W+/OUvhzkqIUQoBXd6LEosJsWeMs7eC9/IAtXZMTlszryXt6rfZE/Vbny6l7vS70bXdUwGEz7dxyetJ/H4POxc+ggrElawImEFQ94hrEZruH+MOTNbc9QWA0nUhIhwO9dmzvo1gpuJOGSxa3GLkpISKisr0XWd6upqGhoayMqa/Lp+Qoj563rPdY40HQ5sfyr3U2GMZm4oioIy/Enm5ox7GfIM8WHdB5xsOcmy+EKSbf7ugydbTlDRVcHSuHxWJZUEKmcjSZqu64HFriOZHj07c9QWA0nUhIhwj66d/RviUUMfZY6auEVsbCx5eXnUDLdMPnjwIM8++2yYoxJChMIrFTeraYXxhaQ7MsIYzdwaSbzuTr+bloEWzrWf5flLP+PLRb+BxWjhaHM5AI/lPz7m8YulC27w0Edvf9+0zzOwa9eM4rA/+eSMjg8HSdSEWAS6+ocYGPISYzMTazOPu2/PoJveQTd2q4kEh2VS5w9uJuKwysuKuN3q1asDidqVK1doaWkhLS0tzFEJIWaiub+JsoYDge3tOZFfTQs2Ugmzmx08tORhbgx1c733OkebjwAKzf3N3JV+N2n2tIifhzae0RW1/mmfZ+BXL0680zgkURNCzDtOt5fvvXERr0/nLx8vBsZP1FweL/+87zIWk4G/fbIUyyTa7Y9qzy/NRMQYEhISyMnJoa6uDoBDhw7xhS8szHbJQgi/V6++EljIOS82j9zY3DBHFB66rpMYlcgjSx/jxYpfcrjxMEbFiNlgZmfeI+EOL+xGJWr905+jZvv85yc9dz5SSKImRIQ7Xt1Bv9PD5zZmkxwTNeH+yTFR7FyTyWvH6zhR08G9hRNPCg+uqMnQR3EnpaWlgUTtwoULbNu2jcTExAmOEkLMRx2D7Xxw/f3A9mLo9HgnI0MYs2Oy2Zaznd2Vr+HVvWxI24jFaMGrezGweN8bg5uJzKQ9v+NLi2/I/OL9rRFikThf143JqLBlReqkj9myIgWTUeHs9e5J7S8VNTEZycnJZGb6m9vous6hQ4fCHJEQYrpeq9yFx+cBINORRX5cQZgjmh/Wp25g59JHMBvMXOg4z5XOyxgV46KZjzaW2WrPvxjIHZUQEa6+c4DcZAdW8+S7MVpMRpYkR1PfObkX1FHt+aXroxjH6tWrA9+fOXOGGzduhDEaIcR03Bi6wb7afYHt7TnbF3UiMkLXdQBKklazPGEF/e5+3qx5g2s918IcWXiNGvo46JzVa/n6+vD1T38e3HwjQx+FiHD9Qx6WpcVM+bh4u5lr7ZPrzjQoFTUxSenp6aSmptLa2orP5+Pw4cPs3Lkz3GEJIaZgT9VuXF7/2pyp9jRWJhaFOaL5YSRZjbHE8NTyp1Eq4HzHed6//m6gE+RiFJyoMRj69vyus2cZfPMtPJcvozv9iaBitWIqKsL26CNY1qwJ+TXnitxRCRHhDIqCx6dP+TiPT8cwyU9InTJHTUxBaWlp4PtPPvmEvr7pt2sWQsytPlcfb1W/Gdjelr1Nqmm38Ok+TAYTd2dsAqB7qHvRJmkweo4aIa6o9f/sZ/T8/T/gPn06kKQB6ENDuE+fpucfvkvfT58L6TXnklTUhIhwsTYzLTem/sLYcsNJzASt/EeMWkdNKmpiApmZmSQlJdHR0YHH4+HIkSM89NBD4Q5LCDEJb9e8yYDHPyw+MSqRkuTVExyx+Iy04c+Py+e3Sr5GgjUBAK/uxagswukBFjO6yYTi8YDXi+52o5gnd38xHueBAwy++RZKVBRRO3di3boVY6q/AZq3tY2hg2U4396L8+23MeUtIerBB2d8zbkmd1RCRLi8lGiabwzS2DX54QaNXQM0dw+yNCV6wn3dXl+gYmdUwGyUT1bF+BRFGTVX7cSJEwzOwnAYIURoDXoGeb3q9cD2A9kPLtq1wSai6zq6rpMfl09ClD9RW5RJGoCioMcEr6UWmoYizr37wGAg9tv/GceXnsWUlYliNqOYzZiyMnE8+yyx3/7PYDDg3PdOSK451+R/lxARbmN+IujwqyO1eLy+Cff3+nz88sg1UIaPnUDwsEerSZEhMGJScnNziYuLA8DlcnH06NEwRySEmMg7tfvodfUAEGeJY13K+jBHNHdG1oubLEWR98Ngozo/DoTmgzlPfT3moiLMhYV33MdcWIi5uBhPfX1IrjnXJFETIsKVZMezLC2G6rY+/ue+yzSM08mxvnOAf957mZq2PgpSYyjJjp/w/NJIREyHoiij5qodPXqUoaGhMEYkhBiPy+tid+WuwPaWrK0YDZFdIRrp4gj+n7/X1cu1nmv4dB9e3TvOkeJWwfPUQlVRUywWDPET36cY4uJQLAtzjqDMURNiEfjtbQX897cuUdvWz3994wKZ8TaWJDsCc9B6B91ca++nsXsQdEiKsfLbD05uTZzgilqUJGpiCvLy8jh16hR9fX04nU5OnDjBfffdF+6whBBj+OD6+3Q6OwFwmB1sTL8rzBHNLp/uw6AY8Pq8nGs/y6HGg9wYusGgZ5B4azwlyatZmVhEVnQWZsPM51tFuuCKmi9Ea6mZly/HU1U1/nV1HU9VFabld666zWdyVyXEIhATZeZbjxezMT8RBWjsGuTI1XbePdfEu+eaOFLZTmPXIAqwIT+Rbz1WTOw0GolIRU1MhcFgGDVX7ciRI7jd7jBGJIQYi8fn4dWrrwS278/csmiSk7KGMl6r3EX3UDfpjgxyY5fg8rk41HCQw42H6HX1BvYNrsCJ0fRo283vQ1RRsz/zNN72dvp/9nN07+0VTt3rY+D5F/C2t+N4+umQXHOuSUVNiEXCZjHx1a0FPLYui3N1N6jr6KfX6QEgJspETpKDkuw4UmKjpnTeQWnNL2agoKCAM2fOMDAwQH9/P6dOneLuu+8Od1hCiCBl9QdoHWgBIMpoY1PG5jBHNLtGqmmtAy18cP090uxpPLPiS6TYUlAUhbeq3+Bo81HiLPEkRvnncuu6LnPSxjFq6GOImkd56huI2r6NwTffZKi8HOvmzRhSUwHwtbUydPgIvvZ2oh5+GE9DI56GRv/1e2/g6+kl+su/HpI4ZpMkakIsMskxUWwrnloyNh6pqImZMBqNrFq1iuPHjwPw8ccfs2HDBozGyJ77IsRC4dN9vFLxUmB7c+bmiF8TbKST5Ud1H2IymHgwZzup9uEEQPdxqu0UafZ0NqZtBGDAPcCB+v3kxi5hVdKqsMU9n41uJhKailrf//pfge997e0MvvHGmPs5330X3n139IOKIomaECLyBTcTcVjk5lpM3fLlyzl37hxOp5Oenh7Onj3LunXrwh2WEAI40niY+j5/xzyL0cJ9mfeHOaK50enspKGvgSRb8qjka2/NWzg9TjbkbiDNkQ6A3WznTPsZbgx1szJx5eJtwz+O0c1EQlNRs95/HzD1KqY+5AxU3uY7SdSEEDMS3EzEIUMfxTSYTCaKi4v55JNPADh06BBr1qzBYJDfJyHCSdd1Xg6qpt2ddg82k22cIyKH1WjB4/OQ4cgIVNg6Bjs40nSEFQkrKUkqCexb2V3JgLufZFuKJGl3EDxHzdffH5JzxvzhH07rOG9bK9YtW0ISw2yTd0EhxIwED310WOUNSkzPihUrsAy3T+7s7OTixYthjkgIcbLlBNU3/F31TIqJrdlbwxzR3PHpOi6fiw5nJx6ffz73mzV7sBgtrE/bQLQlJrDv6bZTKIpCbmwuIE1FxhJcUfMNhCZRWwwkURNCzMjoZiKSqInpsVgsrFy5MrB98OBBudkRIox0XeelihcD2xvSNuAwR4cxorkVY4mhIK6A5v4mjjaXc6btNFe7rrImZS3L45cH9qvoukJl11Wyo3NYnrACQJqKjGFUe/5ZTNS8zc24r1yZtfPPNUnUhBAzElxRk0RNzERRUREmk39EfmtrKxUVFWGOSIjF63z7OS53XgL8zTUeyN4W5ojm3n2Z9xNriWV/3X72VL1OrCWWVUklmI3Da5C6ennv2nv0uft4aMnDgL/ZiLidHhM0R60/NM1ExjLw6i5ufPs7s3b+uSaJmhBiRgal66MIkaioKJYvv/lJdVlZmVTVhAiT4GramuS1xFnjwhjN3NN1ndzYJWzL2Y7VaMHldaGjU99bx6nWT/io7kP+7/kf09TfyJasreTF5qHremA+mxhtVNfHEC14vRhIMxEhxIw4ZR01EUKrVq3i8uXL+Hw+GhsbqampIT8/P9xhCbGoXOm8zJm20wAoKGzL2R7miObeyPDFDWkbsRgtnGg5TkNfA+9ffy+wj8Ps4JGlj7Ix7S4AdHSUaXQhXAz06OD2/KHp+rgYSKImhJgRqaiJULLb7RQWFnJleI5BWVmZJGpCzLGXg6ppq5JKSLIlhTGa2TWyuDXAjaEbOL1OfLqPDEcG4B/2uSZlLcvil1HVXU2/u492Zzs50TlkRWeRMry+mlTTxjcqUQvRgteLgSRqQogZCa6o2aSiJkKgpKSEiooKdF3n2rVr1NXVkZOTE+6whFgUam7UcKz5WGB7R+6OMEYzu4KTqw+uv8/xluO4vEO4vC4KE5azNesB8mLzUBQFhzma0pTS244fIQ1Exhc89JFBZ/gCWWDkrkoIMSPBFTW7WZqJiJmLjo4eVUUrKysLYzRCLC6vBK2btiJhJan2tDBGM7t0/InW/rqP+KjuQzw+N8m2ZMwGM1e7KvjJ+R+xq/JV2gZaA8eMNAvRdV2SsykYlag5nbM2/9iycSO2Jz8/K+cOB6moCSGmTdf1UV0fpaImQmX16tVUVfnXb6qsrKSpqYmMjIwwRyVEZGvoa+BQw8HA9vacyK+m9bh62F//Ecm2FL5Y+BRp9jR8+DjYUMbRpnJOtX7ChY7zbMnayj3p92A3+7sXSpI2RWYTepQVxTkEug7OIbBFTekUXX/xLSwbN+B4+mkA3BcvYoiPx5iZGdjHes/dWO+5O6Shh5PcVQkhpm3I42PkQzGzAUwGeeMSoREXF0deXl5g++DBg3feWQgREq9UvByoMuXH5ZMdkx3miGbPSKJ1qeMiFqOFB7IfIDsmG4PBgNVo5VO5D/GN0m+yPnUDLq+LD66/z4/O/ZDTrafw+rwTnF2MJXiemm8anR+9tbX42tsD2zf+VmNg9+shiW2+kkRNCDFtwdU0qzQSESG2evXqwPeXLl2ira0tjNEIEdlaB1rZX/dhYHt7zqfCGM3sCl7rzGay4fQ4WTGyWDUKPt2HT/eRZEviycIv8FslX2NpXD5tg228cvVlypuPhCv0BW1Ui/6BabToN5nQh1y3nnVmQc1zcmclhJi2UY1ETPJyIkIrMTGR7Oybn+gfOnQojNEIEdl2XX0Vr+5/Tc+JyWFp3NIwRzR7RhqInGr9BJvJRm5MLmaDJfDcyJ+RhC4/Lp/fLvkaTxR8jmRbCutS1gHIOo9TpEcHLXo9jc6PhqQkPJcu4W1pCWVY85rMURNCTNvo1vwy7FGEXmlpKfX19QCcO3eOBx98kISEhDBHJURk6XJ28t61dwLbkTw3bUR50xHerH6DKFMUTo+Tk60n2JSxOZCcjSRrcLOF/13pd7MudT0mg2lUW38xOXq07eb301hLzXrPPQzu2UPXH/xh4LGh/QcY2n9g4oMVheQXfzXla4ab/IYJIaZNGomI2ZaSkkJ6ejrg//T6448/DnNEQkSe3ZW7cfvcAKTb0ymMXx7miGZfXmweGY5MnB5/q/ijTeVc7aoYVU0bqZgZFAO6ruPTfZgMpsBjYmpGVdSmMfTR/szT2B57FENy8jQuvjCrn1JRE0JM26BLWvOL2VdaWkpzczMAp0+fZuvWrcTGxoY5KiEiQ6+rl321bwe2t+XsWBQdDdMdGfze2t/nTNtp9tXupW2wjecu/pT1qRv4dN6ncZijAfDqXoyKEUVRUIj8v5fZNGqO2jSaiShmM46vfAXHV74CQPvTz2B98AFivvnNkMU438jHAUKIaQuuqNmloiZmSXp6Oiku7rxrAAAgAElEQVQpKQB4vV6OHJGJ/EKEyhtVexj0+IehJUclU5xUHOaI5sbIfLw1KWv5i41/GRju+UnrSf7x+Pc42OBfv9Go+D+EDG5AIqZnphW1WxmSkzHERPaHdnJnJYSYtuBmInaLVNTE7FAUZVQHyJMnT9Lf3x/GiISIDAPuAd6s3hPYfjBne8QP6RsZzmhUjPh0Hx6fB0VR2J67g/+08VuUJpfi0328U7uP/3Hy+1zsuAjIUMdQGDVHbRrNRG6V+K8/wPHlX5/xeeYz+a0TQkxbcDMRh1USNTF7srOzA01E3G435eXlYY5IiIVvb81b9Ln7AIi3xlOaUhrmiGbfyLBOl9eFQTFgMpjw+Dx4fV7irHE8veJZfmf118mMzqLT2ckvLj/P0SZ5vQmF4KGP3r6+0J7b7cF9pYKhI+UMHSnHfaUC3e0J6TXCQeaoCSGmLbii5pCKmphFiqJQWlrKgQP+7l7Hjx/nvvvuIyoqKsyRCbEwDXmH2F21O7D9QNaDgWF+kaploIWjTeX0uHpQUMiOyWZT+masJisAbp8bo2JkSWwe31zzexxvPsb++o9Ym3qzHf9imL83W0I99BFA93gYeOllnO+8c1uVTomKImrnTuxPfRHFtDBTnoUZtRBiXpCuj2Iu5ebmEhsbS09PD0NDQxw7doytW7eGOywhFqT3at/hxlA3ADHmGNanbQhzRLNjpI3+xY4L7KvdS6ezM1BFu9R5kQP1+3ko92E2Z96L2WAG/Amb2WDmrvS72ZC2EYNiCDQVEdOnR9+sqPlCMHxd9/ro+d4/4j57FgBDfDyGtDTQdXytrfi6uxl87TU8VVXE/tVfoRgX3n2KJGpCiGkLHvpoNy+8F0CxsBgMBlavXh1o0V9eXs6mTZuwWCxhjkyIhcXtc7Or8tXA9v1ZWwNt5yPJSJI25BliT9Xr9Hv6eTT/MYoSi7nec5091btxepy8VfMmx1qO8UjeIxQmLMdsMOP1edHRA38vkqTNXHCiFoqKmvP993GfPYsxIwPHV7+KZd3aUc+7Tp+m/6fP4T57FucH72N7+OEZX3OuyZ2VEGLagoc+SkVNzIX8/Hyio/1tswcHBzl58mSYIxJi4fno+oe0D7YDYDfZuSf9njBHNLvevf4Ofe4+f+Us415iLDE0DzTh9DjZmv0AqfZU2gZaee7iT/nZxefoGOzAaDBGZPIaTjNtz3+roQMHUKxWYr/znduSNADL2rXEfvvbKFbr5BbFnofkzkoIMW2j2vPLOmpiDhgMBlatWhXYPnz4MB7Pwp8wLsRc8fq8vHr1lcD2vZn3YTaawxjR7NB1HYNioMvZxcWOC+THFbA+1T+882rXVY43HycnJoeHl3yaXy/6CgXxywCo6LrCP3/y3zndeiqc4Uek0XPUZt710Vtfj3nVKoxJiXfcx5iUiHnVKrz19TO+XjhIoiaEmLZRC15LRU3MkcLCQmw2f5vnvr4+Tp8+HeaIhFg4DjUepKm/EQCr0crmjHvDHNHsGGn6UdNTzYBngJWJK4m2RDPoGeRCx3kGPQM8svQxwN/xckXCCixGC8viCwHIjskOW+yRatTQxxC059e9XrBaJ97RavXvuwDJnZUQYtpGNROROWpijhiNxlFVtY8//hifTxajFWIiPt3HKxUvBbY3pW8myhS5nVN1XcfpceL1eSlO8r9mtA60cLWrgqLEYnJicvDqXgyKgfWpG7Cb7OzM28l3Nv0tybYUWeQ6xHxBFTWczhmfz5iSgufSpXHb8OtuD57LlzGmpMz4euEgd1ZCiGmTipoIl+XLl2Md/iS1u7ubc+fOhTkiIea/Y81HudZzDQCzwcz9WfeHOaLQGVnIOvh7RVEoSizmC4VfxDLc0bHP3U+fu48ViSuGd/Z/aR5optfVS1N/Exajv0GRLHIdYvYo9JHlDYZc6N6ZJcKWjRvwdXfT+4N/GbOLpK9/gL5/+1d8XV1YNm6c0bXCRWZJCiGmxefTGfLcfJGNkoqamENms5mioqLAsMeDBw9SWloqaxwJcQe6rvPylZvVtI1pd2E3O8Y5YuHod/dxufMy+XEFJEQljHodSIhKIMYSE2gM0tjXAMCA29/Mwmjwz6++2HEBRVGItkTPcfSLiMGA7rCh9Pn/7nXnIIpj+r+DtieeYOjQx7gOH6Hr1GksGzZgSE0FRcHX0oLr5En0wUEMSUnYnngiVD/FnJI7KyHEtAQPe7SaFAxygyzmWFFREWaz/1Pyjo4OLl26FOaIhJi/Tred5mp3BeBvNb81+4EwRxQ6b1a/wWuVu3j/+rtc7rzMgHt0dSW4e2NhfCFGxcjhpsNUdF2h19VLWf0BjjaVk+HIDMxRE7NjVOfHGTYUMcTEEKeqmPLz0QcHGTp0iMFduxh89VWGDh1CHxzEVFBAnPodDDELMwGXipoQYlqCE7UokyRpYu5ZLBZWrlwZGPZ48OBBioqKpKomxBhevvJi4Pt1KeuItcSGMZrQ8fg8pNnT6Yju5EzbGapuVLMmeQ2rkkvIsGeM6mjp032k2lMpiF9GRdcVfnbxORzmaPrdfdhMNh7Lfzywnwx7nB2jE7WZt+g3ZqQT/73/ivvSZdwXL+Lr7ARdx5CUhLm4GHPRyhlfI5wkURNCTMugNBIR80BxcTEXL17E6/XS3NxMZWUlhYXyibgQwS52XOB8h/8DDQMGHszZHuaIQsdkMPFgzjZWJK7kTNtpzref4+PGQ1R2X2Vd6npWJKwgyZaMQTFgUAzYzQ6+UvwbHG78mEMNBwFYl7qetSlryYrOCrT1F7NjdOfHmSdqI8xFKxd8UjYWSdSEENMSvNi1zE8T4RIVFcXy5csDwx7LyspYtmyZVNWECPJSUDWtJHk1CVEJYYwmtEaqXxmODDIcGRTEFXC67RRXuq7wTu0+rnZfZV3KOpbG5RNnjQscd2/mfWzOuJeuoS4So+68DpcIrVGJWggqapFO7q6EENMyerFreSkR4bNq1SoMBv/vYH19PdeuXQtzRELMH5XdV/mk9WRge3vOjjBGE3oj1a+RVvqFCct5PP8JHl36GPnx+dTcqGZP9eu8d/1drnZVMOi5OS9KUZRAkhbcKVLMnlGLXodgLbVb9f7gX2l/5tmQnzdc5O5KCDEtwa35bdKaX4SRw+GgoKAgsF1WVhbGaISYX4I7PRYnFpNiX5jrSU0kOGGLMkWxLnU9nyt4kh25nyIhKpHTrafYXfUaBxvKqO+tx+MbvfaWJGhzI3iOmm+2KmpBSzUsdHJ3JYSYluCKmkMSNRFmJSUlgRutmpoaGhoawhyREOF3vec6R5oOB7Z35H4qjNHMjeD5ZQlRCTyQ/SCfL/g8mzI2o+s6ZfUH2FO9mxMtx2kbaA1jpIuTHhO6ro+LgdxdCSGmJbiZiN0i011FeMXGxrJ06dLAtlTVhIBXKm5W0wrjC0l3ZIQxmtDTb6mc9Az1MOAeoMvZNerx7Jgcdi59hM8WPEFJUgmdzk7erH6DT1o/mctwBaHv+hjp5O7q/7F33/FxVXfexz8zoy65yb03jI0bGBPANnGjJySBBJIQsulhSdvNJtkneZLsnpxN2ZQnjZQlhGRJJ7TQAwRw78YNDO644N5tdWlmnj/OnfEdWZZmZEl3Rvq+Xy+/pDu6c/XT9cyd87vnnN8RkVbxFxMpK9Q9HwnexIkT2bFjBwBbtmzh4MGD9O/fP+CoRIJxoHI/C/cuSG7PHdr5etMSvei7Tu1k/eH1bDm+mbpYPWX5ZZQXlTNj0FWM7OFu4ERCEcaVX8SwbsN49ehGVh9cxcV9LwZUjr8j+eeoRasqAowkNyhRE5FWSe1RiwQYiYjTq1cvhg0bxu7duwG3rtqtt94acFQiwXhk68PJAhsjuo9gWPdhAUfUtqLxKJFQhN2ndvGnTX+kqr6K4rxiQqEwp+tOc6jqIJuOvc7FfS/h+uE30L3QrRtXkl/K5QMuZ3z5eMoKylSOv4Ol9KhVVjazZ+tEBg8if/z4Nj9uUJSoiUir+HvUlKhJtpg8eXIyUdu4cSNz5syhd+/eAUcl0rGOVh/hxd0vJLc7W6VHcD1kAE/ueJLahlpuGHEjl/SdQmV9BfWxel479hpL9i1m/eF1HK89zi2jb6FvSb9kgldWUAaoiEhHS5mjVtn2Qx9Lbr4Zbr65zY8bFN1CEJFWqdGC15KFevfuzeDBg5PbixcvDjAakWD8bdujyaqGg0sHM6rH6BaekZs2H9vEoeqDTB80g6sGv5WygjL6lw5gSLehXDf8ej4+4RMM7z6c3ad2sfbwWuBMgifBaMuqj6d/+UtqXnqpxf1q5s3n9C9/eV6/KyhqXYlIq1QrUZMsNWnSpOT3GzZs4MSJEwFGI9KxTtae5Nmdzya35wyd22l7jeJAmDAT+7j3fGKoZ8LQbsOYPmgG4VCY5fuXcajqYABRip8/UeM811Grnb+A+k2bWtyvfvMmaucvaHG/bKTWlYi0SurQR11KJHv0798/WUQkFouxdOnSFp4h0nk8sf0x6qK1APQr6c+48osCjqhtJZKxg1UHqY/VEQlHKM4rbnLfUCjEhN4Tmdr/MuqidZyuO92RoUoT4t3ad8HrJjVEIZyb7ZTcjFpEAqehj5LN/L1qa9asoaJC1cWk86uoq+DpHU8lt+cMmdPpetPCoTCHqw7zs7U/ZdWBVcTjcV4+uDr5M79o3H1OFYQLAKhq0LpdQUspJtJBiVr0zTcJlZS0vGMWUjEREWmVahUTkSw2aNAgevfuzdGjR4lGoyxbtoxrr7026LBE2tUzbzxFVYOb91NeVJ4cEtjZHKo+REl+CbtO7yQai7Lq4Cr6l/RnbPk4CiOFAERjUSLhCBV1p9lXuZdwKMyQsiGAW3+tsyWwuSJe5kuYamoyfn7juWb1mzafe/5ZNEZ0714aduyg4NJLM/5d2UCJmoi0inrUJJuFQiEmT57MvHnzAFi9ejUzZsygJEfvqoq0pLqhmse3P57cnjVkdqctOz+h9wT6l/Rj+f5lbDq2iRO1J3h+13OcqD3B2F5j6VnYi8I8l7At3b+U3ad3c+XAK+lV1EtrpgWtqJB4JEwoGoP6BuL1DYTy009HGs81ix04QO2BA80+J9yzJyW3396qcIOmRE1EMtYQjVEfjQMQDkFhnu5MSvYZOnQoPXv25MSJE9TV1bFixQrmzJkTdFgi7eK5nc9yuu4UAD0KejClb272ILQkHnefPX2K+3LTqHcyvnwCKw4sZ9OxTTy/6zleOfIK3Qu6UxDJp6K+gl2ndjGxzySuHX59wJELAKEQ8bJSQifdfMF4dRWh/O5pP73s059y38Sh4n/+h7xx4yia2/R1PZSXR7i8nLwxF2aUDGaT3IxaRALl700rzAtpCIlkpVAoxKRJk1i0aBEAK1euZPr06RQWFgYcmUjbqovW8di2R5PbMwfPIhLunEPSE583iZ6xUT1HM6LHSNYfXsfKAyvZc3o3+yv3ATC578V8YNwdjO55AfnhfPWmZYl4aQkkErWqKuiefqJWNHt28vuqhx4if8yYlMc6G71aRSRjGvYouWLEiBF069YNgJqaGlatWhVwRCJt78XdL3Cs5hgApfmlTB1wWcARtb9EwpVIvqb0u5QPXvRBrh52DX1L+hEixPYT29hfuZ8TNSeIxqNK0rKEf57a+RQUKf/lLyj9pw+2RUhZS69YEcmYv5BIkYY9ShYLh8MpFSCXL19OfX19gBGJtK2GWAOPbH04uX3VoLeSH84PMKKOdbL2ZLJkf2l+GXOGzuV9F76Pqf0voyHWwIu7X+CBzX9m7aG1nKo9FXC0AqmJ2vkuet3ZaeijiGQspUdNFR8ly40aNYr169dTWVlJZWUla9as4Yorrgg6LJE2sfDNBcmFnIsixVw5cFrAEbW/RC/antN7eHDLA4ztNY6bRr0j+fiA0oHcfMEtTOg9gWX7l7Hl+GYe2/Yow7oP545xd1CaXxb0n9Clxct8a6lVtb5Hreqhh1veKSEEJbfe2urfFRQlaiKSsZr6WPL7Eg19lCwXiUSYMGECK1euBGDJkiVcdtllRCK6ySC5LRaP8fCWB5Pb0wZNoyBSEGBE7S8ejxMOhYnFY7x65BWO1xxncNlgAEKkzl8b0+tCRvYYxbrD65i/5yUioYiStCyQspbaefSoVT30UEb7K1ETkS6huq4h+X1xgRI1yX5jxoxhw4YN1NTUcPr0adavX8+lObqujkjCsn1LebPiTQAKIgXMGHRVwBF1nK0ntrLm0BqGdx/OlH7uvZwoNOKfv5YXzuOy/pcxpucY8sNq9maD1DlqrU/USm5rOvGKx+LEDh+m/rXXiB05QuGcOUT69G717wmSXrEikjF/j1qpEjXJAXl5eYwfP541a9YAsHjxYi655BLCYb1+JTfF43Ee8vWmXd7/CorzigOMqGOEQiGqG6pZfWAV1Q1V3DTqnQBNVnQMh8LE43HixOlR2COIcKUJbVVMpOS225r/PXV1VNz7a+rXraP0e99t9e8Jkj6hRCRj/h61Es1RkxwxduxYCgrcsLDjx4+zcePGgCMSab2XD65mx8ntAOSF8pg5ZGbAEbWvRMEQgENVBzlYdYCp/S9jYOnAZsvuh0IhVXvMMv6hj7HKynb7PaGCAsru/CTxWIzKB/7abr+nPemVKyIZ8xcTKVWiJjmioKCAiy66KLm9aNGi5OK5IrkkHo/z4JYzDc+p/ad2mrlXjd+TFXUVACnJ1qCywVwz7DrePvKmDo1N2oa/mEh7JmrgkrW80aOoX7u2XX9Pe9HQRxHJmL88v3rUJJeMGzeOjRs30tDQwOHDh9m8eTPjxo0LOiyRjLx65BU2HXsdcAnMrCFzAo6o7W07sY3Xjm5k16mdRMJ5TO4zmZE9RtGnuA+FkUIm950MND3kUbJbann+9k3UAIjGiJ0+3f6/px0oURORjPl71Eo0R01ySFFREWPHjk0Oe1y0aBFjx45NFiEQyQX+3rSL+1zSaeZfJZKuvRV7eWDzn6lpqCESihCNR9lXsZd+Jf2Z0ncKF/a6kL4l/QiHwkrSclDKHLXK9l1HLbpvH/Wvv064vLxdf097UaImIhlL6VFTeX7JMRMmTOD1118nFouxb98+duzYwejRo4MOSyQtm49tYv3hdYArRz9n6NyAI2o7iaTryR2PU9NQw+yhc5jUZzIHKvez8ehGdpzcznO7nmXriS1M6Xcpo3qM7jRJalfSVuX5axYsOPfvqKkhuncvtQsXQV0dhdOnt/r3BEmJmohkzF/1UQteS64pLi5mzJgxbN68GYCFCxcqUZOc8ZCvN21C74n0Ls7NsuPnsv3ENg5WHmT6oBlcM+xaAPqX9Gdsr3FsOvY66w6vZcfJHew5vYfxvcdzSd8pDC4bTEl+aQtHlmwR7+Zb8Po8qj5W/OKXae1XcOmlLVaIzFZK1EQkYylVH9WjJjlo4sSJbNmyhXg8zu7du9m9ezfDhg0LOiyRZr1x8g1WHliZ3L562NUBRtM+IqEI4VCYCb0nAhCNRQmHwhTlFXFJvymM6DGSV45sYMPh9Ww4soHXj73OrCGzmTVkdrCBS9pSetTOI1ErnDkTzjFsPZSXR7i8nPxJE8nP4XnIStREJGOpPWpK1CT3lJWVMXr0aLZt2wa4XrUPfvCDAUcl0ryHfeumje01jn4l/QOMpu0k5qYdqT5CdUM14VCEPsV9AFdePxQKEY/HCYVC9CzsyVsHz2RUj9GsP7yOlQdWJPdN7CPZzT9HjeqaVh+n22c/0wbRZDe1sEQkYyomIp3BxIkTk4267du3s2/fvoAjEjm3vRV7Wbx3UXJ77tDO05sWDoU5XnOcn6z5EWsOrQHivHJkQ/JnQPK9mlhPbXDZYG4YcSMfn/iJZO+bkrTckJKo1dRomZRmqIUlIhmJx+MpxUSKNfRRclSPHj0YPnx4cnvRokXN7C0SrIe3PEQc16Ad1WMUQ7oNCTiitrW34k0KIgVsPr6J6oZqXj64mm0nthGNRVP2SyRuiV64od00ZDnn5OcTLyxw38diUFfXJoeNHT9O/fbt1G/fTuz48TY5ZtA09FFEMlIfjRPz7n7lhSE/okRNctekSZPYuXMnAJs2beLQoUP069cv2KBEGjlUdYj5e15Kbs8dek2A0bSPiX0m0bu4D8v3L2Pz8c3sr9zPM288zfRBMxjbayzdCrql7K+y/LktXlpCqNYlaPGqKkKFha0+Vs0LL1D9xJNEDxxIeTwycCDF73wHRVfnbu+zXuUikhF/b1phni4hktvKy8sZOnRocnvx4sUBRiPStEe3PkI07q69Q7sNZWSPkQFH1HqL9y7i/o2/5VjNseRjieGMA0sHcssF7+aW0bdwYa8LOVR1kMe2Pcrftj3KluObqWlo/XwmyS7+giKxqtYXFDn9819Qce+vk0lauLyccK9eAET376fiV/dyOs3qkNlIPWoikhH//LTifM0HkNw3adIk9uzZA8Crr77K7NmzKc/RxVGl8zlec4x/7HouuZ3Lc9MaYg0s3ruIivoK3ji5g/KichpiDeSFXXM0Go8SCUUYWz6OUT1Hs/bQWlYdWMGW45vZcXI7l/abytT+l9GvpB/54fyA/xo5H/Fu/sqPrVtLrXbxYmoXLiTUvTsl772NojlzCOW710W8vp6a+fOpevAhahcsoOCSiymcMaNNYu9Iuh0uIhmpqT9Tmr9I89OkE+jbty8DBw4E3BzMJUuWBByRyBmPbXuM+lg9AANKBjCm54UBR9R6eeE8Pjbx41w3/Hou6TeFumgd975yD2sPrUkmafF4nFg8Rn44n8sHXM4dF/0Ts4bMpiSvhJUHVvDbV+9j3aF1Qf8pcp7aYtHrmhdehLw8ehhD8XXXJZM0gFB+PsXXXkuP//xPyMuj5h8vnHfMQVArS0QyUl13pjS/1lCTzmLy5MnJ79etW8epU6cCjEbEOV13mmd3PpPcnjP06pyubBiLx+hX0p+ZQ2YRCUV4+eBq9lXs45GtD/PH13/PrlM7CYVChENhYvEYsXiMnoU9uXb4dXxg3B1M6XcptdFaujearya5J152/oteN+zcSf748eQNPXdhnbyhQ8gfP54Gby5yrtHQRxHJiL9HTRUfpbPo378/ffv25fDhw8RiMZYuXcoNN9wQdFjSxT25/QmqG1wjtk9RH8b3Hh9wROencQGQaYOmkx/JZ9GbC9l6fCtbj2/l8gFXcNXgt1Je5IYfJ3rahnQbypBuQ3nLgMsZpkqPOa8tetTidXWEy8pa3C9cVka8jSpLdjS1skQkI/4etdKCSICRiLSdUCiU0qv28ssvU1lZGWBE0tVV1Vfx1I4nktuzh87tVJUOE2tnXdb/Ldx18aeZNWQ2+eF8Vh5YwT0bfsnivYuoaaghEnKfM4liKokkTWtv5baUOWqtLCYSLi+nftu2Zl8L8Xic+u3bCefovOPO844XkQ6RUkxEi11LJzJ48OBkEZGGhgaWL18ecETSlf39jaepqK8AoGdhTyb3ndzCM3KLfwHr4rxirh1+HXdd/Gkm9ZlEVX0Vz+78O/e9+ms2Ht1ILB5LJmyNny+5qS161AouvpjYoUNU/eEPxKOxs34ej8Wo+uOfiB08SMElF7c61iBp6KOIZMSfqJWpR006kVAoxKRJk1iwYAEAK1euZPr06RQXFwccmXQ1tdFaHtv+WHJ71uDZZyUqnUU4FE72iPQv6c/7xt7OJX2nMP/Neew5vYe/bPoTY3qN4dph1zOobFDA0Upb8c9Ri1W1bvRC8c03U7tkCdVPPU3tipUUvvUqIv36QShE9OBBahcvIXboEKHSUopvvrmtQu9QStREJCP+ddRKizpnw0G6ruHDh9OjRw9OnjxJXV0dK1euZNasWUGHJV3MP3Y+x8naEwB0K+jGpf2nBhxR+/L3roVDYcaWj+PCXmNZcWA5i/cuYuvxrUzoPUmJWicSL/Oto9bKYeaRvn3o/rWvcvqHPyJ2+DDVj/7trH3CvXvT7Qv/RqRPn1bHGiQlaiKSEX+PWkm+EjXpXBK9aomFr1esWMG0adMoKCgIODLpKupj9Ty67ZHk9lWDZibXGevsEnPwEgnblQOnMb73BDYcXs9l/S8LODppSymJWit71ADyx4yh18/upnbZMupfe43YseMQjxPuXU7++PEUTpuWUrY/13SNd76ItJmaOs1Rk85t5MiRrFu3joqKCqqrq1m9ejXTp08POizpIubtfokj1UcAKMkr4YoBVwQcUcfzJ2zdC7pz1eC3Jrc7U0GVrixljlpl6+aoJYTy8ymaOZOimTPPN6yso1e7iGSk2l9MROX5pRMKh8NMnDgxub106VIaGhqaeYZI24jGojyy9eHk9vRBM8iP5G5vwPlqnJQpSes8/D1q8erzS9Q6M73iRSQjKUMf1aMmndQFF1yQLCJSWVnJ2rVrA45IuoLF+xaxv3IfAIWRQqYNVE+udE4pC163sjx/V6BWlohkxF9MRD1q0llFIhEmTJiQ3F6yZAnRaLSZZ4icn1g8xsNbHkxuXzlgGkV5RQFGJNJ+UoY+VtcEGEl2UytLRDKS2qOmYiLSeV144YUUFhYCcPLkSV555ZWAI5LObOWBFew6tQuA/HA+Vw2+KuCIRNqPf+gjNUrUzkWJmohkRD1q0lXk5+czfvz45PbixYuJxc5eVFXkfMXjcR7afKY37bL+b6Ekv7SZZ4jktnipb33K2lriurY2Sa0sEUlbLB6nNqU8vy4h0rmNGzeOfK+089GjR3n99dcDjkg6o3WH17H1xBYAIqEIM4do7T7p5CIR4iVeshaPE1evWpPUyhKRtNU1xIh73xdEQoTDoUDjEWlvBQUFjBs3Lrm9aNEi4vF4M88QydxDm/+a/H5K3yl0L+geYDQiHSNlnlqVKj82RYmaiKTNP+yxKE9JmnQN48ePJy/PLTt68OBBtm7dGnBE0pm8dnQjrx518x/DhJk9dG7AEYl0jHg3f0ERVX5sijIMLfwAACAASURBVBI1EUmbv5BIkYY9ShdRVFTEhRdemNxeuHChetWkzTzo602b2GcSvYp6BRiNSMdRj1rL1NISkbT5e9Q0P026kgkTJhAOu9f83r172blzZ7ABSaew7cRW1hx6Obl99bCrA4xGpGNpLbWWqaUlImnz96gVa7Fr6UJKSkq44IILktsLFy4MMBrpLPyVHseXj6dPcd8AoxHpWP7Kj+pRa5paWiKSNpXml65s4sSJhEJububOnTt58803A45IctnuU7tZtn9pcvvqYdcEGI1Ix/OvpRavVqLWFLW0RCRtqYtd6/IhXUu3bt0YOXJkclu9anI+Ht5ypjdtTM8xDCgdGGA0Ih3PP/Qxph61JqmlJSJpS5mjVhAJMBKRYEyaNCn5/datWzlw4ECA0UiuOlC5n4V7FyS35w5Vb5p0PanFRDRHrSlK1EQkbf4etbJCJWrS9fTs2ZPhw4cntxctWhRgNJKrHtn6MLF4DIAR3UcwrPuwgCMS6Xgx39DHWGVFgJFkLyVqIpI2f6JWqh416aL8vWqvvfYaR44cCTAayTVHq4/w4u4Xkttzh6rSo3RN/jlqGvrYNCVqIpK2lGIimqMmXVTv3r0ZPHhwcnvx4sUBRiO55m/bHqUh1gDA4NLBjOoxOuCIRIKRWp6/MsBIspdaWiKStpRiIvnqUZOua/LkycnvN2zYwIkTJwKMRnLFydqTPLvz2eT2nKFzk5VERboa/xy1WKV61JqiRE1E0lajHjURAPr168eAAQMAiMfjLFmyJOCIJBc8sf0x6qK1APQr6c+48osCjkgkOPFuZxI1qlVMpClqaYlI2qpTetR0+ZCuzT9Xbe3atZw+fTrAaCTbVdRV8PSOp5Lbc4bMUW+adGkpVR+VqDVJLS0RSVtNndZRE0kYOHAgffr0ASAajbJs2bKAI5Js9swbT1HV4IZ3lReVM7HPpBaeIdK5pcxRU6LWJLW0RCRt/jlqxepRky4uFAql9KqtXr2aKlUukyZUN1Tz+PbHk9uzh8whHNI1VLo2f9VHqmuCCySL6SohImnzD30sVnl+EYYOHUqvXr0AqK+vZ8WKFQFHJNnouZ3PcrruFAA9CnpwSd8pAUckkgWKi4iHvVSkvp54Q0Ow8WQhJWoikpZoLE5dg1ugNQQU5WluhUjjXrUVK1ZQU6M7w3JGXbSOx7Y9mtyeOXgWkbBudIkQChEvLU5uavjj2ZSoiUhaan29aYV5IU2CF/EMHz6c7t27A1BbW8uqVasCjkiyyYu7X+BYzTEASvNLmTrgsoAjEske/uGP8Solao0pURORtKQsdq35aSJJ4XCYiRMnJreXL19OfX19gBFJtmiINfDI1oeT21cNeiv54fwAIxLJLqmLXmuOb2NqbYlIWvyFRIry1Zsm4jd69GhKS12Do6qqipdffjngiCQbLHxzAYeqDgJQFCnmyoHTAo5IJLukluhXotaYEjURSUu1Kj6KnFPjXrWlS5fSoInxXVosHuPhLQ8mt6cNmkZBpCDAiESyT8rQR81RO4taWyKSlhoNfRRp1gUXXEBRUREAp0+fZv369QFHJEFatm8pb1a8CUBBpIAZg64KOCKR7ONP1GIa+ngWtbZEJC3+HrUSleYXOUteXh4TJkxIbi9evJhYLBZgRBKUeDzOQ77etMv7X0FxXnEzzxDpmlLnqKlHrTElaiKSFn+PWkmBLh0iTRk7diwFBW5424kTJ3j11VcDjkiC8PLB1ew4uR2AvFAeM4fMDDgikeyUMkdNPWpnUWtLRNLi71ErVY+aSJPy8/O56KKLktuLFi0iHo8HGJF0tHg8zoNb/prcntp/KqX5ZQFGJJK9Uoc+VgYYSXZSoiYiaalRoiaSlosuuoi8vDwAjhw5wqZNmwKOSDrSq0deYdOx1wEIh8LMGjIn4IhEspcSteYpURORtPjXUSspVKImci6FhYWMGzcuub1w4UL1qnUh/t60i/tcQo/CHgFGI5LdUoY+VmroY2NK1EQkLf4etRJVfRRp1vjx44lE3A2NAwcOsH379oAjko6w+dgm1h9eB0CIEHOHXR1wRCLZzV9MJFapHrXG1NoSkbSklOdXMRGRZhUXFzNmzJjk9sKFCwOMRjrKQ77etAm9J1JeVB5gNCLZT+uoNU+tLRFJS7V61EQyMnHiRMJh917Zs2cPu3btCjgiaU9vnHyDlQdWJrevVm+aSItSEjVVfTyLWlsikhb/0MdiFRMRaVFpaSmjR49ObqtXrXN72Ldu2the4+hX0j/AaERyQ8ocNfWonUWJmoikJaWYiHrURNIyceJEQqEQADt27GDv3r0BRyTtYW/FXhbvXZTcnjtUvWki6Yh3OzNHDSVqZ1FrS0TSktqjpkuHSDq6d+/OiBEjktuLFi06986Ssx7e8hBxXGXPUT1GMaTbkIAjEskN/h41ampVIbcRtbZEJC016lETaZVJkyYlv9+8eTOHDh0KMBppa4eqDjF/z0vJ7blDrwkwGpEcU1hAPN+tO0k0CvX1wcaTZdTaEpEW1UdjNMTcXa5ICPIjoYAjEskdvXr1YujQoclt9ap1Lo9ufYRo3N3IGtptKCN7jAw4IpHcooIi56ZETURa5O9NK8oPJefciEh6Jk+enPx+48aNHDt2LMBopK0crznGP3Y9l9zW3DSRzPnXUlNBkVRK1ESkRf7S/EV5umyIZKpPnz4MGjQIgHg8zuLFiwOOSNrCY9seoz7mhmoNKBnAmJ4XBhyRSO7xz1OLqUcthVpcItKilEIimp8m0ir+uWrr16/n5MmTAUYj5+t03Wme3flMcnvO0Ks12kCkFVKHPqpHzU8tLhFpkX/ooxI1kdYZMGAA/fr1AyAWi7F06dKAI5Lz8eT2J6hucI3KPkV9GN97fMARieQmzVE7N7W4RKRF1SrNL9Im/HPV1qxZQ0VFRYDRSGtV1Vfx1I4nktuzh84lHNK1UaQ1Uhe9VqLmp6uKiLRIpflF2sagQYPo3bs3AA0NDSxfvjzgiKQ1/v7G01TUuyS7Z2EvJved3MIzRORcUoqJqEcthVpcItIif49aSUEkwEhEclsoFEqZq7Zq1SqqVeUsp9RGa3ls+2PJ7VmDZxEJ6boo0lqpPWq6HvopURORFvl71EoL1SAROR/Dhg2jR48eANTV1bFy5cqAI5JM/GPnc5ysPQFAt/xuXNp/asARieS2eDdf1cfKygAjyT5K1ESkRf6qj6WaoyZyXkKhUMpcteXLl1NbWxtgRJKu+lg9j257JLl91eCZ5IXzAoxIJPellOdXopZCVxfptKy1O4Hh5/jxQWPMgCaeMx34OnAlUARsA34L/MwYE228v/ecm4AvAVOACLAR+KUx5nfn+zdki2r/HDX1qImctxEjRrB27VoqKiqoqalh9erVzJgxI+iwpAXzdr/EkeojAJTklXDFgCsCjkgk9/nnqClRS6VETTq7k8BPmnj8rFJr1tp3AY8ANcBfgWPAO4AfAzOA25p4zmeBnwFHgT8CdcCtwP3W2knGmC+1zZ8RnMOnati8/1Ry+w8rD7PneC1vn1DOgO4FAUYmkrvC4TCTJk1i2bJlALzwwgu88MILFBQUMHnyZKZNm0Z5eXnAUQrA/sr9PLbtUebvmZcsxw9wSd8p5EfyA4xMJPeF9+yn4Jl5ye2GVas5/ev7KHnHTUQGnHU/vcsJxePxoGMQaRdejxrGmBFp7Nsd13vWA5hhjFntPV4EvARMA243xjzge84IYBNQCUw1xuz0Hu8FrAJGA9ONMcsyjHs+MGv48OF85CMfaXH/ipp6lm09QnlZYSa/Ji0b3zzBffO3U9cQS3k8EoK8SIjPzxnElCFlbf57RbqC3bt3M2/evLMeD4fDRCIRbrvtNsaMGdPSYbTC8vlpthH08sHVfHfld2iINRCNpw6qyA/nc/u4Oxjba2y7BijSWeUvXk3Zl74D9fWEor52RiQCeXl0/+IXKJgypc1/b/TwIQrf+lYi6d8MC+w6q8kmIs6tQF/ggUSSBmCMqcENhQT4VKPnfAwoBH6eSNK85xwHvuNt3tVeAbe3w6dqmkzSAKJxqG2I85N5+zhwqi6A6ERy26lTp1i0aFGTP4vFYtTX1/PQQw9x7NixDo5MEvZX7ue7K79DbbT2rCQN3Hy1v2z6E0erjwYQnUhuC+/ZT9mXvkOopjY1SQOIRqG2llM//BHRAweCCTBLaOijdHaF1toPAsNwPV8bgIVNzDeb6319toljLASqgOnW2kJjTG0az/l7o31yzosbD9DQ+OLZSEM0zjMbj/GxaRqeIJKJ1157jWi0yWmvSdFolOXLl/O2t72tg6ISv8e2PUpDrKHZfaKxKEv2Leado9/VQVGJdA5Fv38UGpp/f9HQQNVTT9PtEx/vmKCykBI16ewGAH9o9Ngb1tqPGmMW+B5LjF3Z0vgAxpgGa+0bwARgFPB6Gs/Zb62tBIZYa0uMMWet4Git/QjwkSZivuTcf07T4sSpb6Ln63ys3HGUWAsjo6NxWLT9NB++vG+b/m6Rzm7Hjh20NPUgFouxYcMGJWoBmb9nXpM9aX4xYqw7vJYbR+r/SCQTBc/MI9TQ/PuLaJS6hQuJf+if2vaXx9q2vdSelKhJZ/a/wCJcFcbTuCTrs8CdwN+ttdOMMeu9fXt4X0+e41iJx3v6HkvnOaXefmclasAIYFbzf0LL8iJhehTnt9j7lana+vSOV1Mfa7FnQERS1dfXp7VfXZ2GFgelpqEmrf1qo3UtJnQikipUld77K15TQ7ylnrdMf3fPXoQKcqMYmhI16bSMMbbRQ68Cd1lrK4AvAt8AbknzcImJpJlU32npOTuBBU08fkHv3r0HD0iz2lFRfoQrLmj7Hq2SgghVdS03PkoK87jwwgvb/PeLdGYFBQVpJWEFOdKY6IyK8opSqjyeS0leMW8ZcHkHRCTSeewrLSVecVYB7rOEykopvubqDogoOylRk67oHlyiNtP3WKJXrMfZuwPQvdF+ie/7eM9pajZ54jmnmvgZxpj7gfvP8fsCL8d6w8WDeOLlN2loZvxjXjjEDZMHdmBUIp3D5MmTWbNmDbFmhuCEw+GUhbGlY80eOofndz7XbG9ZJBRh9tA5HRiVSOdQ8u5bqPzzX5qfp5aXR8m739NxQWUhVX2UruiQ97XU99hm7+tZXUPW2jxgJNAA7EjzOQO947/Z1Py0XPCB6SPIizRfkTYvEuL26SM6JiCRTmTatGlEIs0vHh+JRLjyyis7KCJp7OYL3k1euPn72XnhPN51QboDM0Qkoeyf7ySU3/w6hKH8fMru/EQHRZSdlKhJVzTN++pPul7yvt7QxP4zgRJgqa/iY0vPubHRPjlnSHkJ33nfJRTlh8kLpyZseeEQRflhvvO+SxhSXhJQhCK5q7y8nNtuu438/HzC4dSP4nA4TH5+PrfddpsWvQ7QwNKBfOXyr1IYKSQSSk2qI6EIhZFCvnL5VxlYqlEFIpnKGzGC8nt/Rai4GPIa3RDJyyNUXEz5vb8ib8SIQOLLFkrUpFOy1k6w1p7VwrHWDgd+7m3+0fejh4EjwPuttZf59i8CvuVt/k+jw/0vUAt81lv8OvGcXsBXvc17Wv9XBG/6mL788dMzeNfUIZQW5hEKQWlhHu+aOoQ/fnoG08eo2qNIa40ZM4a77rqLqVOnUlhYSCgUorCwkKlTp3LXXXels9i1tLOp/S/j7rm/4PoRN1CSV0KIECV5JVw/4gbunvsLpva/rOWDiEiTiubOod8Lz1N6xx2EupVBKESoWxmld9xBvxeep2iuhhWHWioPLJKLrLXfAL4CzAPewFV9HA28HSgCngFuMcbU+Z5zMy5hqwEeAI4B78SV4X8YeK8xJuUNY639HHA3bo7aX4E63OLZQ4AfGmO+1Mo/QW9MEUlH8+OTpSW61opISwK7zipRk07JWjsLuAuYgltLrRQ4AazDrav2h8ZJl/e8GcDXcMMji4BtwG+Bu5tYJDvxnHcAXwIuxfVSvwb83Bjzu/P4E/TGFJF0KFE7P7rWikhLlKiJSAq9MUUkHUrUzo+utSLSksCus5qjJiIiIiIikmWUqImIiIiIiGQZJWoiIiIiIiJZRomaiIiIiIhIllGiJiIiIiIikmWUqImIiIiIiGQZJWoiIiIiIiJZJi/oAETk/Dz77LMcOHAg6DBE5DwMGDCAG264IegwJA265orkvly55ipRE8lOaS+uuGLFik3A2HaMRUTa2a5duzbfcMMN44KOowvKeCFbXXNFcl+uXHOVqInkvjLv60lgXRsf+xKgRwbHznT/bJLLsQdB56ttJM5jWUs7StZoz2tuV6JrSGZy+XxlU1sip665StREct82YDCwzhgzuy0PbK2dD8xK99iZ7p9Ncjn2IOh8tQ3fedwWcCiSvna75nYluoZkJpfPVza1JXLtmqtiIiIiIiIiIllGiZqIiIiIiEiWUaImIiIiIiKSZZSoiYiIiIiIZBkVExHJffcD84GdWXDs9oylvd1P7sYehPvR+WoL96PzmGvuR/9nbeF+dB4zcT+5e77uJ3vaEu157DYXisfjQccgIiIiIiIiPhr6KCIiIiIikmWUqImIiIiIiGQZJWoiIiIiIiJZRomaiIiIiIhIllGiJiIiIiIikmWUqIl0AtbakLU2FHQcCYlYvLh0nekCsu01mGt07kREpDGV5xfJcdbavsaYw838PGSMafc3euPfY60tNMbUtvfvleBYa/sB44Ftxpg3g44nF1lr84wxDUHHIRKkxI2KjvisErHWho0xsaDjSIcSNZEcZ609CnwL+FlzDT6vZyvemg/CTD5ErbW3ApcAw4AiYB6wFNhqjKlKxJKNF0k1FtJnrb0S+DlwqffQb4EvGmNOBhdV7rHWfh54FXgNOOB/X2Tr+0REpC2cT7ukq1CiJpLDrLU3A48CHzLG/NH3eAEwApgG7DTGLGjl8XsA1caYOt9jTV5YrbXDgH8HPuM9VA/k+3ZZDPzaGPOH1sTSnqy1pUCtP9HtqJ7IXGStfQvwJ2Ak8DQwHegDvMsY86S1djbQDzgO7DLGbAkq1mxmrX0P8BDwBvAK8DywCthujDnm2+9fgM3AS8aY+iBiFWkP1tq3A1OA08Cjxpg9/hsUulnReVhrI0AcGATkGWN2Nvp5h/xfW2s/ArxojNnT6PHkZ342ff4rURPJYdba53EN4vcbYzZ5j00C/i/wft+uB4Cf4hKlY2cd6NzH/yku4XscWGSM2dro5/4P1F8CnwT+F/gbcAiYDdwFDAfyvKctB/7dGLMkk7+1PVlrDdAD+Aew3hizr9HPs+ainQ2stX8GZgBfNsY8YK0tBJ4CQsCTwA9xc6Brcf/f3zbGvBBUvNnKWvvfwJeBFbge6AHADmABMB9YgnvfbMadw//wnqfXY0CstZcC38Nd5140xhxs9POQMSZure0JnDbGRIOIM9tZa/sC/wZ8xffwH4GPGmOiTQyl12iHHGatnQzcCdwMnAKiwFHciJsHjDGbm3lum13vvJEgzwEfM8Y80sTPC/w3prOBEjWRHGWtLcNd8H4A/KcxptZaOwR4GLgcd4d+HXAxMBl3J+tLxpgfp3PnyutlOu1tNgCvA4uAl4Blxpj9vn274RKzp3EX36XGmN9Za/OBfwbuBn4DjAFmAi/iegGTxwhKo7/zILAaWAgsAzYaY4779o14jYhBuL/rZWPMEx0dc5C883UQ9//5pUQPj7X2F8CncK+TLcA+YBJwFVADzDXGLA8k6Cxlrb0MeAFYC9yLe9/OxM37C3uP1wJvxZ3rHwUUqnistb8FPuJtHsXdxHoQd0087e1TANyPe4+8pOTibNbar+JuKC7H9SrPBt4GfBzXq/wBYC5uJMafjTHbgok0O3gjViqB47nWw2itfS/wfdzNqF24tsIYoKe3Sz3wCPBzY8xSa+0U3HVvhzGmpo1j+QMwBzf642Xf45OAdwPluM+rBcACY0xl0DfG8lreRUSy1EdwF7OlXpJWhvuQewvwbeCnxpgjANbadwF/cN/al4wx69M4/jXe18eBw8DbgU97v3ettXY+7m7YauAmoADYC3wO14DBa8T/3Fr7BWAl7o7ad3FDJD+P600I2vXe15dw5/MqXINhF7DEWrsQ13DYbIyp9vadAXwNMECXStRwr4sosM6XpBVwporwV40xj3uP98X9X38JuBZYHvSHXjYxxqy21v4zrrf7hDHm36y1l+DmeM4CrgQuxJ3vW6214N0wMcZUBBR2V1fofX0JGAV8zPu3xVr7GHAPcANuRMMiY8yLgUSZ/T6Lm7t8uzHmmLX2IVzj+J9xozCu9va7BviGtfZrxpj/DibUrPAC7sbrU9ba5cCbiTnffr4e3XzccPQDWXC9/RbuGnY5sB3oD1zhPT4YqMO9X0Zaaz+Lu9m8E3jJWrsU2IT7O1J6pxM3nK21RcAQXGLXUhJ7C27YfnI4vjei5i4vrjhuZMgngd9Ya79hjKk8j7/9vKlstkju+gjuwp2YfzYIdxfyaWPMfxhjjnhjwgH+jrvDW4a7oKVjvPf1fmPMnbjGx6dwQ7IuxiUqf8Fd9D6Au7iN9p7zq0RZfmvtKFyP1du9D4yf4hK8z1pru2f2J7eLid7Xn+M+LD6IG9p0GLjNe/x+4PvW2tustRfiko4wbqhOV1MCdMNLxj0TcAnuPGPM49bafO9D9DDwM9wdyvFeJdCgGw1Zw3t/PoLrwf2NtXaUMWadMeZ+XOP/v3Hvqx244cM/AP7KmWRBOt63gTW4ht40XAPvadwQ9P+D+7/6Lq7XeXdAMWY1a+0NuKHmf0kMxfdGLryB6+2oBd7lfX8frsfli96w0y7HWnsjcAFwK+6z6Fngh9bad1prh3o3yoCUoaEzcCNZ3t7B4aaw1r4T1y74rjFmtTHmuDFmkzHmd7gbt/uA9wIWl7w9g7vWXe499hfgl8BnrLVXWmv7JI7tS8quwp2XD7UQy7txn1+LjDGnrbVha+3bgK/jErQf4objfhfX6/dF4MvW2kA7tdSjJpKDrLVDcdX2anANvD8DVbj5ZF/w9gl7w/TCxpg6a+0/cHcxL0jj+AW4u3FRXI8ZxphXrLUbcQ3FC3F3Ot+BS+AiuAbl24A1xphdvsNdgbtQ/847zj7vzvN0XDIY2HA4b27VYG9zkTd06Wlr7TxcvBfjGgtzcL2JH8Ld3ZsIrG70d3YVr+BeF5+x1h4DNuB6Rifghu+B+9BLNBhKgCNARMs1pErcIfaGgf0D+L3XsDlljGmw1k7Fvce/iUsA3gWUGmOOnuuY0r6MMa9Za+/BvdZXG2PuBe611l6OG6r3buAyoDvwkLX2Wdy8zd9rvlrSDM4MpwfAWjsa16OxFfiAMeaU96MF1tojuLlsl+KS5K4m0bv4Y9zIlWtwSc6dwHrcZ9Y/cOfzmPc6uwl4Dy7pCNL1wAm8dkTi5rEX42bc++Qi3A29Ys6Msvke7gbvjbhE7CbcKJcF3ufzWlyhtNO48zEdN0qnOZ/CvX4We9tjOHNz5aPesMuwF8da3I3YTwL/AwQ2TUOJmkhuqgd+hfvAu8X7V4m7sC2DlLtNiQbzAFwDO531rqK4C9VDQHIogXfME8BKa+0a3ByMi3GNk0/gEra91toJ3jFGAN/BDW2433f8iPc3dEv7L24fMWAjrlcy2UvhDSnZDGz2CraMxA0pnQlch7uQ39Ph0WaHfbhhONfjhuYV4/4/5+MlvV6SEca99ibhXnv/CCLYXGCM2eZVInsO+KQx5nvej/4JV1Dkce8O8CrUmxY4Y8x91lU+/a61dosxZrExZiXuuliES9Sexb3ubwZmGGP+N8CQs81B3NItRb7H5gBTcQWKTnnXjwJvjtITuJ6OyR0eacC83pxBuBs2XzHG1HuFOWbg5vVNx41u+SLupucj1to3cDcNdvrnYXU0rwBMFJdcJiQqP0ZxPWdVQKE3/NUCHwX64nq3qoDHcP/v03HDwd8L3IFLSp+z1m7F9RruNMasbiaWMlzC+yRnXnf9cL3in0skaV4bpxJ3k+Vy3HkdhhI1EcmEMeYA8CnvQngt8D5cg+AN3GTYY759417jIVFQ5O9pHD+Ku5v0x8QQxib2aQAOenfyVuEaJ1NxvWzX4YYODMVVnPxOYoiLF8sI3NDBQCs/enOs7gbububvPIFLWtd6Sdtg3AfGAx0WaBbxPlDfj7t7+Q7ch+l3cB+6P/Z6ENYaY056hUf+GTeU6U9BxZztvCI1C6y1PwaMdw7zcZPtX0wM0/FeryrPHyBfY+6ruGvqd6y1s303xu7AXQ8/BFTjrs3qAU21Fff6/qFXhKgnrrBIBK/HzJt7lKi+18/72Y4AYg1aOW66wmm8m67GmA3ABmvt73BLG8zCJW2XeV+Pec/7r44P9wyv7bEWN5LnE8BnGlVUfC/u//Zv3nYJZ65vE40xK3Btmje8a+JoXBvjrd6/f8O9x8pwwySbk+iVfAcwyFq7CCjF3ax9wIs3UcE637vWnsT1/PbL/K9vO0rURHJQo+EDzwPPW2v/DTeu+6h/P2+fqbghik82NQG5ieOHgLAxJtrc5Fx7pgriOFzytRw3WfgK3F2pnbihF/7S7FO8WF5IJ5b2lOnfibtgTwCeCTr2oHgN1ZPW2m8aY6z1yhl7RTDqcAtfP+IlaVNwr4UfdNXzlQ7fkLif4hoUv8HdcT6Im78mWcJLIELGmKNeD8CTuHmsn7bWTsQ1Jv+WKOSEez+Ix7shNg/4BW4e5m+8Hz2La3TfDMz3znHimnwlrr36aAeHmw0OA/+Jt/YY0OB9/se8a+oSXNGrX+M+56/G9cSDm98XtKdxhcQ+ZV1p/N/j5m6+Fzc08ynjLS2EW3dzPm6Y4344c2PEGzb/GvCatfYJ3BSO6cC/4hK139C8p3HJ3S3e704Mk1zu9eAmi1x5vZZhoDe+6R9BUXl+kRznXbTjLSQaz+KSuPcYY+a18e8P4z5w7wXebYx5wKUVwwAAG05JREFUzFrbG+hhjDnrDqh11SIvAt5njJnflrFkyma4wKZ1FanuBm5JVDbsSuyZimIh3JzEkH/ejXUVDL+G63UMeQ//BPixabS4qDTNa+yvwA0pfQQ3d0IVHrOUtfYbuIb0TOB23LXwFmPMs96wtVgm15iuwlo7EDd8ehhumZn7cNeOD+GqFy/EDfO9Frdm3TJjzDVNH63zO9dnVePHvZumzwP7jTFXdGSM52KtvQVXnn90ox89CfxXYnimN0/xd7j5zNOaOE7jtfUuwhUfOZTJ3+oNg5yNKx4WB/6P8ZYKsmcqSV6ISypDQZ9HVX0UyTHWLaSalOgNstaG7Jkqj4l9I9baa3GJ0R/TSdIaH7/Rz866ZngfEi/jyrA/413ojiaSNOsqKyUqQHbDzf36YdBJGqQMdQida+ijL/YQ7o7e3V0xSYMzw2iNMXHvLmfj4gi/Bz6DW7bgS7i18r6gJC09XkPkVVwD9h5cr3OF99qTLGSM+QauwflbXIIxD3c9BGi2p74rM8bsN6666TeNMT/xbkb8FXeD5xncfM2XgD/jhtF/71zH6grO9TryfYYlPvtn4YZKZk1PrjHmb8A4XA/afbj/548AHzTGvOx9/oZwvamTOEdPYCJJ831Wz8QNuW92/mfj66cxpsIY85Qx5oO4+WlNzT97J67YWeBz0dWjJpJDrFs40uJ6ozak+ZwBuCqNO4wxzRYSyeT43mT6W3CNlDXGV9Gv0dDMrNNC7GE49wdjV2WtHYObbzMVNwfir7j5U1n5f5yt0ukB9+2b7ME0WtYg6/juvl+BW6dyIG79yq8HHFpWaup1nGhE+xrhn8RV4huNu85U4YbyLeyq74F03//WVWv+Ja5Xt5sJeP0vSH6eRrw5X83tNxA3H20dMNu0sNC111v9TVxVxmFtObTeWjseVxlyKzCrpVjamxI1kRziFe4YDtxsjHnN93hvXBWoemAPrgJSxsOlMjk+bn2Tt+N6yNbh7iQvMsb4Sy73wY0Fv9cYsztbkiBr7ZNkGLv3WEZDJTsL6xZMN7iFmGO40RgngX81xvzet1+y0ZVJQtJVWGvzjCvCk9hu8hw1brxKsNJpKFtrL8AVF9lojNncVa8VLfFe86OBqnPdOLRufc2rcBWGXzPGnOhqNyustcVAsfGKcPkeb/Y8eJ/VlxljnmvvGJuJ4Vyx50GyKnDy7/CGPI7BVbY8YYxZ18QxE/Py/EMfewATjDFLm4llNDC0uRE8/mNbV+zsY7i1YX9sjHkk3b+7vShRE8kR3rDBk7jiHCZxh8pa+1FcVaUp3q6ncMU7fmCMWeErhNGWx38Rl+gU4MrbT/B+9hruTtQC4EHccMhvA+8yxjyVbiztybvreBI3/yGnYg+CtbYEN2dqOG4YyCLckJDP45ZXuNYYsyy4CHODNy/idVwv7h8an7NGjQX1pGWhlpIv/X+dm/f6/4T3L4RbW/GvwH3GqwSYmPuqBBestV8BRuGGgL4C7DHGVDfaJwKUGWNOBhDiOWUau7X2IVzRqev9N0u9/RrPSwvjbm6l9T7L9Ni+oaS9cDcTAl/7U1UfRXLHR3BV9ZYZV5UowpkKcTHgYVxJ3vG4dc1usNZeY4xJd0HpTI5/i7fvadxClXuB23Brt9yJG6ryKdzC0Dvw1m7LhkTHuAqF/4pLSHMq9oB8GBiLW8PnR15j6llc2eIfAP9irV3tvWYSQ8Eux90Rvw84rcYr4CqNDQbuAu6y1q7H3RB4xBizxZxZ/DqM+2yuA26y1s5BxVgCY619G7DKGHPY14hrMqFo1Ojrkjd2mvFfwOdwZfZ34nofL8VV7Pu+73yl3KDowj2T3/G+3oFLdp631i7G3ew54iU+NwK3W2u/nRgBkyU3CzKKHVcF+k+40TpAslfuRuAtXq/YS8BDxphMl7rI+NjeOTye4e9pN0rURHLHJ4GluAsfuHlnBjeO+svGmMcArLVDcb1BnwG+gbtQtdfxT+A+fG8wxjxtXcWpq3DrqN2AW6ekELfW0HxgcXPDFDqC1xD+La5gQ07FHpD3414Xj3nbIa+39YfW2qnez7+PWzst0aC6Effa+Zsx5lRHB5ylbsQlt/fgFve92Pv3bWvti7i1fB43rqx7Yq2hW3E3Dn7a8eGKl6Q9CCyw1i7B9bav8Rqa/sIGcbzEzRsyfUxJ2hnW2htx19qFuBsVJcBbgMS6gc8ZY9Z7+yZ6k0txPRpdLkmz1g4Cdnmbz+I+j76OK1+/HHjJWvsU8N+4c5ns9Qk6SWtF7LNxn7ULEtM1vFEcj+A+oxNuxS0w/5/Az9Oc4/ue9jp2R1LVR5EcYK0dievhecEYs9N7+EpgGm6YYiKJinh33r+Ju2s5wlrbw7ZQNe48jl+NW1vsXm/+zSbcsK734koEN+B6pWbherD+/TxPxXkzrlphA/AtoC85FHtH8xqdA/AWHYXkOlKJz46feF/v9D1nGO7D92VjzBsdF2328ubcDMA14P/FGDMJ16PwY9w6SVcDvwa2W2v/Yq29xlo7BbeA7UpjzK5zHVva1Z2caUx+CzdU7/fW2sSaaYnriX+e4f8BdltrhwQRcJb6F2ATrld+qzFmvTHmPlyVzELc9bVxb9CtwIvWFcPqag4C/w8YirtR+l7gK7hE53LcSIYXccP29wA9vKGl2SDT2D8MvIqbK574zPkuLpF6CTfE/sPAE0B33CLXM9KM5VPAhnY6dodRoiaSG97lff2YtfbL1tpLcZNvjxpjHkjsZNzi03nGmMO4C1QPYGQad9lae/wi3Dyu63ALWoZ8Y7rn4uZ8vQ+4BtcQTRaeCJoxZi2uFzHnYu9A/XFDk057d7kbF4N5GXd38pPWrTsDrpdoOnB/B8eazfrg3otbIVlU5FVjzBeNMf1xa0X9FZcUvA93o+DvuGU1sqbMdldirS3EFb3YiRtK/k1cUv0e3ALXD1lrf22tvd270YW1thyX1EVNCxV2uwqvB+MSXMGmRK9Zou35OK6n/npr7RW+4Y59ced5tDHmQMdHHSzjltz5BW66wV3AKWPM93FzxT+JW28u0WN7Fe4a8WNrbbqjZ9pNK2K/HFekLLHG2ixcMY97gPcbY+42xvzBGHMzrq0xHPh0S3F4c+7nAn8DtrflsTuaEjWR3LATlyjU4IYMrMDdpZoPqeubGVdRqQQ3YTuKGxfensf/Fa4k8NdxvXBYa98O9ASeN8a8ZlzhhM8Zt55KVvDmPjxJDsbegU7hhsgnhsmnJPze8K5f4D5LPuTNa5wJ5KNEze8ErlH6v97rrsG6NQ4TVdBeNMbcjkuKb8cNEevnPfePgUQsFwK9gO3GVdD7LnATbn2le3A3qT6OW8PpQWvtt3C97peh177fVNz14ZA3Pzg5t8+7MXY3bg70nb7njMc14rvka9/3efsvuM/k/wdgjHnDGPOYMea/cZ+/b+CqLzfgXosXBxBuigxjX+3tO4UzRb0uwc1j/L/eMHD/GnHfx/XC9bOuumVzbve+njJesZo2PHaHUqImkgO8oYcfxd1t/xSuF2MrsMFaW+Cb5J54T1+Aa2ikrBHWjsf/IbCPM71OH8PdfV7sPS/ku1hmBV+vUM7F3lG8Ya7X4DWYztEzu9D79wHcHczrgX+YLFjDJ1sYV6b6P3ET1hON1Kg3BBcvaYsYY2qNMX/F3Yk+ATxp2nB9IMlIKVAMLAMwxlQbY/YaY54Cvojrif8wrornSOCruKFU4HrgxcnHDTFPLCrcuN25BHgU+KC1dpDXcJ6Bu1n2qw6LMot4w8sjxphDuLm+b7PW2sTPrbWTcYta/wWX4N4J/CtwbxDx+mUYewXu5l8ceI+33w3AS8ZVg0yM4Ej0wFXg5rr1wfXCNedW7+v3rbXL2vjYHUqJmkgO8O7Cx40xG40xv8IlEx8HlviTCF/y8U7cUIJ7OuL4xq0z9hlgsLX2PuBmXG/c2tb+zR0ll2PvCMaYV/Aaq+f4eQw3V20ErgE7EddLKZ7E3BtjzOmmfu4lbVHfjZDbcA3VwBteXdg63JyVZxv/wEvatuJuYHwSN5f3+7j5Vss07DHFbtx8oFOQWj3X+9yJ4hYLz8d95pTiei7XedfmLilxnryRHHcDX7bWJpKPz+EWAl/ivRbXGGN+ZrKkUmG6sQMfxN2UmgdMAv4D1wP7pPd8f5VVODM88qBpuUjVh7xjL8D1pLXlsTuUqj6K5IBGPVpx7y774qb2tdZegWs8rDHGPNMRx/caokuttV8FfoRbI2ehMabKZke54HPK5dg7ShrnYBFuGMt1uHmNj7d/VLkj3deQdze6O27dH4wxT7drYHJOxpgaWpiX6v2/ngBOWGsTBV/ub+fQcs0buJ7GmsY/8N34ewH3eXMX7vp7CfCljgowB3wRV3zoa9bav+OWx1kOrILknNeGAONrzjljN8Ycsdb+1hhzr7V2LK6C8I24nuymXIGbt9vijUDj5jbeiysW1qbH7mjqURPJIcarMAYpd4KSrLVFuAthGW6NsA45vq8h+gfcnasnccPhwI1Hz1q5HHu2MG79mUTRCyVp56caV2HwHUEH0pVZa0NpVMsNeV9LcI1AcGs2icfrLX7VGLOtmX2qcdePgbiiEwUo4QWSlZZjuM+m3rjlc8pww8uPgJs3HmCI59RS7N77Jw5gjNlsjLHGmCtxn8XJ95dxhay64Yr6HE/8vIXfHUrMP2vrY3e0UDze5W8Wi3Qa1tp83AWxB7DLuyucM8eX3OV9KF4DvGKM2Rd0PCIdxVo7AjfEq8IY84Fgo8lNXhn+J3HD0x4zxrw74JCyjrX2y7hiXweBDxhj5tkcWRC8pdi90Twhc471B61b4+wbwA+MMV/O8He327E7ghI1EWkzTZRvzxm5HLuIBMer3nkxrrLhnqDjyTX2zCLXH8YVoPikMebFoOPKRtbaMbh5wM/lWqGh1sZu3ZqEnwe6Ad81bbg+Z3seu60oURMRERGRQHlDSCcYY1YFHUu28Q/VCzqWTLVF7N7c3YLEcM+21J7HbgtK1EQ6CW/C7EeAJ4xb+yuw47d3LO0pl2MPgs5X29B5zF3ekPCoeuOlI3k9udEcTd5yNvaOpmIiIp3HzcCXgR9nwfHbO5b2lMuxB0Hnq23oPOYYa20hgDGmXkla6yXOo6TH97pryLVEJ9PY2/O1kSuvOyVqIp3HU7hFJL+XBcdv71jaUy7HHgSdr7ah85h7PmytPWGt/XzLu0ozdB4zk8vnK9PY2/NvzYnzqHXURLKUV0Uvnu6dWmPMRuCO9ji+t+/rxpi0jp9pLO2pvc9jZ6Pz1TZ0HnNPJusmesWHJgLdcZVwxaPzmJlcPl/tGXsr9s/Z89gczVETyTLexNbT/guO1+iLNXcR8sZ8x1pqGGZyfP++iePj1hZrk1jaU3ufx85G56tt6DzmvnRLnnvrSk4DXjbGnGr/yHKLzmNmcvl8tSL2NcaYkxnsn/bfmsvnsSlK1ESyjLX2PuBW4H+AB40xa30/C+GGLMcaNQTzjTH1bX18376/Ah5o61jaU3ufx85G56tt6DzmHmttOXAdMN8Yc8D3eAi3/pKS5zToPGYml89XprG359+ay+cxHUrURLKMtfYo0Mv30Ergr8Ajxpjdvv3yjDEN1tp+wA+A7caY/2rL4+MWp+yF60WLt3Us7am9z2Nno/PVNnQec4+19j+ArwPzgaXAAmC1MabCt08Ydw3Eu4k1EthnjKnt+Iizk85jZnL5fGUau7fv1739lrS0fyZ/ay6fx3QoURPJItba6cBi4BFgNXAnMNL7cQPwHPAA8GSiq95aex3wLO7u/fvb6vi48duLvX9XAZVAaVvF0p7a+zx2NjpfbUPnMTdZa7cBozhzjTsELAfmAQuBDcaYqG//7sD9uEWux6k31NF5zEwun69WxL7d2z+RdLTZ35rL5zEdKiYikl0u8r4+ZYz5HfA9a+1bgI8BHwDe7v07Yq19EvgTcK33nO+35fGBzd6+ibtSs4BIG8bSntr7PHY2Ol9tQ+cxx1hrR+N6QBcCXwDeBrwDuAl4J7AdWGKtnQcsM8ZswSXf04FV2d7I6yg6j5nJ5fOVaexAFFewox6XQD3f3P6Z/K25fB7TpURNJEt446kLcQU7ticeM8asAlYBn7LW3gR8AncB+qj3D2CHMWZNGx+/D27I4w3ADmCtN6/mvGNpT+19Hjsbna+2ofOYs8YA3XCNtjXW2teB3wCTcY2+G4EP4RLtV621LwF9gX7APcGEnJV0HjOTy+cro9hx7YduuPm53wNeam7/DP/WXD6PadHQx//f3t3F2FGWARz/b4l8FV0LKpRErUFTw4UxpoCAkdTgjWL4DBJrazAxBiUiSkxE4OG5IKAXJHihGD9ooShCIIApokbZSMCgJqgXJk1IiomiKB8tkZSvtl68c7rHZffsnt2ZPTNn/79kM52Zd94+52lyuu+87zwjtUhmnkL5YvlBRPy9OrYKWBURr/W1m6TcNfoGsB64MiJuqLn/LwOXUu6EXRkRN9QZS5OazuO4MV/1MI/dUw2e7wIujog7Zpw7DDgeOIXy7/UR4Njq9O6IOHo5Y20z8zicLudrkbFPAC9GxFELbA8L+KxdzuNCOaMmtUhEPJaZf6B8qfWO7afcpe+V+Z6IUtZ2e2aeTPlF77YG+s/MPIYyWLut7lia1HQex435qod57KQdlLvvr8w8URUa2AXsysyfU5ZYfRX4IrB9OYPsAPM4nC7na7Gx3zVk+4V81i7ncUGcUZNaJBfwwsZem8zcQCla8FREnDqK/pcSS5OazuO4MV/1MI/jLzO/BVwBbHC56uKZx+F0OV/Dxt7kZ+1iHleNOgBJ0+b7JW9Gm7XA2ykFCUbS/1JiaVLTeRw35qse5nE8Vc8fkpnrKEUKnurKL3ltYh6H0+V8DRt7k5+1y3kElz5KXfZbYCPlnSSj7r/pWJrU5dhHwXzVwzx2RN/gepLybskfjjCczjKPw+lyvoaNvcnP2uU8gksfpdbLzBMpBT0ei4jXrcNezv6bjqVJXY59FMxXPczjeMnMtwIvRAdelNtm5nE4Xc7XsLE3+Vm7mEcHalKLZeZq4DvAJ5qoUDRM/03H0qQuxz4K5qse5lGStBQ+oya1UG9NNXAC8EHg19XxWpYrD9N/07E0qcuxj4L5qod5lCTVwf80pBbqW1N9EuWFjp+r9muZAh+m/6ZjaVKXYx8F81UP8yhJqoNLH6WWqt5hdjtwUkQcM8r+m46lSV2OfRTMVz3MoyRpqVz6KLXXHuCnwPegkWVTw/TfdCxN6nLso2C+6mEeJUlL4n8cUktFxGvALX2H9o2q/6ZjaVKXYx8F81UP8yi1R2ZOAWfMOLwxIqaWP5rZZeZuSgn5gyJiYo7mWiFc+ihJkqSRyMwngXcCGRHX1tV2xnVTlIHaC8De6vB5EfHo0AH/f78bgd9Uu6dExO8XcM0a4F/AocAlEXFzdXwnZaB2CPAWcKAmZ9QkSZK0MlwWEVtr7G8K+Btl8LgFmHegBlxEGaS9TFkeDUBErAfIzHXArhpjVIf5jJokSZI0pKrC663V7kWZ+YYFXLal2t4fEc83E5nGhQM1SZIkaXF6A7VjgI8NapiZ76G8WxFgW5NBaTy49FGSJEkCMnMVsIky8/V+ynNjzwAPAzdGxGP97SPiicx8BDi9uua+Ad33ZtOeBn5Rc+gaQ86oSZIkacXLzDdSBlC3AmdSZsn2AmuBC4FHM/PSWS7tzY6dVRULma3vCeDT1e7tVWVYaSBn1CRphCwbLUmt0Rug/QX4OvBQROzNzDcDlwDXAjdl5uMR8UjfdXcC3wYOBz4J3DxL3x8G1vX9PdK8HKhJ0hyWo2x0n/6y0a8s4vqZ8dRWNpqyTOcl+spGS9I4ycwzgXOAJyk3y57rnYuI3cD1mbkP+CZlEHdW3/k9mXkvpaLjFmYfqPWWPf4pIv7cyIfQ2HHpoyS1w2URcVz1s6R3+1SmKGWjYfoXhPnMWTY6Io4DTqohLklqo89U2639g7QZflxtN2bmITPO9ZY/npqZ7+4/kZlHABfMaCfNyxk1SRpDEXEgM28FrqaUjb48Il6d5zLLRktaqU6rtpdn5iXztD2S8vzav/uO/Qp4Cjge2AxE37lzgDcBrzE92JPm5YyaJI0vy0ZL0sKsrbaTwLEDfnqO7L84IvYB26vdzVXxkJ7eTbAHI6J/cCcN5IyaJHWEZaMljaGXqu0RC2jbGxztHdhqcXqTF2dHxP2L7GMb8DXgXcCHgIcz8zjgo33npQVzRk2SOsCy0ZLG1LPVdu2gRpl5GHD0jGvq9HS1PXGxHUTEX4E/Vrubq+0mSiGm54GfLTo6rUgO1CSpG/rLRn8cWB0Rk8Aa4ErKsw83ZebpM667k3LH+lBK2ejZWDZa0qg8Xm1PG9gKTqYMePqvqdPvqu35S+ynd3Pswsw8nOnVCndExMtL7FsrjAM1SWq5WcpGPxARe6GUjY6I6ylFQ1ZRykYfFBF7gHur3bmqP1o2WtKo3F1tT8jMswe0+0q13UUzA7Wt1XZDZg6slDvX6oTKTyivWJkErgLeVx132aOG5kBNktrPstGSxlJEPESpmAiwPTM/n5mTvfOZuT4zt1NuVgFcFRH7G4jjQeCeavdHWRxcjpmZazLz7My8D7hxQD/PAjuq3d6Ns50znyGWFsJiIpLUfpaNljTOPkUpdnQa5WXR383M3ZQl26urNgeAqyOiye+pLZRJjHOAa4BrMnMPMEH5nuzZOk8/24BzmZ4Q8SaYFsUZNUlqP8tGSxpbEfEMcAblRtIOSmGPo6rTO4HvAx+IiOsajuPFiDgXOIsyu/YPSjXKQ4EnKDezLgC+ME9XDwD/qf68n+nvX2kozqhJ0twsGy1Jy6CqNrudFgxqImIH08sXF3P9q8Db6otIK5UzapI0N8tGS5KkkXBGTZLm9jjlmYk2lI1+B6Vs9A1L6GcbsIFSNvpLWDZa0spyS2beUv15Y0RMjTKYftUzeZPzNtSK4oyaJM3NstGS1H3PUVYm9P+8MtKIXm9mfE8Pbq6VYOLAgQOjjkGSWiszf0l5juu/wBWU2ac91bn1lPeXbaqabxq2IllmTlEeor84IrYOaHc3cB6wD7gOuDki/lmdW0N5afVngeci4uIB/dxDqUa2n3KzbmdEvHeBsa6jDEaJiImBjSVJ0pK49FGSBrNstCRJWnYufZSkASwbLUmSRsEZNUmah2WjJUnScnNGTZIkSZJaxhk1SWoHy0ZLkqSDHKhJ0mj1ykb3a2PZ6JdGHYQkSSuJ5fklSZIkqWV8Rk2SJEmSWsaBmiRJkiS1jAM1SZIkSWoZB2qSJEmS1DIO1CRJkiSpZRyoSZIkSVLL/A89oBz+imxKrwAAAABJRU5ErkJggg==\n", 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" ] @@ -1437,12 +1437,12 @@ }, { "cell_type": "code", - "execution_count": 69, + "execution_count": 32, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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"text/plain": [ "
" ] @@ -1495,439 +1495,17 @@ "plt.savefig('test2.svg')" ] }, - { - "cell_type": "code", - "execution_count": 60, - "metadata": {}, - "outputs": [ - { - "data": { - "image/svg+xml": [ - "\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", 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"metadata": {}, "source": [ "We can also check the gap function of the superconducting phase and study its symmetry in momentum space.\n", - "There we can see, that it is constant......" + "There we can see, that it is constant." ] }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 36, "metadata": {}, "outputs": [], "source": [ @@ -1936,22 +1514,22 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 35, + "execution_count": 39, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -1968,11 +1546,11 @@ ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": {}, - "outputs": [], - "source": [] + "source": [ + "---" + ] } ], "metadata": { diff --git a/doc/user_guide/Linearized Eliashberg equation on the attractive Hubbard model.ipynb b/doc/user_guide/Linearized Eliashberg equation on the attractive Hubbard model.ipynb index 367c0be09..fdbb3da4d 100644 --- a/doc/user_guide/Linearized Eliashberg equation on the attractive Hubbard model.ipynb +++ b/doc/user_guide/Linearized Eliashberg equation on the attractive Hubbard model.ipynb @@ -11,7 +11,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "Starting run with 1 MPI threads at : 2019-05-15 18:39:07.048894\n" + "Starting run with 1 MPI rank(s) at : 2020-08-17 10:55:55.432570\n" ] } ], @@ -191,7 +191,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -601,7 +601,7 @@ "" ] }, - "execution_count": 5, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" } @@ -641,7 +641,7 @@ "If $\\lambda=1$ a phase transition to a superconducting state is found.\n", "For further information see the documentation [here](../theory/eliashberg.rst).\n", "\n", - "To solve it in the same order as the RPA we need the non-interacting Green's function $G^{(0)}$ and the particle-particle vertex $\\Gamma$ is approximated by a fequency independent and local vertex $U$.\n", + "To solve it in the same order as the RPA we need the non-interacting Green's function $G^{(0)}$ and the (singlet) particle-particle vertex $\\Gamma$ is approximated by a fequency independent and local vertex $2U$.\n", "\n", "First we setup our model by using previously established `ParameterCollection` `hubbard` as a template and alter it to the parameters of the repulsive Hubbard model.\n", "To do this use its method `alter` and supply the parameters that shall be changed as keywords.\n", @@ -650,7 +650,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -666,7 +666,7 @@ "t = 1.0" ] }, - "execution_count": 6, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" } @@ -689,7 +689,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -698,7 +698,7 @@ "triqs_tprf.tight_binding.TBLattice" ] }, - "execution_count": 7, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" } @@ -720,7 +720,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -729,7 +729,7 @@ "pytriqs.gf.gf.Gf" ] }, - "execution_count": 8, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -752,7 +752,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -761,7 +761,7 @@ "pytriqs.gf.gf.Gf" ] }, - "execution_count": 9, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -790,7 +790,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ @@ -799,7 +799,7 @@ "wmesh_boson = MeshImFreq(beta=temperature_to_beta(repl_hubbard.T), S='Boson', n_max=repl_hubbard.nw)\n", "wmesh_boson_kmesh = MeshProduct(wmesh_boson, g0_wk.mesh[1])\n", "gamma_pp = Gf(mesh=wmesh_boson_kmesh, target_shape=g0_wk.target_shape*2)\n", - "gamma_pp.data[:] = repl_hubbard.U" + "gamma_pp.data[:] = 2*repl_hubbard.U" ] }, { @@ -815,16 +815,16 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "0.999970584562773" + "0.9999705817303945" ] }, - "execution_count": 11, + "execution_count": 14, "metadata": {}, "output_type": "execute_result" } From f64551071bfc9200f49592b43129df57b3098ec0 Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 17 Aug 2020 11:09:22 +0200 Subject: [PATCH 073/121] [eli] remove c++ functions from python doc --- doc/reference/python_reference.rst | 4 ---- 1 file changed, 4 deletions(-) diff --git a/doc/reference/python_reference.rst b/doc/reference/python_reference.rst index 645f8d407..6c2997a7f 100644 --- a/doc/reference/python_reference.rst +++ b/doc/reference/python_reference.rst @@ -52,10 +52,6 @@ Linearized Eliashberg equation .. autofunction:: triqs_tprf.eliashberg.power_method_LR .. autofunction:: triqs_tprf.eliashberg.implicitly_restarted_arnoldi_method .. autofunction:: triqs_tprf.eliashberg.preprocess_gamma_for_fft -.. autofunction:: triqs_tprf.eliashberg.eliashberg_product -.. autofunction:: triqs_tprf.eliashberg.eliashberg_product_fft -.. autofunction:: triqs_tprf.eliashberg.gamma_PP_singlet -.. autofunction:: triqs_tprf.eliashberg.gamma_PP_triplet Hubbard atom analytic response functions ======================================== From c18d5a863f4b0ba7abc1c2678e9d97b803c3adbc Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 17 Aug 2020 11:51:16 +0200 Subject: [PATCH 074/121] [eli] update python function docstrings --- python/triqs_tprf/eliashberg.py | 26 +++++++++++++++----------- 1 file changed, 15 insertions(+), 11 deletions(-) diff --git a/python/triqs_tprf/eliashberg.py b/python/triqs_tprf/eliashberg.py index 00e90cd63..4f76fa2ea 100644 --- a/python/triqs_tprf/eliashberg.py +++ b/python/triqs_tprf/eliashberg.py @@ -37,12 +37,14 @@ # ---------------------------------------------------------------------- def solve_eliashberg(Gamma_pp_wk, g_wk, initial_delta=None, Gamma_pp_const_k=None, - tol=1e-10, product='FFT', solver='PM', symmetrize_fct=lambda x : x): + tol=1e-10, product='FFT', solver='IRAM', symmetrize_fct=lambda x : x): r""" Solve the linearized Eliashberg equation Returns the biggest eigenvalues and corresponding eigenvectors of the linearized Eliashberg - equation. The Eliashberg equation implementation is using fourier transformations for - computational efficiency. The eigenvalues are found using an iterative algorithm from scipy. + equation, for a particle-particle vertex in the random phase approximation, + as described here :ref:`eliashberg_rpa`. The Eliashberg equation implementation is + using fourier transformations for computational efficiency. The eigenvalues are found + using an iterative algorithm from scipy. Parameters ---------- @@ -60,7 +62,7 @@ def solve_eliashberg(Gamma_pp_wk, g_wk, initial_delta=None, Gamma_pp_const_k=Non Gamma_pp_const_k : float or np.ndarray or Gf, optional Part of the pairing vertex that is constant in Matsubara frequency space :math:`\Gamma(\mathbf{k})`. If given as a Gf its mesh attribute needs to - be a MeshBrillouinZone. + be a MeshBrillouinZone. If not given, the constant part will be fitted. tol : float, optional Relative accuracy for eigenvalues (stopping criterion). product : str, ['FFT', 'SUM'], optional @@ -68,16 +70,17 @@ def solve_eliashberg(Gamma_pp_wk, g_wk, initial_delta=None, Gamma_pp_const_k=Non 'FFT' : triqs_tprf.lattice.eliashberg_product_fft, which uses Fourier transformation for optimal computational efficiency. - Restrictions : + 'SUM' : triqs_tprf.lattice.eliashberg_product, uses the explicit sum. - Restrictions : wmesh of Gamma_pp_wk must be atleast twice the size - of the one of g_wk. - solver : str, ['PM', 'IRAM'], optional + Restrictions : wmesh of Gamma_pp_wk must be atleast twice the size of the one of g_wk. + + solver : str, ['IRAM', 'PM'], optional Which eigenvalue solver shall be used: + 'IRAM' : Use the Implicitly Restarted Arnoldi Method implemented in :func:`implicitly_restarted_arnoldi_method`. + 'PM' : Use the Power Method implemented in :func:`power_method_LR`. - 'IRAM' : Use the Implicitly Restarted Arnoldi Method implemented in :func:`implicitly_restarted_arnoldi_method`. symmetrize_fct : function, optional A function that takes one parameter: A Green's function :math:`G(i\nu_n, \mathbf{k})`. The mesh attribute of the @@ -85,7 +88,8 @@ def solve_eliashberg(Gamma_pp_wk, g_wk, initial_delta=None, Gamma_pp_const_k=Non (MeshImFreq, MeshBrillouinZone). This function is applied after every iteration of the eigenvalue solver and can be used to enforce a specific - symmetry. + symmetry. If no symmetries are enforced, caution is need, because + unphysical symmetries can occur. Returns ------- @@ -164,7 +168,7 @@ def preprocess_gamma_for_fft(Gamma_pp_wk, Gamma_pp_const_k=None): Gamma_pp_const_k : float or np.ndarray or Gf Part of the pairing vertex that is constant in Matsubara frequency space :math:`\Gamma(\mathbf{k})`. If given as a Gf its mesh attribute needs to - be a MeshBrillouinZone. + be a MeshBrillouinZone. If not given, the constant part will be fitted. Returns ------- From aa1dc474c6bddf2b1dbc7be7a3cc977d5314d6ca Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 17 Aug 2020 12:36:09 +0200 Subject: [PATCH 075/121] [eli] add new test --- test/python/eliashberg/CMakeLists.txt | 1 + .../solve_eliashberg_functionality.py | 51 +++++++++++++++++++ 2 files changed, 52 insertions(+) create mode 100644 test/python/eliashberg/solve_eliashberg_functionality.py diff --git a/test/python/eliashberg/CMakeLists.txt b/test/python/eliashberg/CMakeLists.txt index b2f36d756..5c32dca6c 100644 --- a/test/python/eliashberg/CMakeLists.txt +++ b/test/python/eliashberg/CMakeLists.txt @@ -5,6 +5,7 @@ set(PREFIX eliashberg-) add_python_test(preprocessing_gamma ${PREFIX}) add_python_test(gamma_creation ${PREFIX}) +add_python_test(solve_eliashberg_functionality ${PREFIX}) add_python_test(semi_random_initial_delta ${PREFIX}) add_python_test(product_summation_vs_fft ${PREFIX}) add_python_test(eigenvalue_solver ${PREFIX}) diff --git a/test/python/eliashberg/solve_eliashberg_functionality.py b/test/python/eliashberg/solve_eliashberg_functionality.py new file mode 100644 index 000000000..67b6655e0 --- /dev/null +++ b/test/python/eliashberg/solve_eliashberg_functionality.py @@ -0,0 +1,51 @@ +from triqs_tprf.ParameterCollection import ParameterCollection +from triqs_tprf.utilities import create_eliashberg_ingredients + +from triqs_tprf.eliashberg import solve_eliashberg + + +def test_wrong_input_for_product(g0_wk, gamma): + wrong_input = "false" + + try: + solve_eliashberg(gamma, g0_wk, product=wrong_input) + except NotImplementedError as e: + expected_message = ( + "There is no implementation of the eliashberg product called %s." + % wrong_input + ) + assert str(e) == expected_message + +def test_wrong_input_for_solver(g0_wk, gamma): + wrong_input = "false" + + try: + solve_eliashberg(gamma, g0_wk, solver=wrong_input) + except NotImplementedError as e: + expected_message = ( + "There is no solver called %s." + % wrong_input + ) + assert str(e) == expected_message + +if __name__ == "__main__": + p = ParameterCollection( + dim=2, + norb=1, + t=1.0, + mu=0.0, + beta=1, + U=1.0, + Up=0.0, + J=0.0, + Jp=0.0, + nk=2, + nw=100, + ) + + eliashberg_ingredients = create_eliashberg_ingredients(p) + g0_wk = eliashberg_ingredients.g0_wk + gamma = eliashberg_ingredients.gamma + + test_wrong_input_for_product(g0_wk, gamma) + test_wrong_input_for_solver(g0_wk, gamma) From 78459118f1ebc613e6fce0628add84db1656e58d Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 17 Aug 2020 12:45:30 +0200 Subject: [PATCH 076/121] [eli] add solving for specific number of gaps --- python/triqs_tprf/eliashberg.py | 14 ++++++++++---- .../eliashberg/solve_eliashberg_functionality.py | 7 +++++++ 2 files changed, 17 insertions(+), 4 deletions(-) diff --git a/python/triqs_tprf/eliashberg.py b/python/triqs_tprf/eliashberg.py index 4f76fa2ea..f86b2945e 100644 --- a/python/triqs_tprf/eliashberg.py +++ b/python/triqs_tprf/eliashberg.py @@ -37,7 +37,7 @@ # ---------------------------------------------------------------------- def solve_eliashberg(Gamma_pp_wk, g_wk, initial_delta=None, Gamma_pp_const_k=None, - tol=1e-10, product='FFT', solver='IRAM', symmetrize_fct=lambda x : x): + tol=1e-10, product='FFT', solver='IRAM', symmetrize_fct=lambda x : x, k=6): r""" Solve the linearized Eliashberg equation Returns the biggest eigenvalues and corresponding eigenvectors of the linearized Eliashberg @@ -91,6 +91,10 @@ def solve_eliashberg(Gamma_pp_wk, g_wk, initial_delta=None, Gamma_pp_const_k=Non symmetry. If no symmetries are enforced, caution is need, because unphysical symmetries can occur. + k : int, optional + The number of leading superconducting gaps that shall be calculated. Does + only have an effect, if 'IRAM' is used as a solver. + Returns ------- Es : list of float, @@ -148,7 +152,7 @@ def matvec(delta_x): es, evs = [es], [evs] elif solver == 'IRAM': - es, evs = implicitly_restarted_arnoldi_method(matvec, initial_delta, tol=tol) + es, evs = implicitly_restarted_arnoldi_method(matvec, initial_delta, k=k, tol=tol) else: raise NotImplementedError('There is no solver called %s.'%solver) @@ -294,7 +298,7 @@ def semi_random_initial_delta(g_wk, nr_factor=0.5, seed=None): return delta -def implicitly_restarted_arnoldi_method(matvec, init, tol=1e-10): +def implicitly_restarted_arnoldi_method(matvec, init, tol=1e-10, k=6): """Find the eigenvalue with the largest real value via the Implicitly Restarted Arnoldi Method @@ -307,6 +311,8 @@ def implicitly_restarted_arnoldi_method(matvec, init, tol=1e-10): method with. Restriction: len(init.shape) == 1. tol : float, optional The tolerance at which the iterative scheme is considered to be converged. + k : int, optional + The number of eigenvalues and eigenvectors desired. Returns ------- @@ -323,7 +329,7 @@ def implicitly_restarted_arnoldi_method(matvec, init, tol=1e-10): """ N = init.shape[0] linop = LinearOperator(matvec=matvec, dtype=np.complex, shape=(N, N)) - Es, U = eigs(linop, which='LR', tol=tol, v0=init) + Es, U = eigs(linop, k=k, which='LR', tol=tol, v0=init) Es = Es.real return list(Es), list(U.T) diff --git a/test/python/eliashberg/solve_eliashberg_functionality.py b/test/python/eliashberg/solve_eliashberg_functionality.py index 67b6655e0..2139a4056 100644 --- a/test/python/eliashberg/solve_eliashberg_functionality.py +++ b/test/python/eliashberg/solve_eliashberg_functionality.py @@ -28,6 +28,12 @@ def test_wrong_input_for_solver(g0_wk, gamma): ) assert str(e) == expected_message +def test_k_input(g0_wk, gamma): + for k_input in [1, 3]: + Es, evs = solve_eliashberg(gamma, g0_wk, k=k_input) + assert len(Es) == k_input + assert len(evs) == k_input + if __name__ == "__main__": p = ParameterCollection( dim=2, @@ -49,3 +55,4 @@ def test_wrong_input_for_solver(g0_wk, gamma): test_wrong_input_for_product(g0_wk, gamma) test_wrong_input_for_solver(g0_wk, gamma) + test_k_input(g0_wk, gamma) From 2304e24d4bbe20bc467b5a33200cf9564c94be70 Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 17 Aug 2020 13:00:16 +0200 Subject: [PATCH 077/121] [eli] update doc --- doc/theory/eliashberg.rst | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/doc/theory/eliashberg.rst b/doc/theory/eliashberg.rst index 67a1728b3..35dec1345 100644 --- a/doc/theory/eliashberg.rst +++ b/doc/theory/eliashberg.rst @@ -193,6 +193,8 @@ which we list in the table below. Because all other combinations are unphysical it is possible to restrict the gap to the allowed symmetries while solving the linearized Eliashberg equation. +.. _eliashberg_rpa: + Random phase approximation for the irreducible particle-particle vertex ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ @@ -320,7 +322,7 @@ Note, that this simplification is only allowed, if the solutions of :math:`\Delt are restricted to the allowed symmetries, otherwise unphysical solution can occur. Also note, that the RPA particle-particle vertices in Eq. :eq:`singlet_gamma_2` and :eq:`triplet_gamma_2` only depend on the difference -between the two fermionic Matsubara frequencies and momenta. +between the two fermionic Matsubara frequencies, i.e. a bosonic Matsubara frequency and one momentum. We can therefore write the linearized Eliashberg equation :eq:`linearized_eliashberg_3` as @@ -331,7 +333,7 @@ We can therefore write the linearized Eliashberg equation \Delta^{\mathrm{s/t}}_{\bar{e}\bar{f}}(K')\,, :label: linearized_eliashberg_5 -which is the form it is implemented as now. +which is the **form it is implemented as now** in :meth:`triqs_tprf.eliashberg.solve_eliashberg`. This allows us to get rid of the summation by using the convolution theorem From 66524beea5b1ad0fc2c9c2368f16cf0a581ce305 Mon Sep 17 00:00:00 2001 From: Stefan Date: Mon, 17 Aug 2020 17:13:49 +0200 Subject: [PATCH 078/121] [eli] adjust to TRIQS 3.0.0 --- .../PHT_Hubbard_Model.ipynb | 851 ++++++++++++++++-- ...tion on the attractive Hubbard model.ipynb | 32 +- python/triqs_tprf/ParameterCollection.py | 2 +- python/triqs_tprf/eliashberg.py | 8 +- python/triqs_tprf/lattice_desc.py | 241 +++-- python/triqs_tprf/plotting_tools.py | 6 +- python/triqs_tprf/symmetries.py | 6 +- python/triqs_tprf/utilities.py | 6 +- test/CMakeLists.txt | 2 +- test/python/eliashberg/eigenvalue_solver.py | 2 +- .../fft_product_constant_vs_full.py | 2 +- test/python/eliashberg/gamma_creation.py | 2 +- test/python/eliashberg/preprocessing_gamma.py | 2 +- .../previous_implementation_two_band.py | 8 +- .../eliashberg/product_summation_vs_fft.py | 4 +- test/python/eliashberg/symmetrize_delta.py | 6 +- test/python/symmetrize_gf.py | 4 +- 17 files changed, 987 insertions(+), 197 deletions(-) diff --git a/benchmark/eliashberg/particle_hole_transformation/PHT_Hubbard_Model.ipynb b/benchmark/eliashberg/particle_hole_transformation/PHT_Hubbard_Model.ipynb index 8dbdaf46c..fba7bff77 100644 --- a/benchmark/eliashberg/particle_hole_transformation/PHT_Hubbard_Model.ipynb +++ b/benchmark/eliashberg/particle_hole_transformation/PHT_Hubbard_Model.ipynb @@ -12,7 +12,7 @@ "\n", "import numpy as np\n", "\n", - "from pytriqs.plot.mpl_interface import plt" + "from triqs.plot.mpl_interface import plt" ] }, { @@ -133,7 +133,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "Starting run with 1 MPI rank(s) at : 2020-08-17 10:44:43.599610\n" + "Starting run with 1 MPI rank(s) at : 2020-08-18 10:29:06.218793\n" ] } ], @@ -166,7 +166,7 @@ { "data": { "text/plain": [ - "Text(0.5,0,'DOS')" + "Text(0.5, 0, 'DOS')" ] }, "execution_count": 6, @@ -175,12 +175,14 @@ }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "dark" + }, "output_type": "display_data" } ], @@ -211,7 +213,7 @@ "To get physical information about the Hubbard model we will calculate the spin and charge susceptibilites in the random phase approximation (RPA) limit to see at which parameters they diverge and a phase transition occurs.\n", "\n", "To use the RPA we need the non-interaction particle-hole bubble which is contstructed via the non-interaction Green's function.\n", - "We therefore first construct a Matsubara frequency mesh object by using `MeshImFreq` from `pytriqs.gf`.\n", + "We therefore first construct a Matsubara frequency mesh object by using `MeshImFreq` from `triqs.gf`.\n", "This constructor needs to know the inverse temperature `beta` in $1/\\mathrm{eV}$, which we can get from the temperature in $\\mathrm{Kelvin}$ by using the converter function `temperature_to_beta` from `triqs_tprf.utilities`, the statistic of our particle `S`, in our case a Fermion, and the number of points to use `n_max` in one dimension.\n", "With this mesh object and the dispersion relation `e_k` we can then use `lattice_dyson_g0_wk` from `triqs_tprf.lattice` to construct the non-interaction Green's function for a specific filling given by `mu`.\n", "The non-interaction particle-hole bubble is then constructed from this `Gf` object by using `imtime_bubble_chi0_wk` from `triqs_tprf.lattice_utils`.\n", @@ -234,7 +236,7 @@ " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", "Two-Particle Response Function tool-box \n", "\n", - "beta = 11.6045250062\n", + "beta = 11.604525006165701\n", "nk = 1024\n", "nw = 100\n", "norb = 1\n", @@ -250,7 +252,7 @@ } ], "source": [ - "from pytriqs.gf import MeshImFreq\n", + "from triqs.gf import MeshImFreq\n", "from triqs_tprf.lattice import lattice_dyson_g0_wk\n", "from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk\n", "from triqs_tprf.utilities import temperature_to_beta\n", @@ -287,7 +289,7 @@ "$$\n", "\n", "These kind of equation is implemented as `solve_rpa_PH` in `triqs_tprf.lattice` and we wrapped it in the function `get_chiRPA` to immediately obtain the charge- and spin-susceptibilites in RPA from given parameters.\n", - "We can plot them for $\\nu=0$, using the `Idx` object from `from pytriqs.gf`, in the same fashion as the bandstructure.\n", + "We can plot them for $\\nu=0$, using the `Idx` object from `from triqs.gf`, in the same fashion as the bandstructure.\n", "There we can see, that the spin-susceptibiliy has a peak at the M-point, which will lead to an antiferromagnetic (AFM) state for large enough $U$." ] }, @@ -321,10 +323,20 @@ "execution_count": 9, "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/kaeser/my_triqs_installations/triqs_3.0.x/lib/python3.8/site-packages/triqs/gf/gf.py:323: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " dat = self._data[k]\n", + "/home/kaeser/my_triqs_installations/triqs_3.0.x/lib/python3.8/site-packages/triqs/gf/gf.py:323: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " dat = self._data[k]\n" + ] + }, { "data": { "text/plain": [ - "Text(0.55,0.18,'$\\\\chi^{(c)}$')" + "Text(0.55, 0.18, '$\\\\chi^{(c)}$')" ] }, "execution_count": 9, @@ -333,22 +345,24 @@ }, { "data": { - "image/png": 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+ "image/png": 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\n", "text/plain": [ "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "dark" + }, "output_type": "display_data" } ], "source": [ - "from pytriqs.gf import Idx\n", + "from triqs.gf import Idx\n", "\n", "ax_bs = plt.subplot(111)\n", "\n", - "ax_bs.bsplot(chi_s_wk[Idx(0), :], path)\n", - "ax_bs.bsplot(chi_c_wk[Idx(0), :], path)\n", + "ax_bs.bsplot(chi_s_wk[(Idx(0), slice(None))], path)\n", + "ax_bs.bsplot(chi_c_wk[(Idx(0), slice(None))], path)\n", "\n", "ax_bs.set_ylabel(r'$\\chi(\\nu=0, \\mathbf{k})$', rotation=0, ha='right')\n", "ax_bs.text(0.62, 0.6, \"$\\chi^{(s)}$\", transform = ax_bs.transAxes, size=22, color='C0')\n", @@ -413,10 +427,101 @@ "cell_type": "code", "execution_count": 11, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.604525006165701\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/kaeser/anaconda3/envs/triqs_3/lib/python3.8/site-packages/scipy/optimize/zeros.py:776: ComplexWarning: Casting complex values to real discards the imaginary part\n", + " r = _zeros._brentq(f, a, b, xtol, rtol, maxiter, args, full_output, disp)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 15.472700008220936\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 23.209050012331403\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 46.418100024662806\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n" + ] + } + ], "source": [ - "%%capture\n", - "\n", "from triqs_tprf.ParameterCollection import parameter_scan\n", "\n", "Ts = [1000, 750, 500, 250]\n", @@ -439,7 +544,7 @@ { "data": { "text/plain": [ - "Text(0.625,0.3,'AFM')" + "Text(0.625, 0.3, 'AFM')" ] }, "execution_count": 12, @@ -448,12 +553,14 @@ }, { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "dark" + }, "output_type": "display_data" } ], @@ -577,10 +684,123 @@ "cell_type": "code", "execution_count": 13, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.604525006165701\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.604525006165701\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.604525006165701\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.604525006165701\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.604525006165701\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.604525006165701\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n" + ] + } + ], "source": [ - "%%capture\n", - "\n", "mus = [-.5, -.25, -0.1, 0.1, .25, .5]\n", "\n", "hubbard_models = parameter_scan(hubbard, mu=mus)\n", @@ -601,7 +821,7 @@ { "data": { "text/plain": [ - "Text(0.125,0.3,'AFM')" + "Text(0.125, 0.3, 'AFM')" ] }, "execution_count": 14, @@ -610,12 +830,14 @@ }, { "data": { - "image/png": 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\n", 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\n", 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\n", 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TCrJ48eKirbWUZClEHolu2kR8/34AlJISqhYvZtCgQQZHBfbzz0dJfjDGDx4kummTwRGJ7mppacn8HQq3Gy1ZjqK0+QkV6S1YkGQpRF4JPvucvu1cdAkjxo6lPO25kFGO1tfjn5Y+K1ZuxRYal8uF1WrJ7EEVBUpTV5fNu3Zl9vh5RJKlEHlCU9UOt2CdV1xhYDQdBQIBGqdP1cdyK7bwKIqS+TpLgLTnlq7WtswfP09IshQiT0TWbyB++DAASnk59gvONziilH79+hGYMIF4ciWS+P79RLdsMTgq0R0Zb3eXpFWlFoHevmwZS5YsyVn/4lySZClEnki/BetYtAjFmuHJGD3gdrsZP3ky7g6zYpcYGJHorvLy8ozXWQJQVa1vNmzezNq1a4tyqS5JlkLkAU1VO3TH2T1yOK2t+dU+rE+fPrguu0wfB59/Xm7FFpBgMEg0lvnuOlp1KlmWtrQAxVlrKclSiDwQWbsW9ehRAGKlJYTGj89pH9iuclw4B8XjASC+dx/RrdsMjkh0Vba+2KQny+pIhAsvvJB+/fpl5VxGkmQpRB4ILlmqb4dnzabfgAGYTPn366nY7TgWptrfSa/YwpGVOkuAPqlkWdLcwty5c6lOS6DFIv9+G4XoZTRNI/Tif/Tx4M9ex4gRIwyM6NSsl1yib4fSkrzIb83NzdnpBFVaipZ8vq60ttKanKRWbCRZCmGw6DvvEE8unKuUleE4d3ZiOaU8FI/H2eR0oNpsAMR27SKWXKBa5DePx4PVloUrS0WBqip96H9vR+bPkQckWQphsFDaupWO+fNRkokoH5nNZsr79SM4dqy+L/zaSgMjEl2VzclY6c8tbceOZe08RpJkKYTB0p9XOhcvOsUr80P//v1RZ5ytjyVZFga/3080kqW1JtNqLbe+8goPP/xw3s3m7ilJlkIYKPr+LmI7dwKg2e1Epk0zOKLOVVdXM/LaT+rj0KqVaPG4gRGJrigrK8Nut2fl2FpaS0b/3n3s2LGj6GotJVkKYaDQi6lbsP6JE2nL9HqDWWIZMwZTv74AaE3N0s2nAAQCgazUWQInXNey2BaBlmQphIGC6clyxtn06dPHwGi6TlEU7BfM0cfhFa8ZGI3oCkVRUMhCb1g6rmvZR1O59NJLGT58eFbOZRRJlkIYJF5bS3Rjcqkrs5l+11yNLY8n9xzPMecCfTskzy3zntPpxGLJ8Koj7dKuLD3BUFEuAi3JUgiDhF55FZIzFG0zzmbguHEGR9Q9reNSM2Ij69ahJm+/ifzU1NREKJylBudpV5bU19NYZM8rQZKlEIYJvbxM33ZcfLGBkZyegNNJeMjgxCAWI/LmW8YGJE6ptLQ0e3cubDa05Io0SixGtLY2O+cxkCRLIQyghcOEV6zQx46L5xsYzempqqoiMGGCPpZbsfktHo/rdzKyorJC37QfOZK98xhEkqUQBgivXo2WvG1pHjoEy6hRBkfUfSUlJVQuvlQfh1+TST75LBgMEo1mb7a1NmCgvr3hkUf485//zPvvv5+18+WaJEshDOBP6wXbOGFCQS51pSgKZyxaBMnavdjOncQP1xgclTiZ0tLSrNVZAmiDB+vb5vd3UVtby7Ei6uYjyVKIHNM0jeBLL6d2nHduXq4w0hWK04n9nHP0cWilXF3mK7/fTzQaydrxtUGD9O3qujoA6pJ/FoPC/A0VooDFdu5ESa7MoDoclM2bZ3BEPWNPKyGR1nf5y2w2oyhZ/MgflLoNW9HczDVXXsnChQuzd74ck2QpRI6lz4J1XTSP/mnfyAuRfU6qOUFwxWtoqmpgNOJkHA5H9uosEyfQmxMocZUhNjsOhyN758sxSZZC5Fjo5dQtWMeCBQV7C7ZdY3UVsfYC9MZGotu2GRuQOKHGxkZCoWB2T5K2VFf9li2JGbhForB/S4UoMPGGRiJr1yUGioLjosK+BQtQUlpKcPx4fRxavuIUrxZGSTRSz+6VnpaWLE01NShKdtrrGUGSpRA5FHr1VUjeprROnYo5bR3AQuV0OolOT62WIs8t81M8HkfTsnyLvDqVLM3JWstiubqUZClEDjU9/7y+bb5wzileWTgURWHMdZ/Rx5F161CDWb7dJ7otFAoRi2U3cWlVqS9/h9as4ec//zkvvfRSVs+ZK5IshcgRLRpFfeMNfRw6e7qB0WSWbeBALKNHJwbhMJHVq40NSHxASUlJ1hv1a2lXlvb6esLhcNGUj0iyFCJHgqtXY2pLdO2JVlVRNWuWwRFllv0CKSHJZ21tbVmtswQg7bFCSUsrAC0tLdk9Z45IshQiR6KvvKpvm+dcUFTT6gEcabeVQ9L6Lu9Yrdbs1lkClJSgJa9eHeEwH5kzh1tuuSW758wRSZZC5Eh6fWWfq64yMJLsMM84G5J1fLHt7xKvrzc4IpHObrdnt84SwGRCGzpUH1YdPFQ0M2IlWQqRA7Hde4jt2gUkW8Sdd67BEWVeSFEIDh+uj8Or1xgYjTheQ0ND9ussAUaM0DeDb72Fv0jWOZVkKUQOpDcisF9wPkqR3YIF8Hg8hM9KLWAdeP11A6MRx6uoqMh6nSWANjKVLC1bt2G1WrN+zlyQZClEDrQsWapvF+JCz12hKAru88/Xx/G33zYwGnG8aDSKmoNWhNqwYWjJW6/Krl3UHzjA7t27C3JlnXSSLIXIskhDA+r69frYOneuccFk2ZDLPgTJ9n2xrdtQi2QmZDGIRCK5aRDgdMIZZwCgqCrP//Rn/Otf/6KpqSn7584iSZZCZFn9kqUoyQ+pyMiR2AYOMDii7DGVlmJtb32nqkTWydVlvvB4PFmvs2ynpT237Hf0KAAHDx7MybmzRZKlEFlmSnt2ZymSrj2nYpuZWt8yLM0J8kZrayuRSJbrLJPSZ8RWNDbSp0+fgp8VK8lSiCzS4nHUlav0cfVVVxoYTW7YZ87Ut8NvvmVgJCKd3W7HbDbn5Fxa3z769lBF4dprr2XChAk5OXe2SLIUIosi6zegNjYCYOrbF8eUKQZHlH2xiakPxcimTWjSJzYvWK3W3C0H17evvmk6dBhN02SCjxDi5DqsXXnxfJQCX7uyK8xVVYQHJJ7LKrEY4fUbDI5IQGI9y3A4lJuTud1oLhcASijE4U2biMViuTl3lhT/b64QBgqlrbjguHi+gZHkjtPpJDL+LH0s9Zb5obKyEofDmZuTKQqk3Yota2ou+HpLSZZCZMmxjRuJvbcjMbDZOjQaL2aKolB50UX6WH17/SleLXIlHA7n9OpO65O6Fdu69R3efvtt3n333ZydP9Oy3ChQiN6rZclS2r/Hq9OmYUreluoNKufP52hyO7JuHVokgpKjsgVxYrFYLPuLP6fR+vfXtw8uX8EbsRgDBw5k7NixOYshk+TKUogsUFUVLW0WrHvRJQZGk3uWgQMwDxkCgBYKEd3yjsERCbfbjdWawy8sgwbqm32O1QJw+PBhggU64UuSpRDZEAjgSrvlVLr4UgODMYZd6i3zSi7rLCHZ9i45oa1PXR2DnS7mFnD3KkmWQmRBeMVrkPxgsp51FpaBAzt5R/GxzUrVW/pXrTrFK0UuOBwOLJbc1FkC4HJ1aKp+kd3Geeedh9OZo0lGGSbJUogs6FAysqA4G6d3JjQutQJJdN3baLnoSypOymw2J2ap5pCW1ojAvOoNGpM1x4VIkqUQGabF44SWvaKPi3WVkc64Ro8mVl4OgMnvJ7Jtm8ER9W7Nzc05vQ0LoE2cqG8r69ZRf/BgTlY+yQZJlkJkWP3Klaj19QCY+vTBOmWywREZ4/h6y+AbbxoYjaioqMCRg/UsO+jTB619BZJIBOfmLQXbI1aSpRAZpKoqRx5/Qh/b5s3tFV17TqZv2izguKxAYqhQKGRIFx1tUurqsnHpi9x333088sgjOY+jp3rvb7EQWdDY2IgrrQjfuWCBgdEYz3Xuufp2ZM2agu8PWshUVUUj93//2qhRqe3t29i3bx87d+4kHA7nPJaekGQpRAZpNTXYDxxIbFutOHrBklynYhk9GqW8DAC1ro7Yrt0GR9R7uVwurJbct5zTBg/Wt6vqGzDF46iqyoHk70mhkGQpRAY51q3Tt23nzsbkdhsYjfEUkwn7Oal6y4jUWxqmpaXFmKs5txutugoAk6oyq08fbrjhBkaOHJn7WHpAkqUQGRR6eZm+7VrYu2/BtrPMmKFvNy9fblwgvZzL5cJqNabDqTZ4iL49JhoryMWgJVkKkSGq30/49Tf0cW8tGTlecOwYfTu2dt0pXimySVGUnNdZttOGD0vFsXkLNTU1xAus7laSpRAZEl65Uu/aYxk3FsugQQZHlB/KzjkH1ZEoWTDX1hItsGdVxSLX7e7SaSNSnXyU9evRYjG5shSiN6qrq6PmkUf1sVxVpjjcbmLjUitNRNasNTCa3qu8vDz3dZbtBg1C8ySe3yv19Vg2baaxsZEtW7YUzAxpSZZCZMCRgwexpBXdOxcuNDCa/KIoClXz5unj6NtSb2mEYDBINBY15uRmM9r0s/Vhw78e4K677uLJJ59k7969xsTUTZIsheihWCxGYNUqzH4/AEr//r22a8/J2NIm+UTkuaUhjL6CU9NWoanashlTcqmu9esLY3FwSZZC9JDFYmHE3n362PWhxb26a8+J2KZNheTfSXT7dtSWFoMj6n2MqrPUDRqkt74zR6IM27OXsrIyBqfVYeYz+Y0Wooe0eJzoS6lVRpy9cO3Kzpg8HqxnJfvEahqRArmaKCbNzc3Gds1RFNS0mttZjY1cdtllzEi765DPJFkK0UORtWtR6+oAMFVXd7jlKFLSe4Q2LF9hYCS9k8fjwWoz8MoS0M6erm/b3tmKuaWFlgK5yyDJUogeCi5Zqm87Fi1CMedwgd0CEh6bmhEblabqOWf0M0sAysv1MhJFVTGteI2ampqCWLZLkqUQPVBXW9shWTo/JLdgT8ZzXqqpumnbNrSoQTMzeym/3080YvzfuTp1qr5tWr4cp9MJYMiKKN0hyVKI09TW1sbOZ55BrakBQCkvwz57tsFR5a+yM89E69cPAFM4TFQWg86psrIy7Ha70WGgpc0UVzZs5Mi77/LAAw/w61//mlAoZGBkpybJUojTdPToUTxpBfbOhQtRrMY+E8pnZrMZ1+xZ+lhKSHIrEAgYV2eZrrwcbfhwAJR4nKOPP8GePXsIBoO8ncc1uJIshThNTqeT0rRnb47Fiw2MpjBIvaVxFEVBIT9azKlpV5djd+/Rt+uSE+XykSRLIU5TdUMjlqNHAVA8HhxzLjA4ovxnT0uW4bWyGHQuOZ1OLBZjVh05njZ1Klqy7tb93ntMs1hYsGABl112mcGRnZwkSyFOU2jJEn3bcfF8lDx4HpTvLGPHoJSUAKAePUZ0375O3iEypampiVA4T54JVlSgnZ1qfzfl7fUMGDCAYDCYt1+gcvI1w+fzrQJmAWO9Xu/7x/3s+L+ZeV6vd3kXj2sCtgGDgJFer/doBsIVolOaphF8IZUsnXILtksUs5nY2LGY1yae9basXEn1sGHGBtVLlJaW0mKzGR2GTl24AGXtWhRNw7R6Deq2bewdMoThw4fjzsNF07N+Zenz+a4AzgMeOT5R9pTX61WBnwBu4PZMHluIk9E0jejmzcTeT/xzVlwu7PPmGhtUAYlNGK9vB1evMTCS3iUej0M+XbX164c2bZo+NN17H263m2g0iqqqNDQ0GBjcB2U1WSav/H4MaMCdWTrNg8Ae4Cafzzc8S+cQAgBVVVm9ejWH/vo3fZ9j8WJMLpeBURUWZ1rLMzZtMi6QXiYYDBKN5lcto3rJQrTkupam199A2bmT7du386c//Yn777/fsPU3TyTbV5aXAOOBVV6vd3s2TuD1emPAfYAV+HI2ziFEu7q6OkJtbZhfXqbvc3/0IwZGVHiqLpwDyS5Hpj17UZubDY6odygtLc2LOssOzjgDbXJqZqzpH/fy2muv0dDQQHNzM6+88oqBwXWU7WT5+eSfj2T5PA8n//yMz+eTQjeRNY2Njbg3bsTc1gaAecAAbOdKI4LusJWVYR2f1lT9bWmqngt+v59oNH+u1Nqpl1yib5tXruTcvn2BxGo+lZWVRoX1Ad2e4OPz+YYCNwGLgcGAB6gFdgHrgNu9Xm/Q5yp8SEQAACAASURBVPNVAZeTuAX7+OkG6PP5vgD89bjd3/R6vb9sH3i93h0+n28TMBm4DHjqdM8nxKmMHj2aY5vfof1mlvOaq2U5rtNgm3EO0c1bAAivWYPjonmdvEP0lNlsRlHy8N/qoIGoEydi2pL49zD0lVeZeNWVDBkyhIkTJ3by5tzp1t+cz+e7GtgOfA+YAjiAEDAQuBD4XHIMMI/ErdGdXq+39nSC8/l8HwfuPm73t9ITZZrXk3/KEvUia9TGRmKvvaaPXR+RW7Cnwz4jVTYQWSfNCXLB4XDkTZ3l8dRFqatL06vLmebxUF1dTV1dHYFAwMDIUrqcLH0+30DgARIJ8sfAEK/X6/F6veWADZgGXO/1etunW52X/PO0+hf5fL7FwL+Oi/FbXq/3Fyd5S/tvnFSGi6wJPv0MJBuAW6dNwzpqpMERFSZberJcv0GaqudAY2MjoVDQ6DBObMgQ1IkTAFA0DfOf/gyaRiAQ0Lv6GN1ovTtfMy4DnMAzXq/3++k/SE6y2ZD8X7v2KW+buxuUz+ebAzxB4sq03bdPkSgB2qfVneXz+Uq8Xm9rd88rRGcCTzyhb8vEntNn6tePWJ8+WGprIRymbf16SmbONDqsolZWVkab3WF0GCelXnEFytZtiaW71r2NuuI1rHMvRFVVDh06xNNPP82MGTM4J302dQ515zZse2KdmUxmnTkj+Wd3m/2dDTxHIjG3+47X6/15J+9rP48C9OvmOYU4qXg8zpYtW6hbu5bopuR3P5sN5+X525or3ymKQmzCBH3ctmqVgdH0DvF4HE3L43Uj+/dHS5ssZ/7FL6GxkVAoxGOPPUZdXR1Lly5l7dq1pzhI9nQnWT4C7AD6Ayt8Pl/I5/Md8fl8J2s0UJ38s7GbMf0MKE0bf8fr9f6sC+9LP0/1SV8lRDcdOnSI+vp6av5+j77PsWABpooKA6MqfNbpqYJ0JTnZR2RPKBQiFosbHcYpqZdfjlZWBoDS1IT5R3dg0jS95EVRFMrLyw2JrcvJ0uv11gMfI3W7007iCu5kbRbaC3q6O1c5PabVXUyUkJpYBB2vSoU4bZqmcejQIVBVSl9/Q9/vkluwPdZvYWounrZpc972BC0WJSUl2PKo3d0JuVyo135SH5pWr8Fxzz+4+OKL6du3L1OmTDGsnKRLydLn8yk+n+9nJCbrbCHxPLLU6/UqXq/3ZDeQ25NoT74GzPT5fD/p4mvTv+bX9+CcQugURWHq1KkM3rsXS2Pi5oWpuhrH3AsNjqzw2caNRSlN3ERSa2uJS1P1rGpra8vLOsvjaWedhXpJ6ouU+eFHcDz7HAsXLmTixIm0trby/vvv05asdQ4GczNpqasTfP4X+BbwR6/X+5UuvqeOxC3b7t6regb4cNr4Oz6f76jX6/1tJ+9LP0/+LoomCo7D4aD0mef0WySuj39MFnnOAMVkwnb2dMKvvApAeM1aLNJUPWusVmt+1lmegLp4MRw6jOmddwAw/+a3aCUlaMkkqigKjY2NRKNRHnjgAQYMGMDixYtxOrN3U7Grf3NfS/55fM3jqbyX/LO7/Vp/C/zhuH2/9vl813byvmHJP5uBI908pxAnFV67LlULaLXiufEGYwMqIvazpd4yV+x2e97WWX6AyYR6/WfR0r48me/8McqriS9WZrOZeDzOCy+8QENDA++88w733ntvVm/ld5osfT6fg0TTAYA+3Th2e5OAs0/5qhP7OvB02lgB7vX5fItO8Z72VWVfT65GIsRpS/+la7s79R3RdfVVmPv3NyKkomQ5e7q+3Zb2TFhkXkNDQ/7WWZ6I3U785i+inZEorFDiccw/+CHKkqVA4nfUlNY966yzzkJJNmXPhk6TpdfrDQE1yeFffD7fgvb+qz6fz+7z+cb6fL7v+3y+jx731va54FN9Pp+5O0Elk921wOq03VbgCZ/Pd7JirPZkubI75xLieJqmsXXrVvbv30901y5C//mv/jPPzV80MLLio4wfj9beVH3vXmL1+bUsUzGpqKjAnsd1lifkdhO/9Uto/RLVgIqqYrnzx5gefwJFUTj33HOZN28eI0aMYODAgXoD9vYvu5m80uzqbdj/l/xzNPBfIOTz+RqAIIn2d3eQuP2Zbh2wm8Rak3O7G5jX6w2S6C27K223G3jB5/ONTX9t8up3Hj3sQysEwNGjR6mrq2P37t3svfMn+hqA9vnzsY4ebXB0xcVRXk5kROpJTYvUW2ZN+zqRBaesjPjXvoo2cKC+y/zb32H6+S8gGmXIkCFccMEFWCwWmpqaOHToEIFAgIaGBu6++2527NiRkTC6lCy9Xu8/gAXAk8BBIEaiNGQ/8AKJyT9vHPceDfhHcviJ0wku2VP2UjpO2KkC/uvz+Qal7bsMKAGWe73e9OQqRLdomsaRI4lH3ubmZpxpSwSV3CJXldlgSVsAWNki9ZbZEolEEgtAF6KSEuJf/QrasKH6LvMzz2L+ylehpkbfZzKZcLlc1NbW8uSTT3Ls2DEefvhh/vvf/57oqN3S5ae9Xq/3ZeDlbh7/n4AXuNrn833Z6/WGT3DcU95k9nq9O+n8WWl7Yc7fTvkqITqhKAqTJk3iwIEDBH7zW5T2PrBTJmObNcvg6IpTn/nzaXj0MQBi62W5rmzxeDw05Xud5am4XMS/8hVMDz+MaV2i5bhpyzson/ks8a98Ge2KyyH5zDIQCFBbm1q/Y9CgQSc8ZHdkdR6x1+s9DPwFqASyMoXQ5/ONIlFqsg14NBvnEL2LyWRikMNB2dIX9X0lN9+c1ckDvVmHpuobN6GFP/CdWmRAa2srkUj+11meks2Get11xK/8MFry91EJBrH8/BeYv/4N2L0HAJfLxVVXXcWoUaMYOXIkLpcLv9/fo5rMXBTd/AhoA77t8/myMW/5u4AZ+L7MghWn6/iJAM133ImWLHq2jBqF49JTTcQWPWHu2xdz++21cJjIlneMDahI2e12zOZuzbXMT4qCNn8+8du+gZZcKBrAtO5tLJ+9HlOyp6zD4eC8887jvPMSC2DV1NRw8OBB4vE4TU1NbN7cvTU+sp4svV7vMeA64D6g59fCaXw+n4nEBKBver3epzt7vRDH0zSN/fv3s2vXLj1hht98k+CTqfXDy+74EUqh1KcVKNvZM/TtiEGNsoud1WrtUGpR8IYNI/7tb6HOm5e6ylRVzE8/g+Xjn8T04IMQieh3hCwWC1arlb179/Lggw/y1FNPsWzZsi7PmM3JJ4DX630KeKrTF3b/uCqJtTWF6DZN09i5cyeHDx8GwGazMfiMM2j6/v/TX+O84nIcF5xvVIi9x6SJkFz+rGH5ckpuudnggIpPY2Mj4XAIh6OIWmfbbKhXXwUzz8H05FOYkjNfFb8f85/vxvT0M8RvuQVt3lz9eebWrVv1NTJXrVpFnz59mDRpUqenKqKvGUJ0X/qCsg0NDbTd8w9i7yV/4Vwuyn5wu1Gh9SrapIn6trJlizRVz4LKysriSpTpBg5E/fKtxL94U4dbs8rhGiy3/wDzrV+BnYkFssaNG8egQYMwmUxMnTqV8ePHd+kUcm9JFL1QKER9fT1tbW2MGTNG368oCmPHjiUcDuNwOBjpcFL3y1/pPy/5n29gPuOMEx1SZFjZlCn43W7Mfj/m5hbCO3fikJrWjAqHw8RiscJpedddioI2YQLxceNQVq3CtGQpSiAAgGnTJpQbP4d65ZVYv/A55s6dS1tbG+Xl5V2+NS1XlqKoqarKmjVr2LlzJzU1NR+YDWcymZg0aRJjRoyg+X//Fy35c8uY0Xg+9zkjQu6VLFYr5ilT9HF8wwYDoylOsVgsvxd/zhSzGe3CC4l7f4A6by5aMhkqqor5ySexfPJTWFavpqysjHA4rK9e0hlJlqKomUwmKtIWaa6v/+DqbaZ4nMYv3UrkrWR3RbOZit/8WlYWybHStGfDkbXSVD3T3G43VmsB11l2l8uFevXVxL/7HdSxaXeUmpqwfPPbmH7/B6yK0uUr7SK9HhcipU+fPqiqSnV1NdXV1R1+pkUiNNx8S4f+ryXf+Dq2yZNzHWav16Heco3MiM209jrLvF8AOtP690f90pfQNm9O9JRtTnRmNT/6GM6WVhx3/7lLh5ErS1FUQqHQB/b179+fyZMnM3DgQOx2u75fbWuj/sbPdWyUfsvNlHz9ax84hsg+2+TJkLyaj+3aRbxBmqpnksPhwGIpgjrL06EoaJMn03LbbRwcOkTfHVm6lJZf/LJLh5BkKYpGKBRi3bp1HD169KSvidfXE3j8Ceq/8EWOTJ5K+NXl+s88t36J0u9/Tzr1GERxOrFOTM2KDb61+hSvFt1lNpv18oneyllexoYPX8E7E1IzYNv+fBexffs6fa/chhVFQdM0tm/fTiwW491338Vms1FRUYGmaUS3biX08jJCLy8junGjvopIupLbvkHJbd+QRGmw6LixkOwP2/Taa3gWX2pwRMWjubmZSCSCo9CW6coATdNQVZWysjIWTZzIs8BZkQimHTtBVQk+/QwlX/vqKY8hyVIUhVAopM901TQNs9lMbM8eGm65legpVrKwjB1DyS234PrINbkKVZzKpEnw4EMAxN+WpuqZVFFRgb8XJcqatjYOtLRwzoABmM1mbDYbHo8HD/CF8y8g1NBEYMdOAGKHa059MCRZiiLhdDqZMWMGO3bswOVyYVuzlmNf+SpaS0vHF5pM2M6ejmP+fBwLF8j6lHmm5ILzaU1um3fuRAuFUBy95wM+m0KhUHHXWSZpmsaqgwfZ1dQIwMCyUqaPHNXhNQoQ3bRJH1sGDuj0uMX9tyZ6FavVyrixY2n7/R+o/9WvU7db7Xaciy/FcfF8HBdeiCmtlETkl5IhQ2gbOhRt3z6UaJTIli3YZ8zo/I2iU6qqolH8nZEURUFTU+t2bjx2jGkjRuqPWDRNI/DQw6k7TiYTji7c7pdkKYqGpmk0/+83CTz2uL7PPGAAlX//q5SCFAhFUXDOPIdAcsJFZM1aSZYZ4nK5sFqKu3ZYVeM4HE7mnnkmNZs3M6yyiotGj04lynCYtr/8hfDKVfp73DfcgHXUqJMdUifJUhSs9r6u7beV/P+8t0OitM2eReXdd2E+rrZS5DfbjBn6/4+yAknmtLS0EA6HO5RPFTpV03i/sZFRFRWYFAVNg/KKckyKic/PPhd38r9V0zQia9fiv/c+1LRFoe0XzaPs9u936VySLEXB2rt3L0eOHGHIkCH0qTlCs+//9J85r7mGil/9QrrwFCDbOWnLda17G03TZJZyBrhcLqzW4vnIbw6Hee3AfuqDQaLxGHPHj8ekmPR/K+2JMl5zhLZ//pPocS0UXZ/6FOV3/qjLnxFSZykKUjgc5vDhw8RiMfZt2EDDF2+G5JWmddJEKn7+U0mUBcoycqT+XFltbCScXAVG9IyiKEVVZ7mjoZ765Az4jceO4Y9EO3yp0sJh/A8/QuNtt3VIlKaKCsp//UvKf/aTbn1GSLIUBSkUCiXadsXjDLzrL5C8taKUl1P5t7/KDMoCpigKwTPP1MfNr71mYDTFo73dXbGY2rcfVS4XZkXhvJEj8STb+GmaRnj1Ghq//g2CTz6pf4lGUXB/5tP0W7kC98c/3u27FcVzTS56lbKyMs455xxqfvwTaJ/VpihU/ukPWAYNMjY40WPKlMmwZg0A4bVr4aYvGBxR4SsvL6etCOosw+EwJSUl9K+s5KqyMuKaSr+SUgDiNTW03fOPDmUhANapUyi/844eTfSTZCkKllpzBOWf9+qT4Utu+waOuXONDElkiHP2LOJ//RsA5ne2GhxNcQgGg0Rj0YKcEdsSDtMcDjOkvIyqqiocyTtH1R4PAFo0RvDppwmkX0mSuOVa+v3v4fr4x1C6uG7lyUiyFAWr5Sc/QUs2TreedVan7apE4eh7wQXU2GwQicD+/cTr6mRWcw9pJ2jzWAhaI2Fe3L2bUDzGpY7RTOzbr8PPo++9R9vdfyF+8GBqZ/KWa+m3vpmxump5ZikKSvsvfHjtOoJPPa3vL/P9EMXcS1dUKEImpxPbpEn6WEpIeq4Q6yw1TWPlgQMEYlFUTWPZrl2Ek1eOWlzF/8ijNN/+gw6J0jplMn2WPE/5T36c0QYkkixFwYjFYrz55pvsfO89Gm+/Xd/v+NCHsJ8728DIRDZ0KCGRxaB7rLm5mXA4bHQY3aIoCjP796fUbsdsMnHV5CnYLRbUxiZafvQjgv/+t96pS3G5KPP9kD7PPtPhi1amyG1YUTCOHDlCJBKh5ZFHcW15J7HTbu9yUbEoLOmLQYclWfaYx+Oh2VZYV5YAw88YwNBBg6ht8zO0spLYgQO03HEnatp6p/bzzqP817/M6uQ+SZaiYDQ2NqIEg1Q/9pi+r+SLN2EZPNjAqES2WKdP17cjmzejBoKYXE4DIypshfbMUtO0xJJiTgcmxYTH7iD67ru0/PRnaH5/4kWKQsk3vk7J17+W9ccwchtWFIwJEyYwbtt2LE3NAJj698Pz5VsNjkpki7myksiAMwBQYjHa5Lllj/j9fqKRqNFhdErVNNTkMntnDDgDk5JIU9Ft22j+0R16olQ8HqoeuJ/S/7ktJ/MVJFmKwhEOE3/gQX1YetttmNxuAwMS2aQoCuqEifq47fXXDYym8JWVlRVEX9h3amt5ZscO6iNhbNZEo4Ho++/T8tOfJWZHA6bqaqqfeCynpWKSLEXBCDz+BOqxY0DiqlIWbC5+jpnn6NuWbdsNjKTwBQIBorH8vrJsCYfZeOwozZEwz2zfzt76emIHDtJy54/Rkq3tTH370uepJ7FNnNjJ0TJLkqUoCFosRutdd+ljz003oRTAt2TRM30XLNC3Y+vXo6mqgdEUNkVRUMjv3rCNoZAeYb+SEgaZzbT87GdobW1AoslA9SMPYRkxPOexSbIUeS0ej/Pee+/R8NhjxPftBxL9X92f/pTBkYlcsIwYjqmqCgCtuZnYzp0GR1S4nE6nvpxdvhpaVsY1Y8cxqrqaS0ePoe03v0U9ehRIlIZUPfQA1jFjDIlNkqXIa/X19dQcPkzz7/+o7/PceIM8q+wlFEXpUEIi9Zanr6mpiVA4ZHQYJ6UlJ/WMGDSIj0ydRsnzLxDbti3xQ0Wh4o+/z0r9ZFdJshR57ciRI7g3bMR+4ACQ+HbpvuEGg6MSudSx3lJmxJ6u0tLSxEo9eSoej+vlLZEtWwg+95z+s9JvfRPnJZcYFRogdZYizw0ZMoTm//xHH7s+dS3mysy1sBL5T0lbKaJt1etUGhhLIYvH44luN3n22FLVNBQSTRPKy8vRwmHa/pyan2CfNxfPV75sXIBJcmUp8prrwAEs7atOWK2U3HSTsQGJnLOMH4+aXKTXfOQI0SNHDI6oMAWDQaLRWOcvzLHtdXU8teM9th47RiQWI/DMM6h1dUBiQk/Fr3/V7bUns0GSpchr/vvu17edl1+GOVmkLnoPR2kpkVGj9HHb628YGE3hKi0tzbs6S1XTeLehnpZIhJX79rLj3e0En35G/3npd7+DuW9fAyNMkWQp8pba1NRhZRH3ddcZGI0wknPWTH1baV/sW3SL3+8nGo0YHUYHTaEQgWii9tNhsTDk9TchObZOmojrEx83MrwOJFmKvBQKhfA//niH9SptZ0/v5F2iWFVceKG+Lct1nR6z2Yyi5NdHfqXTydVnnsncESO4sLoPkeXL9Z+Vfve7ebXsXn79zQkBqKrKujVraPjL3/R97s9elxfPLYQx7GlflKLvbEVNdnMRXedwOPKyzrJPZSWzRo7izLXrILlWpXXaNOwXnG9wZB1JshR5p6GhAevmzVhqagBQSkpwXnWlwVEJI5kqKrCMHp0YxGJEN2w0NqAC1NjYSCiUX18ywuEwsVgMtamJ0Msv6/tLv/61vPtyLMlS5J1wOEz5y8v0setjH5UmBKJDvaX/9VUGRlKYEo3UHUaH0YHb7aKstIzgc8+nnlVOnIj9onkGR/ZBkixF3ulvNuNZv0Efu6/7jIHRiHwRnTBe325d/pqBkRSmRNF/fvTWPRbws/noUaIaKIEgwbRa6pKvfSXvripBmhKIPBR47HGIxwGwzZ6FNa1sQPRelpkzaV8zw7xtG1oohOLIryulfBYKhYjF4thsxk+aebeunt3NTWysPcY1NTWUhcMAWMaOwWFwp56TkStLkVc0VcX/yCP62H3ttQZGI/JJ2ahRRPr3B0CJRAil3X0QnSspKcmLdneReJx9LYkF3LV4nNK0ulnPFz6PYsrPtJSfUYleK/LGm6nVRcrKcF66yOCIRL4wm824L7hAH0ffesvAaApPW1tbXtRZmhSFs/v2o5/bw6Rjx1DqGxL7KytxXZm/E/kkWYq8UVtby7F77tHHrquvQnE6DYxI5BvP3Dn6dviNNw2MpPBYrda8qLO0mExMOOMMrps1k9kHDur73Z/+VF7fVjf+b06IpMPvvguvLtfHrk98wrhgRF6yz56tb0fWr9ebVojO2e32vKizVDUVRQHFHyC2OdWNyfXJ/P59l2Qp8kIkEkFd+iKm5PRxy4QJ2NJmPwoBYO7XD8vIkYlBOExEnlt2WUNDQ37UWWoaJrOZ8Ftv6RP5rNOmYRkyxODATk2SpcgLZrOZvmkL+7qv/aSB0Yh8Zps9S99uefVVAyMpLBUVFYbXWbYv8FxRXkF41ev6fteVHzYwqq4x/ppcCEDdswfaV0W32XBdcbmxAYm81XLmKP2DKyQrkHRZNBpFVVXMBvZbfX7X+zhMJsYfOcqQ7dsTO00mnJdfZlhMXSXJUuSFwBP/1rcd8y/CVCELPIsTc51/Pu1zOpWtW9GCQZkI1gWRSIR4PG5YsmwJh6lP9vQtX/c2QzQNANusWXmzDNepyG1YYThNVQk++ZQ+dl1ztYHRiHxXPnIkkYEDAVBiMSJvrzc4osLg8XgMrbM86vfr22MOpmbBOhdfakQ43SbJUhgu9OabxA8dAkApL8dx0UUGRyTymdVqpXx+6t9I+A25FdsVra2tRCLG1VmeWVnJ5SNGMK//GVQka6kBnHnased4kiyFoWKxGHvvulsfO6+4HCXPVnMX+cdx7rn6ttRbdo3dbjf0eSXAoD59mNzYiKImetRap0zGPOAMQ2PqKkmWwlB1hw7hfmu1PnZdc42B0YhCkT4jNrJxI2pbm4HRFAar1YrJwFZy0ViUWDRGZM0afZ9zUeF06JJkKQwVeuklzMmH/tqgQdimTzM4IlEIzNXVWM86KzGIRgm/Ka3vOtPY2Eg4bFwTB4vZgsdhJ7Jxk77PUUDtLCVZCkN5XkutS+i65uq8XJpH5CdTer3lSy8ZGElhqKysxOEwZtZwYyiIyWxC2b0H2lcYGTGioFYUktIRYZh4XR3h5cv1cenHP2ZcMKLgNI8dQ3uJfWSlLAbdmXA4TCwWy3nLu5iq8tz77wMwZ/MW2tOj/fzzchpHT8mVpTBM8JlnU+tWzpiBZehQgyMShaR0zhxUqxUA0/79xA/XGBxRfovFYoYs/lwfDKJqGqqmUb4/NQvWltbntxBIshSGCfw71YhAaitFd1X07098wgR9HFr5moHR5D+3243Vmvs6y0g8jsdqxRyLUXnkqL7fnnYbvRBIshSGaNywgeimzYmBzVYQ7a5EfrFYLFR9aLE+Dq+QZHkqRtVZDi4t5SNjx/H5vv0wJe8kWc48E3OfPjmPpSckWQpDNDz4kL6tXHA+pvJyA6MRhcqethh0eOUqNDX3txkLhcPhwGIxps7S4XBge3+XPi60q0qQZCkMEItGMb/0sj52Xi23YMXpsZ41DlNVFQBqQwPRrVsNjih/mc1mMGC2uaqptLS0dPj/xjZLkqUQnYq8tRprXR0A8ZISygqo1krkF8Vkwj4ndXUZXL7CwGjyW3NzsyG3YU2Kib4VFcSSM2JBriyF6JLw00/r254rP4xJ2tuJHghPnqxvt73yioGR5LeKigocOV7Pcn9LM3saGwjt3AHtC7uPGlUQq4wcT+osRU5pwSDBF5boY89HP2pgNKIYRKdOpf1JnLZhI2owiEmW7PqAUCiU8zrLjUeP0hAK0brubdp7cxXiVSXIlaXIseB/X0JrbQXAPHw41mlTDY5IFLqKMaMJty/ZFY0SWb26k3f0TqqqoqHl7HzReJzGUKK9Xt9jx/T9tlkzcxZDJkmyFDl1fG2ltLcTPeXxeHDMmaOPw6+tNDCa/OVyubBarDk7X1zTGFNZSR+nk7519fp+25QpOYshkyRZipyJHj1K6NXl+th59VXGBSOKhqIoVKZNEgu9JvWWJ9LS0kI42Zc1FxwWCzMHDOTTI0diS15hKmVlmAu0U5ckS5EzjY8+pq9jFxo3DsuQIQZHJIqFbfYsSLa+i21/l/jRo528o/dxuVxYrbmfpqLt3adv2yZOLNi7SZIsRc6En0rNgjV9aHHB/tKI/GNyubCdfbY+Dr3yqoHR5CdFUXJeZxmLx4imNSOwTpqY0/NnkiRLkRPR997DtGMHAJrNRtXHZBasyCzHgov1bX/ajGuRYES7u4ryCtS9e/WxdWLhJkspHRE5Efj3k/q265KFlCZnLwqRKfUTJtA+fSXy+uuofj8mt9vQmPJJeXk5bTmqs2wJh9lWV0sft5vRu3bRfj1rkytLIU5Oi8c7JEvnNdcYGI0oVs5RIwkPGQyAEokQTptMJiAYDBKNRXNyrtpAgHcbGtiwdRuK3w8U9uQekGQpciD8+huoR44AYKqqwjH3QoMjEsWovLyctunT9XHwP/8xMJr8o2m5q7FsDCdmv1Yn21pCYU/uAUmWIgdaHn1U33Ze+WEUa+5qvUTvYbfbOfPzn9fHoZeXoUVzcyVVCHJZZzmkpJQJlZWMTl5VQmFP7gFJliLL1ECAyIupb/ihefMMjEYUO8fkSZgHDQJAa2kh/OZbBkeUP5qbm3NWZ9nX7ebcESMY2ZaWLAt4cg9IshRZFlyyFCVZkBweOBD7lMmdvEOI06comLZBoQAAGjtJREFUCo5LLtHHIbkVq/N4PFhtubmy1DSNeDRGLG0mbCFP7gFJliLLAk88kdq+cA7lssizyDLnolSyDL74H1kQOimXzyw1NJTWFr0PtOJ2Yy7wJiSSLEXWxGtqiKx6PTFQFIbdfHNBP+AXhUGZOgXKygBQjxwhunmzwRHlB7/fTzSSm2e4JsWEu6VVH1tGj0YxFXa6KezoRV4LPP0MJL/N2s89F8/IEQZHJHqDhuZmWtJu+QVflFuxAGVlZdhzsHbsltpjLNuzm/c3bND3WceNzfp5s02SpcgKTdMIPP64PnZ+RGorRW5UVlbSltb6TpJlQiAQyEmdZU1bGwfa2mjZvVvfZx0ryVKIE4pu3UrsvUR7O8XpxLn4UoMjEr2FzWajdMHFaMmrqPjOnUR37e7kXcVPURQUsv8YpDk547aioVHfZx0zJuvnzTZJliIr/A89om+b51+EIm3HRA6NmTwZ57y5+lhmxYLT6cRiyX6H0zmDBzOzf3+qWlr0fZYxo7N+3myTZCkyTg0GCTyZam93YOqUnM7EEwLoWEIit2JpamoilOysk0393B5m9u2LOXmFqZSUYKquzvp5s02Spci44HPPQ3LKeKRfPzxz5mAq8JlwovA4Lr4YzGYAIuvX9/o1LktLS7HZbFk/TywWI3zwoD62DB9WFLPg5RNMZFzgoYf1bfXyy+g/YICB0YjeylxZgW3mzMRA0wgufdHYgAwWj8f12enZpCgK5tp6fWwZPjzr58wFSZYio6I7dhBZuzYxsFgY9uVbpRGBMEQ4HKZ56hR9nN4gozcKBoNEo7Gsn8diMWNukGQpxCn5H3xI33YsXIi5Tx8DoxG9mcVi4cjkSajJSS3RDRuJJhcg741KS0uzXme5Yv8+nt+xg4PvvqfvswwbltVz5ookS5ExWihE4Il/62P3pz5pYDSitzObzZQOHox/2lR9X+DRxwyMyFh+v59oNJLVcxwLBKgNheBY6vmwWa4shegouHQpWlMTAOZBg7DPmWNwRKK3Gzp0KH1vvFEfB/79ZK9dtstsNqMo2fvIj6sq/mgUNI3S5rSykRGSLIXowP9gamJP45wLaGltPcWrhci+srIyKi5dhKlfXwDU2lpCr75qcFTGcDgcWa2zNCkKV40ezaLqaqyxxLNRpawMU0VF1s6ZS5IsRUZEd+0m8uabAGiKQt3sWTmZpi5EZxSLBddHPqKPe+ut2MbGRkKhYNaOrygKZXYHo9MWmLYMG1oUZSMgyVJkSOCh1MSewLSpuIcNw+l0GhiRECmuj31M3w69vIx4ba2B0Rgj0UjdkdVzRCIRIh1qLIvjFixIshQZoLa14U+rrRx4662MLYLGyaJ4WEaOwDQlWUYSixH4979P/YYiFI/H0bTsru1psVow1xdf2QhIshQZEHj4EbRkH0jz8OG4Lp6Py+UyOCohUnbu3EnNOTP0ceChR3pdC8ZQKEQsFs/a8TVNw2qxoqV1SpJkKUSSFovR9vd79HHJTV9ASbYYEyJfVFZW0jrzHOKOxG3I2K5dqeYZvURJSUlW5xG8uGc3j7yzhfrde/R9kiyFSAq+sIR48hmFqbIS50c/0sk7hMi9yspKHBUVqBfP1/cFHn7kFO8oPm1tbVmts2wJh/FHozgaU0tzmYukIQFIshQ9oGkabXffrY/jV11JPAdLAAnRXSaTiXPOOYcBN39R3xd87nnUtGWkip3Vas1anWVcVQnGYrgCgVTZSHkZ5sriKBsBSZaiByJvvUV08xYAVKuVPdOnsW/fPoOjEuLEFEXBOmUKlnGJyWdaMEjw6WcMjip37HZ71uoszSYT1551Flek9YEupluwIMlS9EDbX/6qb7decD7xsjIGyAojIo8pioL7k6k2jG1/vwctnr1JL/mkoaEhq3WWNrOF6lDqNq8kSyGA6PvvE3rpZX1c/qUvMXDgQJkFK/Ke6yPXoJSUAImJPsHnXzA4otyoqKjIap1lOBwmcqg4ayxBkqU4TW1//Zu+7Vi4gAGzZ3HmmWcaGJEQndM0jX0NDTRdslDf1/r736Op2a0/zAfRaBQ1i/+dVpsV87FUswfLqFFZO5cRJFmKbovt20fg8dTagJ60SRNC5DNFUaivr6fu4vmo7WUk775HaMlSgyPLvkgkklgAOhvHjsdRUIgfPqzvs0qyFL1dy49/CpHEswnbjBnYzjnH4IiE6Lp+/fqhlpTQmnZ12fKLX6LFsr8wspE8Hk/W6ixf3ruHhzZtJN7ekEBRsAwflpVzGUWSpeiW8Np1BJ9/Xh87v/OtommULHqHfv36MWbMGEb/6P9Szy7ff5/AE0908s7C1traSiSSnTrLtmiUymO1KMmuSJYRI1CKrDe0JEvRZZqm0fx/P9LHrbNm8nY4LOUioqDYbDbOOOMMLFVVHR4htP7qN2ihkIGRZZfdbseche5aqqahqhr9jxzR99nSWgsWC0mWosuCzz5HdP16ADSLhbqPfwxN0/D8//buPT7K8krg+G8mV0JCSJASBIRVuRREiZVtxYpUqlIVWkSLtSLoitVSrdqu7Xarx+O2tbW1VVm1LV5QsWgrW11rjdRFtLWAWolSPkpBC9LGkISQhNxvs388b+Ik5DIzmWHIzPl+PvlM3us8ubzvmfe5nCc7O84lMyYy2cuvxH/UUQC0lZRQ99iaOJcodtLS0vD7o3/L9/t8fPHjUzilvKJzXfpMC5YmSQUaG6m5/Yedy2mXfpms448nMzOT/Pz8OJbMmMj5hw4l5+vXdS4fvGcl7bW1cSxR7Bw4cICmptg8Ofv3leHbvdstpKWRedZZMXmfeLJgaUJS+8tVtO3dC4A/L4+RN/07hYWFFBYWWpulGbSam5vZd+qnaBnpni7bKyu7JNtIJPn5+WRmxqgdMag3cebcMxMqzV0HC5amX81vbqXmzp92LufceAP+3Fx8Ph8ZGRlxLJkxA/POO++wd98+9i9a1Lmu9r77af3ggziWKjaamppojUGPX9+7O0jdurVzOfuaa6L+HkcCC5amT+3V1VR+dQV4F1laYSFDl1wa51IZEx3jxo0D4OBps2jxMs4EGhup/OrXaG+IXWq4eGhtbY3+5M+VlfDoo52LmZ+bR8Ypn4juexwhLFiaXgUCAapu+nZn9SvZ2WT8+Ef40tLiWzBjoiQvL4+CggKmTZ/O6HvuBq8DTMvWrRxY8bWEyhs7dOhQ0tKiOM6yupqU++4n5eBBABqHDGGI3BK98x9hLFiaXtU/tqbLmMp9y69k6759bNu2LWbjtYw5nHw+H1OmTGHkyJFknFxIrt7aua3xhfVU33wLAW/s4GAX1XGWpftI+enP8HlJCNr8fjbPP48s70k9EVmwND1q2rKFqlukc7l94Reo8apX6urqYjbVjzHxlH3F5WRfc3Xnct0jj1J73/1xLFH0ZGZmkpo68HGWvjfeIOXOn+CrrASg3efjlblnkjt3bj9HDm52xzOHaHju9xy4/gZoaQEgbdo0ht/+Aw7u3UtZWRnjx4+PyXgtY44Ew77zH7SVlNDwzP8CUPOD20kZPZqsCxbGuWQDk5KSAgPpud7YiP+pdfi3bOlcFcjMxP/DH7Dw3HMT5gm8NxYsTadAWxsH7/wpB+++p3Odf8QI8h9+kNScHKZOncro0aMZHjTBqzGJpL6+nvfffx//VcsZua+M5s2bAThw4zcgEGDIgvmDts2+urqa5uZmMiOYpsv39tv4f/MUvqqqznWBsWNpvPk/OfrMM5Niaj57PDC0NzTQuOEl9n95SZdAmTJhPEf95klSx4zpXJeXl2fjKk1Cqq+v5/XXX6eiooKyqiqavncbqZMnuY0tLRy47uuUzvwk1d/7Pi273otvYSOQl5cXfqCsqsK/6gFSVj3QJVC2n3M2rQ89SMq0aUlTy2RPlkmqZdd7NP7hDzRtfJmm117rnEWkQ8bs08m7996EHFxsTE+ysrIYNWoUpaWl+Hw+/Lm5jHjsMcoXfJ52L+9pe3k5tff/nNr7f076v84k6+KLGTL/fPyD4MmqsbGR1tbW0PobtLfj+9Of8D/7LL7Gps7VgeHDqbv6K7yRn8fMtFSOT6ImGQuWSaph3ToO3rOyx205X7+OoTdcz7bt2/lYYwOjR4+2p0mTFCZNmkRLSwvjxo3rbG74WNHvqXvoYep+/WvaS/d17tv82us0v/Y6gepqsq9aHq8ih6w9ECCQkgIhdPLxP/or/Js2dz3+/POoWbqUok1/pnbXLioqKliyZEnSpLu0YBkFqvogcIW3OFFEdoV5/Czgu8CngExgF/AQsFJEYjLQK+OM2V2CZerkSWTMnk3WggWkFc5g586dVFVVUVVVRUVFBdOnT7eAaRKe3+9n+vTpXdaljBzJsG/dRM43bqRp48vUrV1L44v/5xJ1pKUxZNEFnfs+88wzFBcXA3DttdeGHUhieS8YmpND6idOJpRuOO3LluLbvAVfIEDgmGNou+mbBAoLOVhaSl1dHeCGotTU1FiwNKFR1fm4QFkLhD39hqp+HlgHNAJPApXAfOBnwGnARVErbJD0k09myKJFZJx2KpmzZ5MyenTntkAg0GVG9fz8fAuUJqkFAgFISSHzs3PJ/Oxc2srLqX9qHe3l5aSMGAHAjh07KC4uJj09PaLxjLG+F9TU1NDQ0MCQEOaZDJxwAu0XXQjZ2bQvuRS8SaOPPvpoZs2axebNm1m8eDETJkwYSJEGFQuWA6CqI4FVuH/sAuCMMI8f5h3fBswRkTe89TcDG4ALVfViEXkiqgUHfOnp5N9zV8/bfD4mT55Mc3MzqampjAnq4GNMsmlra2PHjh2kpqYyYcIE0tPTSRk5kpzg8Zh1dTz77LNMmzaN2trasOd4PRz3gqysLNLTQ8/g0x40G0tbWxutra0cd9xxjBs3jhkzZnCUN7VZskiOltnY6ZieYEWEx18IjASe6Lg4AESkEVcVAxDzrMStra3UdpuWyO/3c8IJJzB16lR7qjRJq6mpia1bt1JWVkZJSQl/+9vfetzvd16mq3PPPTfSt4r5vcDn84V1LX/44Yc8//zzNDQ0kJ+fz9ixY0lNTcXn8yVdoAQLlhFT1WXAF4CrRWR/hKc503st6mHbK0A9MEtVYzK1R2NjI2+99Ravvvoq27dvP2R7SkqKBUqT1NLS0txgfk9PtSzFxcW8++67nH/++QMZbxjze8HBgwdpbAxtPsvi4mLWr19PWVkZb775Jnl5eQwdOjTSt04IVg0bAVUdD9wNrBGRpwdwqsne6yEfV0WkVVX/DkwDjgXe6aEcy4BlPZx3Rihvnp6eTnV1NYFAgIaGBurr65NicLExofL7/Zx00kmUl5dTWVl5SEKOqqoqioqKOPHEE5kyZcpA3irie0Go94Hc3FxKSkrw+Xw0NzfT3t5OZmYmdXV1ZGRk4Pf7qaurIycnp0tgLCkpoba2luzssLtkJBQLlmFSVT/wCK5Dz3X97N6fXO+1upftHet7S5kzgTDbSYP5/X7y8/OpqKggJyeHFi+9nTHmI36/n1GjRjFq1Kgu6wOBAE8//TTp6enMmzdvoG8zkHvBBEK4D/j9fo455hiGDRtGc3MzbW1tDBkypMdgWVBQQFVVFS0tLSxYsCDpAyUkabBU1d3A+DAOeVxEOiZxvAH3j3meiByIdtm66agD7a23927g5R7WHz9ixIgxBQUF/b7Bsccey8SJE20SZ5OU7rrrLqqre4tPh5o+fToXXOCGimzatIk9e/ZwySWXhNTDdID6uhfsJoT7gM/nY9iwYQBdOvoEP0Xm5OQAkJGRwcKFC60pJkhSBkvgPVz37FCVAKjqROD7wMMi8vsolKPjKs3tZfuwbvt1ISKrgdW9HBtSVmOrdjXJLD8/P6wZdDqCyf79+9mwYQMzZsxg4sSJ0ShKxPeCaNwHemIzC3WVlL8NEYl0LplpQAZwuape3ss+O1UVYGEI7Zk7gFOAScBfgjeoairwL0Ar8H6E5TXG9OGyyy6L6Ljy8nLa2tooLi7uTELQ3cqVLunH4sWLQ2nPtHvBES4pg+UA7AYe7GXbebixlr8Barx9+7MB+DIwD1jbbdtsIAt4RUSauh9ojImf4cOHU1hY2OO2nTt3Ultby9SpU8nIyAh1lh67FxzhfIk+B9nhoqobcW2Zh6S7U9VcYDRQLSIfBq0fhqsSHgacFjQQORN38ZwKfCnCgcj2hzUmDlavXs2ePXu6p7vzQVzuBXYfCF+PjbQ2zvLwWIjr7n178EoRqQGWAynARlV9QFXvAIpxF8dTuOxAxpjEYPeCQcqCZZx57Zpn4AYeLwKuBVqAG4GLRcQ+GRqTBOxecGSzatjEZX9YY44c8Rp/YfeB8Fk1rDHGGBMJC5bGGGNMP2zoSBIrKiqitLQ03sUwZlArKCiIRrq7qFPVu8aPDydRmQHYs2fPRqBYRK4PXm/BMnH120ayZcuWd/kogbMxJgJ79uzZMW/evAFlUY+RGeHOq2mAXvLsWrBMbh3ZkatxXdSTwQxcSjH7mc1Adfxej9Qs4/a3jtwhvzsLlsltFzAGV+UwJ85lOSyCkkfYz2wGJOj3uqufXeOiezWiGRjr4GOMMcb0w4KlMcYY0w8LlsYYY0w/rM3SGGNMF6q6GljabXUrbkalA8BfgdeAtSLy9xDPeRZwCfBp3AxNPqAU+BPwKxFZH8I5JgMrgM8AE4B0oAz4EDe12UbgDyJSGUqZwmHBMrmtxv1z7Y5rKQ6v1djPbKJjNYn/e20BOgKPDzcrSj5wHPB54Huqug74qoiU93QCVc0HHsdNP9ahHpeK7zjva6mqvgBc0lugU9WrgJW4AIl3fBUwEhgLzASuBm4A7orkh+2L5YY1xhjTRdCT5cvde1Cr6nDgU8Ay4CJcc94/gU+KyD972PfPwMeBJuDHwIMistvbfgxwBfAtIBM3I8ssEanqdp7TgD/iAvaLwH8Bm0WkWVV9wPHA2bg5QZ8Ukbuj8Gvowp4sjTHGhMwLZEVAkRdUf4sbgrYOF0SDrcIFygbgcyLycrdzfQDcqqobvHN+HPgl8MVu57kWFyjfBuaJSFvQOQLATu/rXlUdEoUf8xDWwccYY0xERKQI+Ka3+ElVnd+xTVVPAS70Fm/pHii7necVQLzFi1T1E912me69Ph8cKHs5V0Oo5Q+HBUtjjDEDsQrY531/SdD6r3ivVcC9IZznv3FZpoKP7W5M2KWLEquGTUKqGkpDdV73doPBSFWvxF3MRSLyuV72eQ44F1ghIvcdzvJFU9DfNQBMFJH3etnvJWCOt3i5iKyOfekSQzJdO6Hy2g03AF8CTg/aNMd7XR/K056INKjqelw76Jxum98ApgKLVfW3IvI/Ay54mCxYJjftY1vjYStFDInIA17V0AJVXSEiXT7hquo1uED5/GAOlEFacdf1vwHf6b5RVSfiUrR17Gcik/DXTpi24YLlGFVN89Yd772+FcZ53sYFy4mqmioird76O3BVulnAOlXdA7yEG77yGi6VY5/VswNlF0sSE5Fb412Gw2Q5cCpwh6q+KCI7AFR1EvATYD+uR14i2Icbc3a5qt4SdLPpcCWuo8TvgC8c7sIliiS6dkJ1IOj7/G7b9odxnopu5ykDEJHtqvpZXC3RNGA8rjfuMm/falV9Avi+iOwN4/1CZm2WJuGJSBkuYGYBa1Q1VVVTgTXeuqtEJJEm9lyFG/R9fvBK7xP/UlxX/u1xKJdJDgFCmCKwF70eJyKbcB195gA/Al7BJUkAN/vLV4Btqnp6jycYIAuWJimIyDPAQ8ApwC3e10xgdTzaP2JsLVCHe4oMtgAYhQumxkRTXtD3B+j6NDkijPME73tIcgIRCYjIyyLybRE5A/f0+WngEVyQzgWejMXwEQuWJplcD/wd15b3HVzmleviWaBYEJGDwBPAPFUdG7RpOe6T+K/jUjCTyDqGdvxDRFpEpAXo6GB2UhjnOdF73dlDE8IhRKRNRF4VkWW4D8AAo+maLSgqLFiapOEFkduAFO/rGm9dIlqF+xmvAFDV8cBZwOMiUh/PgpnEoqrpwFxv8Y9Bm17yXs8O5UnP2+dsb7HXMZl9eDDo+0kRHN8nC5YmaXgX47eCVl0Ur7LEmohswfVQvEJV/bgqWT9WBWuibznwMe/7x4PW/9J7HY5Lft6fr+GqUQF+EUE56oK+b47g+D5ZsDTJ5A5gCnA3UIwLJPP7PmRQW4XrNTgPuBz4i4hsjW+RTCJR1XNw+V4BNonIcx3bROR1oKM/wG2qOruP85zOR8Nx1onIG922z1HVlH6KE5wQoTiU8ofDho6YpKCqZ+M+3W7DPV1OxA10XqWqJ4hIRV/HD1KP4XoN/gKX+eS2+BbHJAJVzeWjROpfxD107eWj1HbBrsQN9ZgMrFfVO4AHvJywqOo4XFPBt3GJ1HfgnlS7+wkwQlUfAZ7Djats8WpNxgNXAd/w9i3G9ZSNKguWJuF5UwQ9jJtu6FIRaQL+qqo34542f07PF/qgJiJVqvoUsARXRbU2zkUyg88sVQ0eVpWDG27VIYDrMLaipw+cInLAmzFkLa7N/GbgZlWt847NDtr9ReBiETnQ/Ty4a3cCLn+sAO2qWu0dnxa03zvAwlgkKLBgaZLB/cDRwE0i8nbQ+juB+cAiVb1URNbEpXSx9V1cVVh5AndmMrGThhtuBNCG601dipv8eQshTP4sIvtxnXzO4dDJn98HXsVN/lzUx2k+A5yD60g0E5cdaDguE1UpLkvQb4E1IhL19kqwYGkSnKouwVUVvYILjp1EpF1Vl+JSbK1U1Y0i8o84FDNmvOquD+JdDjO4eEMxlkX5nC8AL0R4bCPwjPcVF9bBxyQsb2LZlbhPw5eJSHv3fbxPxTfgPqU+5E0ka4wxXfgCgVCS6BtjjDHJy54sjTHGmH5YsDTGGGP6YcHSGGOM6YcFS2OMMaYfFiyNMcaYfliwNMYYY/phwdIYY4zphwVLY4wxph8WLI0xxph+WLA0xhhj+vH/+yTT3YpyU2IAAAAASUVORK5CYII=\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "dark" + }, "output_type": "display_data" } ], @@ -721,10 +945,137 @@ "cell_type": "code", "execution_count": 17, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.604525006165701\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/kaeser/anaconda3/envs/triqs_3/lib/python3.8/site-packages/scipy/optimize/zeros.py:776: ComplexWarning: Casting complex values to real discards the imaginary part\n", + " r = _zeros._brentq(f, a, b, xtol, rtol, maxiter, args, full_output, disp)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.604525006165701\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.604525006165701\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.604525006165701\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.604525006165701\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.604525006165701\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n" + ] + } + ], "source": [ - "%%capture\n", - "\n", "mus = [-.5, -.25, -0.1, 0.1, .25, .5]\n", "\n", "hubbard_models = parameter_scan(hubbard_next_nearest_neighbor_hopping, mu=mus)\n", @@ -745,7 +1096,7 @@ { "data": { "text/plain": [ - "Text(0.08,0.1,'AFM')" + "Text(0.08, 0.1, 'AFM')" ] }, "execution_count": 18, @@ -754,12 +1105,14 @@ }, { "data": { - "image/png": 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\n", 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\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "dark" + }, "output_type": "display_data" } ], @@ -885,10 +1238,159 @@ "cell_type": "code", "execution_count": 20, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.604525006165701\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.604525006165701\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 15.472700008220936\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 15.472700008220936\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 23.209050012331403\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 23.209050012331403\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 46.418100024662806\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 46.418100024662806\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n" + ] + } + ], "source": [ - "%%capture\n", - "\n", "Ts = [1000, 750, 500, 250]\n", "hubbard_models = parameter_scan(hubbard, T=Ts)\n", "\n", @@ -912,7 +1414,7 @@ { "data": { "text/plain": [ - "Text(0.07,0.15,'CDW')" + "Text(0.07, 0.15, 'CDW')" ] }, "execution_count": 21, @@ -921,12 +1423,14 @@ }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "dark" + }, "output_type": "display_data" } ], @@ -992,7 +1496,7 @@ " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", "Two-Particle Response Function tool-box \n", "\n", - "beta = 11.6045250062\n", + "beta = 11.604525006165701\n", "nk = 1024\n", "nw = 100\n", "norb = 1\n", @@ -1078,7 +1582,7 @@ "metadata": {}, "outputs": [], "source": [ - "from pytriqs.gf import Gf, MeshProduct\n", + "from triqs.gf import Gf, MeshProduct\n", "from triqs_tprf.eliashberg import solve_eliashberg\n", "\n", "def get_lambda_delta(p, g0_wk=None):\n", @@ -1149,7 +1653,7 @@ { "data": { "text/plain": [ - "Text(0.07,0.15,'SC')" + "Text(0.07, 0.15, 'SC')" ] }, "execution_count": 26, @@ -1158,12 +1662,14 @@ }, { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "dark" + }, "output_type": "display_data" } ], @@ -1188,7 +1694,7 @@ "ax_pd.spines['left'].set_bounds(Ts[-1], Ts[0])\n", "ax_pd.spines['bottom'].set_bounds(min(ax_pd.get_xticks()), max(ax_pd.get_xticks()))\n", "\n", - "ax_pd.text(0.9, 0.5, \"in-plane AFM\", transform = ax_pd.transAxes, size=22, color='C2', rotation=90)\n", + "ax_pd.text(0.9, 0.2, \"in-plane AFM\", transform = ax_pd.transAxes, size=22, color='C2', rotation=90)\n", "ax_pd.text(0.07, 0.15, \"SC\", transform = ax_pd.transAxes, size=22, color='grey')" ] }, @@ -1232,7 +1738,7 @@ { "data": { "text/plain": [ - "Text(0.52,0.6,'$|\\\\downarrow \\\\rangle$')" + "Text(0.52, 0.6, '$|\\\\downarrow \\\\rangle$')" ] }, "execution_count": 28, @@ -1241,12 +1747,14 @@ }, { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "dark" + }, "output_type": "display_data" } ], @@ -1321,17 +1829,198 @@ "And as we know the in-plane AFM, defined by $\\langle S_z S_z \\rangle$, is symmetric to the CDW, defined by $\\langle nn \\rangle$, for $U=0$.\n", "The same is true for the out-of-plane AFM, defined by $\\langle S_x S_x \\rangle$, and the superconducting phase, defined by $\\langle \\Delta \\Delta^\\dagger \\rangle$.\n", "\n", - "The calculated phase doagram confirms this." + "The calculated phase diagram confirms this." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.604525006165701\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 2\n", + "\n", + "Approx. Memory Utilization: 0.06 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/kaeser/anaconda3/envs/triqs_3/lib/python3.8/site-packages/scipy/optimize/zeros.py:776: ComplexWarning: Casting complex values to real discards the imaginary part\n", + " r = _zeros._brentq(f, a, b, xtol, rtol, maxiter, args, full_output, disp)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.604525006165701\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 2\n", + "\n", + "Approx. Memory Utilization: 0.06 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 11.604525006165701\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 2\n", + "\n", + "Approx. Memory Utilization: 0.06 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 15.472700008220936\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 2\n", + "\n", + "Approx. Memory Utilization: 0.06 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 15.472700008220936\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 2\n", + "\n", + "Approx. Memory Utilization: 0.06 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 15.472700008220936\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 2\n", + "\n", + "Approx. Memory Utilization: 0.06 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 23.209050012331403\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 2\n", + "\n", + "Approx. Memory Utilization: 0.06 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 23.209050012331403\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 2\n", + "\n", + "Approx. Memory Utilization: 0.06 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n", + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 23.209050012331403\n", + "nk = 1024\n", + "nw = 100\n", + "norb = 2\n", + "\n", + "Approx. Memory Utilization: 0.06 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n" + ] + } + ], "source": [ - "%%capture\n", - "\n", "# Density operator\n", "n = np.eye(2)\n", "# Spin operator\n", @@ -1369,7 +2058,7 @@ { "data": { "text/plain": [ - "Text(0.5,1,'Hubbard with $\\\\mathrm{Zeeman}=\\\\xi$')" + "Text(0.5, 1.0, 'Hubbard with $\\\\mathrm{Zeeman}=\\\\xi$')" ] }, "execution_count": 31, @@ -1378,12 +2067,14 @@ }, { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "dark" + }, "output_type": "display_data" } ], @@ -1428,8 +2119,8 @@ "ax_pd_left.text(0.3, 0.5, \"SC\", transform = ax_pd_left.transAxes, size=22, color='grey')\n", "ax_pd_left.text(0.07, 0.5, \"CDW\", transform = ax_pd_left.transAxes, size=22, color='C1', rotation=90)\n", "\n", - "ax_pd_right.text(0.35, 0.5, \"in-plane AFM\", transform = ax_pd_right.transAxes, size=22, color='C2', rotation=60)\n", - "ax_pd_right.text(0.89, 0.65, \"out-of-plane AFM\", transform = ax_pd_right.transAxes, size=22, color='C0', rotation=90)\n", + "ax_pd_right.text(0.45, 0.5, \"in-plane AFM\", transform = ax_pd_right.transAxes, size=22, color='C2', rotation=60)\n", + "ax_pd_right.text(0.89, 0.2, \"out-of-plane AFM\", transform = ax_pd_right.transAxes, size=22, color='C0', rotation=90)\n", "\n", "ax_pd_left.set_title(r'Hubbard with $\\mu=\\xi$', color='grey', size=24)\n", "ax_pd_right.set_title(r'Hubbard with $\\mathrm{Zeeman}=\\xi$', color='Grey', size=24)" @@ -1442,12 +2133,14 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "dark" + }, "output_type": "display_data" } ], @@ -1485,7 +2178,7 @@ "\n", "ax_pd_left.text(0.3, 0.25, \"SC\", transform = ax_pd_left.transAxes, size=22, color='grey')\n", "\n", - "ax_pd_right.text(0.35, 0.5, \"in-plane AFM\", transform = ax_pd_right.transAxes, size=22, color='C2', rotation=50)\n", + "ax_pd_right.text(0.35, 0.2, \"in-plane AFM\", transform = ax_pd_right.transAxes, size=22, color='C2', rotation=50)\n", "\n", "ax_pd_left.set_title(r'with $\\mu=\\xi$', color='grey', size=24)\n", "ax_pd_right.set_title(r'with $\\mathrm{Zeeman}=\\xi$', color='Grey', size=24)\n", @@ -1505,7 +2198,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 33, "metadata": {}, "outputs": [], "source": [ @@ -1514,27 +2207,37 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 34, "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/kaeser/my_triqs_installations/triqs_3.0.x/lib/python3.8/site-packages/triqs/gf/gf.py:323: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " dat = self._data[k]\n" + ] + }, { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 39, + "execution_count": 34, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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"text/plain": [ "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "dark" + }, "output_type": "display_data" } ], @@ -1555,21 +2258,21 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 2", + "display_name": "Python 3", "language": "python", - "name": "python2" + "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", - "version": 2 + "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.15" + "pygments_lexer": "ipython3", + "version": "3.8.5" } }, "nbformat": 4, diff --git a/doc/user_guide/Linearized Eliashberg equation on the attractive Hubbard model.ipynb b/doc/user_guide/Linearized Eliashberg equation on the attractive Hubbard model.ipynb index fdbb3da4d..0b2f13142 100644 --- a/doc/user_guide/Linearized Eliashberg equation on the attractive Hubbard model.ipynb +++ b/doc/user_guide/Linearized Eliashberg equation on the attractive Hubbard model.ipynb @@ -11,7 +11,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "Starting run with 1 MPI rank(s) at : 2020-08-17 10:55:55.432570\n" + "Starting run with 1 MPI rank(s) at : 2020-08-18 10:41:49.147374\n" ] } ], @@ -20,7 +20,7 @@ "\n", "import numpy as np\n", "\n", - "from pytriqs.plot.mpl_interface import plt\n", + "from triqs.plot.mpl_interface import plt\n", "from triqs_tprf.tight_binding import create_square_lattice\n" ] }, @@ -197,7 +197,7 @@ { "data": { "image/svg+xml": [ - "\n", + "\n", " \n", " r7zB;QZ@ttQ1#RH) zLo%sDM-WSJnxJN4^*U*m`84J@@VE#QlnC{q#>(-EtA&g9Ma~g`edHIu+DOlYG_6V(8>JHYXR|$+r zDs1fxH0aYtZOs9*X}r4-$VYW6iPkc7%-Q2KxbDKIWWE&8r4=6J;@3p#yJ|MFm zbD#t{;s5eqJkh;>TV!oT^DH^(jXOFKShZ3VcA!XjxrHQIvARC0v?Bday+t!TOY;KN zUc(E;PxpqfCqC{4Z1OCZh5*ng(*-N&Wq>3UnxhJF46wgi4Z^ICWQR7%UJJQ z&NzvVBTiWKRNStnPP@^I{@~S2Bo&P5FGM8OlrRCm(yaN~KvN$|L*f=@RA#h?g83t+ z8g2M#d&8kBX#X_Jra_ZHmoZJO$_$FSVjGs`5ig@8+C>TxlO*B~&ly&@eSE-mUJ5&r z;MfFfUXpy}su90|(4MtQ<0GMdlJvyEmHY>rhcwwkbxp{ 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z|6@8@e8l?Ur*#D3{PpjxABHX$tsnlAA-sP0X&;};vahcnT6+*&@PuQB@J9)P!!O6K z)-JYR!n)7vD}OZ(9KQecYvq4nU8-`$m!%g7w2s`$%VfHC`Y2|6Bg^`$oqE>3>_v>L(SEeiA_h5kwF{gnyuZ`s>fB5f}Td=hSEzj;#4>I_SUcxjj;Y zn|nU@hr?hwZls>$P(HW6wW! zJ@UuimqBzAy)WbIybAwY^6KB$ACaQ|7||awf6M;({QM57q33r@`q%9I@b_iN5BvSC jLpp0n&iv)ymmT)|b4Bt%1QA5|TjBo!NV;ht0C)ue0*|h3 literal 0 HcmV?d00001 diff --git a/test/python/eliashberg/preprocessing_gamma.py b/test/python/eliashberg/preprocessing_gamma.py index 18023aa51..d02bac953 100644 --- a/test/python/eliashberg/preprocessing_gamma.py +++ b/test/python/eliashberg/preprocessing_gamma.py @@ -5,6 +5,10 @@ from triqs_tprf.ParameterCollection import ParameterCollection from triqs_tprf.utilities import create_eliashberg_ingredients from triqs_tprf.eliashberg import split_into_dynamic_wk_and_constant_k, dynamic_and_constant_to_tr +from triqs_tprf.eliashberg import preprocess_gamma_for_fft + +from triqs_tprf.utilities import assert_parameter_collection_not_equal_model_parameters, write_TarGZ_HDFArchive, read_TarGZ_HDFArchive +import triqs_tprf.version as version def test_split_into_dynamic_wk_and_constant_k_mesh_types(gamma): gamma_dyn, gamma_const = split_into_dynamic_wk_and_constant_k(gamma) @@ -34,8 +38,43 @@ def test_dynamic_and_constant_to_tr_mesh_types(gamma): assert type(gamma_const_r.mesh) == MeshCyclicLattice +def test_preprocess_gamma_for_fft_types(gamma): + gamma_dyn_tr, gamma_const_r = preprocess_gamma_for_fft(gamma) + + assert type(gamma_dyn_tr.mesh) == MeshProduct + assert type(gamma_dyn_tr.mesh[0]) == MeshImTime + assert type(gamma_dyn_tr.mesh[1]) == MeshCyclicLattice + + assert type(gamma_const_r.mesh) == MeshCyclicLattice + +def save_new_preprocess_gamma_for_fft_benchmark(filename, p): + eliashberg_ingredients = create_eliashberg_ingredients(p) + gamma = eliashberg_ingredients.gamma + + gamma_dyn_tr, gamma_const_r = preprocess_gamma_for_fft(gamma) + + p.gamma = gamma + p.gamma_dyn_tr = gamma_dyn_tr + p.gamma_const_r = gamma_const_r + + write_TarGZ_HDFArchive(filename, p=p) + +def test_preprocess_gamma_for_fft_benchmark(gamma, p): + p_benchmark = read_TarGZ_HDFArchive(p.benchmark_filename)['p'] + model_parameters_to_test = ['dim', 'norb', 't', 'mu', 'beta', 'U'] + assert_parameter_collection_not_equal_model_parameters(p, p_benchmark, model_parameters_to_test) + + np.testing.assert_equal(gamma.data, p_benchmark.gamma.data) + + gamma_dyn_tr, gamma_const_r = preprocess_gamma_for_fft(gamma) + np.testing.assert_equal(gamma_dyn_tr.data, p_benchmark.gamma_dyn_tr.data) + np.testing.assert_equal(gamma_const_r.data, p_benchmark.gamma_const_r.data) + + if __name__ == '__main__': p = ParameterCollection( + filename = "preprocess_gamma_for_fft_benchmark_new.tar.gz", + benchmark_filename = "preprocess_gamma_for_fft_benchmark.tar.gz", dim = 1, norb = 2, t = 2.0, @@ -47,6 +86,7 @@ def test_dynamic_and_constant_to_tr_mesh_types(gamma): Jp = 0.1, nk = 3, nw = 500, + version_info = version.info, ) eliashberg_ingredients = create_eliashberg_ingredients(p) gamma = eliashberg_ingredients.gamma @@ -56,3 +96,7 @@ def test_dynamic_and_constant_to_tr_mesh_types(gamma): test_split_into_dynamic_wk_and_constant_k_mesh_types(gamma) test_split_into_dynamic_wk_and_constant_k_mesh_values(gamma, U_c, U_s) test_dynamic_and_constant_to_tr_mesh_types(gamma) + test_preprocess_gamma_for_fft_types(gamma) + + #save_new_preprocess_gamma_for_fft_benchmark("preprocess_gamma_for_fft_benchmark.tar.gz", p) + test_preprocess_gamma_for_fft_benchmark(gamma, p) From 082eac9625b25b23bba7f3a43b9d275797fe644b Mon Sep 17 00:00:00 2001 From: Stefan Date: Tue, 18 Aug 2020 15:25:54 +0200 Subject: [PATCH 081/121] [eli] adjust to fix of TRIQS/triqs#755 --- c++/triqs_tprf/lattice/eliashberg.cpp | 36 ++---------- c++/triqs_tprf/lattice/eliashberg.hpp | 21 +++++-- doc/reference/cpp_reference.rst | 2 + doc/reference/python_reference.rst | 2 +- python/triqs_tprf/eliashberg.py | 56 +------------------ python/triqs_tprf/lattice_desc.py | 9 +-- test/python/eliashberg/preprocessing_gamma.py | 2 +- 7 files changed, 29 insertions(+), 99 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index 02aba6601..15b29986d 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -111,8 +111,7 @@ g_wk_t eliashberg_product(chi_wk_vt Gamma_pp, g_wk_vt g_wk, return delta_wk_out; } -chi_wk_t get_dynamic_wk(chi_wk_vt Gamma_pp) { - +std::tuple split_into_dynamic_wk_and_constant_k(chi_wk_vt Gamma_pp) { auto _ = all_t{}; //auto [wmesh, kmesh] = Gamma_pp.mesh(); auto wmesh = std::get<0>(Gamma_pp.mesh()); @@ -131,44 +130,17 @@ chi_wk_t get_dynamic_wk(chi_wk_vt Gamma_pp) { for( const auto w : wmesh ) Gamma_pp_dyn_wk[w, k] = Gamma_pp[w, k] - Gamma_pp_const_k[k]; } - return Gamma_pp_dyn_wk; -} - -chi_k_t get_constant_k(chi_wk_vt Gamma_pp) { - - auto _ = all_t{}; - //auto [wmesh, kmesh] = Gamma_pp.mesh(); - auto wmesh = std::get<0>(Gamma_pp.mesh()); - auto kmesh = std::get<1>(Gamma_pp.mesh()); - - // Fit infinite frequency value - auto Gamma_pp_dyn_wk = make_gf(Gamma_pp); - - auto Gamma_pp_const_k = make_gf(kmesh, Gamma_pp.target()); - - for (const auto k : kmesh) { - auto Gamma_w = Gamma_pp[_, k]; - auto tail = std::get<0>(fit_tail(Gamma_w)); - for (auto [a, b, c, d] : Gamma_pp.target_indices()) - Gamma_pp_const_k[k](a, b, c, d) = tail(0, a, b, c, d); - } - - return Gamma_pp_const_k; + return {Gamma_pp_dyn_wk, Gamma_pp_const_k}; } -chi_tr_t dynamic_to_tr(chi_wk_vt Gamma_pp_dyn_wk) { +std::tuple dynamic_and_constant_to_tr(chi_wk_vt Gamma_pp_dyn_wk, chi_k_vt Gamma_pp_const_k) { auto Gamma_pp_dyn_wr = fourier_wk_to_wr_general_target(Gamma_pp_dyn_wk); auto Gamma_pp_dyn_tr = fourier_wr_to_tr_general_target(Gamma_pp_dyn_wr); - return Gamma_pp_dyn_tr; -} - -chi_r_t constant_to_r(chi_k_vt Gamma_pp_const_k) { - auto Gamma_pp_const_r = make_gf_from_fourier<0>(Gamma_pp_const_k); - return Gamma_pp_const_r; + return {Gamma_pp_dyn_tr, Gamma_pp_const_r}; } e_r_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, g_tr_t F_tr) { diff --git a/c++/triqs_tprf/lattice/eliashberg.hpp b/c++/triqs_tprf/lattice/eliashberg.hpp index 7b056dbba..34740333d 100644 --- a/c++/triqs_tprf/lattice/eliashberg.hpp +++ b/c++/triqs_tprf/lattice/eliashberg.hpp @@ -146,10 +146,23 @@ namespace triqs_tprf { g_wk_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const_r, g_wk_vt g_wk, g_wk_vt delta_wk); g_wk_t eliashberg_product_fft_constant(chi_r_vt Gamma_pp_const_r, g_wk_vt g_wk, g_wk_vt delta_wk); g_wk_t eliashberg_g_delta_g_product(g_wk_vt g_wk, g_wk_vt delta_wk); - chi_wk_t get_dynamic_wk(chi_wk_vt Gamma_pp); - chi_k_t get_constant_k(chi_wk_vt Gamma_pp); - chi_tr_t dynamic_to_tr(chi_wk_vt Gamma_pp_dyn_wk); - chi_r_t constant_to_r(chi_k_vt Gamma_pp_const_k); + + + /** Split Gamma in dynamic and constant part by tail fitting + + @param Gamma_pp : particle-particle pairing vertex :math:`\Gamma(i\omega_n, \mathbf{k})`. + @return Tuple of Gamma_pp_dyn_wk, the dynamic part of Gamma, which converges to zero for :math:`\omega_n \rightarrow \infty`, and Gamma_pp_const_k, the part of Gamma that is constant in Matsubara frequency space :math:`\Gamma(\mathbf{k})`. + */ + std::tuple split_into_dynamic_wk_and_constant_k(chi_wk_vt Gamma_pp); + + + /** Fourier transform Gamma parts to imaginary time and real-space + + @param Gamma_pp_dyn_wk : The dynamic part of Gamma, which converges to zero for :math:`\omega_n \rightarrow \infty`. + @param Gamma_pp_const_k : The part of Gamma that is constant in Matsubara frequency space :math:`\Gamma(\mathbf{k})`. + @return Tuple of Gamma_pp_dyn_tr, the dynamic part of Gamma, which converges to zero for :math:`\omega_n \rightarrow \infty`, but now in :math:`\tau`-space, Gamma_pp_const_r, the constant part of Gamma in real-space. + */ + std::tuple dynamic_and_constant_to_tr(chi_wk_vt Gamma_pp_dyn_wk, chi_k_vt Gamma_pp_const_k); e_r_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, g_tr_t F_tr); /** The particle-particle vertex in the singlet channel diff --git a/doc/reference/cpp_reference.rst b/doc/reference/cpp_reference.rst index 3e5dfb243..f51c7db49 100644 --- a/doc/reference/cpp_reference.rst +++ b/doc/reference/cpp_reference.rst @@ -105,6 +105,8 @@ Linearized Eliashberg equation /cpp2rst_generated/triqs_tprf/eliashberg_product /cpp2rst_generated/triqs_tprf/eliashberg_product_fft + /cpp2rst_generated/triqs_tprf/split_into_dynamic_wk_and_constant_k + /cpp2rst_generated/triqs_tprf/dynamic_and_constant_to_tr /cpp2rst_generated/triqs_tprf/gamma_PP_singlet /cpp2rst_generated/triqs_tprf/gamma_PP_triplet diff --git a/doc/reference/python_reference.rst b/doc/reference/python_reference.rst index 6c2997a7f..a6f9ca87f 100644 --- a/doc/reference/python_reference.rst +++ b/doc/reference/python_reference.rst @@ -48,10 +48,10 @@ Linearized Eliashberg equation ============================== .. autofunction:: triqs_tprf.eliashberg.solve_eliashberg +.. autofunction:: triqs_tprf.eliashberg.preprocess_gamma_for_fft .. autofunction:: triqs_tprf.eliashberg.semi_random_initial_delta .. autofunction:: triqs_tprf.eliashberg.power_method_LR .. autofunction:: triqs_tprf.eliashberg.implicitly_restarted_arnoldi_method -.. autofunction:: triqs_tprf.eliashberg.preprocess_gamma_for_fft Hubbard atom analytic response functions ======================================== diff --git a/python/triqs_tprf/eliashberg.py b/python/triqs_tprf/eliashberg.py index aae2875ae..621f3ade2 100644 --- a/python/triqs_tprf/eliashberg.py +++ b/python/triqs_tprf/eliashberg.py @@ -32,8 +32,7 @@ from triqs.gf import Gf from .lattice import eliashberg_product from .lattice import eliashberg_product_fft, eliashberg_product_fft_constant -from .lattice import get_dynamic_wk, get_constant_k, dynamic_to_tr, constant_to_r - +from .lattice import split_into_dynamic_wk_and_constant_k, dynamic_and_constant_to_tr # ---------------------------------------------------------------------- def solve_eliashberg(Gamma_pp_wk, g_wk, initial_delta=None, Gamma_pp_const_k=None, @@ -203,59 +202,6 @@ def preprocess_gamma_for_fft(Gamma_pp_wk, Gamma_pp_const_k=None): return Gamma_pp_dyn_tr, Gamma_pp_const_r -def split_into_dynamic_wk_and_constant_k(Gamma_pp_wk): - r""" Split Gamma by tail fitting constant part in frequency - - Parameters - ---------- - Gamma_pp_wk : Gf, - Pairing vertex :math:`\Gamma(i\omega_n, \mathbf{k})`. The mesh attribute of - the Gf must be a MeshProduct with the components (MeshImFreq, MeshBrillouinZone). - - Returns - ------- - Gamma_pp_dyn_wk : Gf, - The dynamic part of Gamma, which converges to zero for - :math:`\omega_n \rightarrow \infty`. - Its mesh attribute is MeshProduct with the components - (MeshImFreq, MeshBrillouinZone). - Gamma_pp_const_k : Gf, - Part of the pairing vertex that is constant in Matsubara frequency space - :math:`\Gamma(\mathbf{k})`. Returned as a Gf with mesh attribute - MeshBrillouinZone. - """ - Gamma_pp_dyn_wk = get_dynamic_wk(Gamma_pp_wk) - Gamma_pp_const_k = get_constant_k(Gamma_pp_wk) - return Gamma_pp_dyn_wk, Gamma_pp_const_k - -def dynamic_and_constant_to_tr(Gamma_pp_dyn_wk, Gamma_pp_const_k): - r""" Fourier transform Gamma parts to imaginary time and real-space - - Parameters - ---------- - Gamma_pp_dyn_wk : Gf, - The dynamic part of Gamma, which converges to zero for - :math:`\omega_n \rightarrow \infty`. - Its mesh attribute is MeshProduct with the components - (MeshImFreq, MeshBrillouinZone). - Gamma_pp_const_k : Gf, - Part of the pairing vertex that is constant in Matsubara frequency space - :math:`\Gamma(\mathbf{k})`. Its mesh attribute is MeshBrillouinZone. - - Returns - ------- - Gamma_pp_dyn_tr : Gf, - The dynamic part of Gamma, which converges to zero for - :math:`\omega_n \rightarrow \infty`, but now in :math:`\tau`-space. - Its mesh attribute is MeshProduct with the components - (MeshImTime, MeshCyclicLattice). - Gamma_pp_const_r : Gf, - The constant part of Gamma with mesh attribute MeshCyclicLattice. - """ - Gamma_pp_dyn_tr = dynamic_to_tr(Gamma_pp_dyn_wk) - Gamma_pp_const_r = constant_to_r(Gamma_pp_const_k) - return Gamma_pp_dyn_tr, Gamma_pp_const_r - def semi_random_initial_delta(g_wk, nr_factor=0.5, seed=None): r"""Create a delta based on the GF with random elements diff --git a/python/triqs_tprf/lattice_desc.py b/python/triqs_tprf/lattice_desc.py index 0183ad5d1..fb4d6f7f9 100644 --- a/python/triqs_tprf/lattice_desc.py +++ b/python/triqs_tprf/lattice_desc.py @@ -32,6 +32,7 @@ # Add here anything to add in the C++ code at the start, e.g. namespace using module.add_preamble(""" #include +#include #include #include @@ -567,13 +568,9 @@ module.add_function ("triqs_tprf::g_wk_t triqs_tprf::eliashberg_g_delta_g_product (triqs_tprf::g_wk_vt g_wk, triqs_tprf::g_wk_vt delta_wk)", doc = r"""""") -module.add_function ("triqs_tprf::chi_wk_t triqs_tprf::get_dynamic_wk (triqs_tprf::chi_wk_vt Gamma_pp)", doc = r"""""") +module.add_function ("std::tuple triqs_tprf::split_into_dynamic_wk_and_constant_k (triqs_tprf::chi_wk_vt Gamma_pp)", doc = r"""""") -module.add_function ("triqs_tprf::chi_k_t triqs_tprf::get_constant_k (triqs_tprf::chi_wk_vt Gamma_pp)", doc = r"""""") - -module.add_function ("triqs_tprf::chi_tr_t triqs_tprf::dynamic_to_tr (triqs_tprf::chi_wk_vt Gamma_pp_dyn_wk)", doc = r"""""") - -module.add_function ("triqs_tprf::chi_r_t triqs_tprf::constant_to_r (triqs_tprf::chi_k_vt Gamma_pp_const_k)", doc = r"""""") +module.add_function ("std::tuple triqs_tprf::dynamic_and_constant_to_tr (triqs_tprf::chi_wk_vt Gamma_pp_dyn_wk, triqs_tprf::chi_k_vt Gamma_pp_const_k)", doc = r"""""") module.add_function ("triqs_tprf::e_r_t triqs_tprf::eliashberg_constant_gamma_f_product (triqs_tprf::chi_r_vt Gamma_pp_const_r, triqs_tprf::g_tr_t F_tr)", doc = r"""""") diff --git a/test/python/eliashberg/preprocessing_gamma.py b/test/python/eliashberg/preprocessing_gamma.py index d02bac953..30db755e2 100644 --- a/test/python/eliashberg/preprocessing_gamma.py +++ b/test/python/eliashberg/preprocessing_gamma.py @@ -4,7 +4,7 @@ from triqs_tprf.ParameterCollection import ParameterCollection from triqs_tprf.utilities import create_eliashberg_ingredients -from triqs_tprf.eliashberg import split_into_dynamic_wk_and_constant_k, dynamic_and_constant_to_tr +from triqs_tprf.lattice import split_into_dynamic_wk_and_constant_k, dynamic_and_constant_to_tr from triqs_tprf.eliashberg import preprocess_gamma_for_fft from triqs_tprf.utilities import assert_parameter_collection_not_equal_model_parameters, write_TarGZ_HDFArchive, read_TarGZ_HDFArchive From 3c66cee136756a7fb1ad3ce99e5f03e4747b8c00 Mon Sep 17 00:00:00 2001 From: Stefan Date: Tue, 18 Aug 2020 15:44:51 +0200 Subject: [PATCH 082/121] [eli] adjust to fix of TRIQS/triqs#725 --- c++/triqs_tprf/lattice/eliashberg.cpp | 34 +++------------------------ 1 file changed, 3 insertions(+), 31 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index 15b29986d..1be68fed7 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -49,33 +49,17 @@ g_wk_t eliashberg_g_delta_g_product(g_wk_vt g_wk, g_wk_vt delta_wk) { auto F_wk = make_gf(delta_wk); F_wk *= 0.; -/* The rest of this function contains a lot of boiler plate code due to issue - #725 in the TRIQS library. - It will be changed later -*/ auto k_arr = mpi_view(kmesh); - auto _ = all_t{}; - #pragma omp parallel for for(unsigned int idx_k = 0; idx_k < kmesh.size(); idx_k++){ auto k = k_arr(idx_k); - auto g_left_w = make_gf(wmesh, g_wk.target()); - auto g_right_w = make_gf(wmesh, g_wk.target()); - auto delta_w = make_gf(wmesh, delta_wk.target()); - auto F_w = make_gf(wmesh, F_wk.target()); - - g_left_w = g_wk[_, k]; - g_right_w = g_wk[_, -k]; - delta_w = delta_wk[_, k]; - for (const auto w : wmesh) { for (auto [A, B] : F_wk.target_indices()) for (auto [c, d] : delta_wk.target_indices()) - F_w[w](A, B) += - g_left_w[w](A, c) * g_right_w[-w](B, d) * delta_w[w](c, d); + F_wk[w, k](A, B) += + g_wk[w, k](A, c) * g_wk[-w, -k](B, d) * delta_wk[w, k](c, d); } - F_wk[_, k] = F_w; } return F_wk; @@ -177,27 +161,15 @@ g_tr_t eliashberg_dynamic_gamma_f_product(chi_tr_vt Gamma_pp_dyn_tr, g_tr_vt F_t " (" << tmesh_gamma.size() << ") must be the size of the mesh of Delta (" << tmesh.size() << ")."; -/* This function contains a lot boiler plate code due to issue - #725 in the TRIQS library. - It will be changed later -*/ - auto r_arr = mpi_view(rmesh); - auto _ = all_t{}; #pragma omp parallel for for(unsigned int idx_r = 0; idx_r < rmesh.size(); idx_r++){ auto r = r_arr(idx_r); - auto delta_t = make_gf(tmesh, delta_tr_out.target()); - - auto Gamma_pp_dyn_t = Gamma_pp_dyn_tr[_, r]; - auto F_t = F_tr[_, r]; - for (const auto t : tmesh) { for (auto [A, a, B, b] : Gamma_pp_dyn_tr.target_indices()) - delta_t[t](a, b) += -0.5 * Gamma_pp_dyn_t[t](A, a, B, b) * F_t[t](A, B); + delta_tr_out[t, r](a, b) += -0.5 * Gamma_pp_dyn_tr[t, r](A, a, B, b) * F_tr[t, r](A, B); } - delta_tr_out[_, r] = delta_t; } return delta_tr_out; From 975af1fb2e3513d9d04ff97a0ca2c1ec9a873c8c Mon Sep 17 00:00:00 2001 From: Stefan Date: Tue, 18 Aug 2020 15:52:56 +0200 Subject: [PATCH 083/121] [eli] remove benchmark timer --- c++/triqs_tprf/lattice/eliashberg.cpp | 33 --------------------------- 1 file changed, 33 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index 1be68fed7..09464e6e2 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -23,7 +23,6 @@ #include "eliashberg.hpp" #include #include "../mpi.hpp" -#include #include "gf.hpp" #include "fourier.hpp" @@ -178,55 +177,23 @@ g_tr_t eliashberg_dynamic_gamma_f_product(chi_tr_vt Gamma_pp_dyn_tr, g_tr_vt F_t g_wk_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const_r, g_wk_vt g_wk, g_wk_vt delta_wk) { - triqs::utility::timer t_all, t_g_delta_g_product, t_fft_F, t_dynamic_product, t_fft_delta, t_constant_product, t_combine; - t_all.start(); - - t_g_delta_g_product.start(); auto F_wk = eliashberg_g_delta_g_product(g_wk, delta_wk); - t_g_delta_g_product.stop(); - - t_fft_F.start(); auto F_wr = fourier_wk_to_wr(F_wk); auto F_tr = fourier_wr_to_tr(F_wr); - t_fft_F.stop(); - // Dynamic part - t_dynamic_product.start(); auto delta_tr_out = eliashberg_dynamic_gamma_f_product(Gamma_pp_dyn_tr, F_tr); - t_dynamic_product.stop(); - - // Constant part - t_constant_product.start(); auto delta_r_out = eliashberg_constant_gamma_f_product(Gamma_pp_const_r, F_tr); - t_constant_product.stop(); // FIXME // This raises warnings when used with random delta input, e.g. eigenvalue finder - t_fft_delta.start(); auto delta_wr_out = fourier_tr_to_wr(delta_tr_out); - t_fft_delta.stop(); - // Combine dynamic and constant part - t_combine.start(); auto _ = all_t{}; for (const auto w : std::get<0>(delta_wr_out.mesh())) delta_wr_out[w, _] += delta_r_out; - t_combine.stop(); - t_fft_delta.start(); - t_fft_delta.stop(); auto delta_wk_out = fourier_wr_to_wk(delta_wr_out); - t_all.stop(); - - std::cout << "all:\t" << double(t_all) << "\n" \ - << "g_delta_g_product:\t" << double(t_g_delta_g_product) << "\n" \ - << "fft_F:\t" << double(t_fft_F) << "\n" \ - << "dynamic_product:\t" << double(t_dynamic_product) << "\n" \ - << "fft_delta:\t" << double(t_fft_delta) << "\n" \ - << "constant_product:\t" << double(t_constant_product) << "\n" \ - << "combin:\t" << double(t_combine) << "\n" ; - return delta_wk_out; } From 86dcaf472c0f17cdba6b0ee3fca4c2b80ae0e35e Mon Sep 17 00:00:00 2001 From: Stefan Date: Tue, 18 Aug 2020 16:12:14 +0200 Subject: [PATCH 084/121] [eli] combine loops --- c++/triqs_tprf/lattice/eliashberg.cpp | 26 +++++++++++--------------- 1 file changed, 11 insertions(+), 15 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index 09464e6e2..e4b487216 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -48,18 +48,16 @@ g_wk_t eliashberg_g_delta_g_product(g_wk_vt g_wk, g_wk_vt delta_wk) { auto F_wk = make_gf(delta_wk); F_wk *= 0.; - auto k_arr = mpi_view(kmesh); + auto meshes_mpi = mpi_view(delta_wk.mesh()); #pragma omp parallel for - for(unsigned int idx_k = 0; idx_k < kmesh.size(); idx_k++){ - auto k = k_arr(idx_k); - - for (const auto w : wmesh) { - for (auto [A, B] : F_wk.target_indices()) - for (auto [c, d] : delta_wk.target_indices()) - F_wk[w, k](A, B) += - g_wk[w, k](A, c) * g_wk[-w, -k](B, d) * delta_wk[w, k](c, d); + for (unsigned int idx = 0; idx < meshes_mpi.size(); idx++){ + auto &[w, k] = meshes_mpi(idx); + + for (auto [A, B] : F_wk.target_indices()) + for (auto [c, d] : delta_wk.target_indices()) + F_wk[w, k](A, B) += + g_wk[w, k](A, c) * g_wk[-w, -k](B, d) * delta_wk[w, k](c, d); } - } return F_wk; } @@ -160,15 +158,13 @@ g_tr_t eliashberg_dynamic_gamma_f_product(chi_tr_vt Gamma_pp_dyn_tr, g_tr_vt F_t " (" << tmesh_gamma.size() << ") must be the size of the mesh of Delta (" << tmesh.size() << ")."; - auto r_arr = mpi_view(rmesh); + auto meshes_mpi = mpi_view(F_tr.mesh()); #pragma omp parallel for - for(unsigned int idx_r = 0; idx_r < rmesh.size(); idx_r++){ - auto r = r_arr(idx_r); + for (unsigned int idx = 0; idx < meshes_mpi.size(); idx++){ + auto &[t, r] = meshes_mpi(idx); - for (const auto t : tmesh) { for (auto [A, a, B, b] : Gamma_pp_dyn_tr.target_indices()) delta_tr_out[t, r](a, b) += -0.5 * Gamma_pp_dyn_tr[t, r](A, a, B, b) * F_tr[t, r](A, B); - } } return delta_tr_out; From 7e4416e26c90b39feb5540b42b475bc33bb024ea Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 19 Aug 2020 16:59:45 +0200 Subject: [PATCH 085/121] [eli] add user guide for RPA limit --- doc/documentation.rst | 1 + ...the random phase approximation limit.ipynb | 450 ++++++++++++++++++ 2 files changed, 451 insertions(+) create mode 100644 doc/user_guide/Solving the linearized Eliashberg equation in the random phase approximation limit.ipynb diff --git a/doc/documentation.rst b/doc/documentation.rst index 109b5d878..fd41c204e 100644 --- a/doc/documentation.rst +++ b/doc/documentation.rst @@ -14,6 +14,7 @@ Tutorials user_guide/Lattice BSE on Hubbard atom.ipynb user_guide/dmft_susceptibility/dmft_susceptibility user_guide/Linearized Eliashberg equation on the attractive Hubbard model.ipynb + user_guide/Solving the linearized Eliashberg equation in the random phase approximation limit Python reference manual ----------------------- diff --git a/doc/user_guide/Solving the linearized Eliashberg equation in the random phase approximation limit.ipynb b/doc/user_guide/Solving the linearized Eliashberg equation in the random phase approximation limit.ipynb new file mode 100644 index 000000000..1744a550d --- /dev/null +++ b/doc/user_guide/Solving the linearized Eliashberg equation in the random phase approximation limit.ipynb @@ -0,0 +1,450 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "nbsphinx": "hidden" + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Starting run with 1 MPI rank(s) at : 2020-08-19 16:58:28.975762\n" + ] + } + ], + "source": [ + "%matplotlib inline\n", + "\n", + "import warnings\n", + "warnings.filterwarnings('ignore')\n", + "\n", + "from triqs.plot.mpl_interface import plt\n", + "from triqs.gf import Idx\n", + "from triqs_tprf.plotting_tools import bsplot\n", + "\n", + "def plot_delta(delta, lamb):\n", + " fig, axs = plt.subplots(figsize=(8, 5), ncols=2)\n", + "\n", + " nw = delta.data.shape[0]\n", + " axs[0].plot(range(-nw//2, nw//2), delta[:, :].data[:,500, 0, 0].real *1e3)\n", + "\n", + " axs[0].set_xlabel(r\"$i\\nu_n$\")\n", + " axs[0].set_ylabel(r\"$\\Delta$ (meV)\")\n", + "\n", + "\n", + " im = axs[1].imshow(delta[Idx(0), :].data.reshape(nk, nk).real, cmap=\"RdBu\")\n", + " axs[1].set_xticks([])\n", + " axs[1].set_yticks([])\n", + "\n", + " axs[1].spines['top'].set_visible(True)\n", + " axs[1].spines['right'].set_visible(True)\n", + "\n", + " axs[1].set_xlabel(\"$k_x$\")\n", + " axs[1].set_ylabel(\"$k_y$\")\n", + "\n", + " axs[1].text(16, 16, \"$\\Gamma$\", size=20)\n", + " axs[1].text(32, 0, \"$M$\", size=20)\n", + " axs[1].text(32, 16, \"$X$\", size=20)\n", + " \n", + " fig.suptitle(r\"$\\lambda = %.3f$\" % lamb, fontsize=20)\n", + " \n", + "\n", + "def plot_chi(chi_s_wk, chi_c_wk):\n", + " path = [(r'$\\Gamma$', 2*np.pi*np.array([0.0, 0.0, 0.0])), \n", + " ('X', 2*np.pi*np.array([0.5, 0.0, 0.0])),\n", + " ('M', 2*np.pi*np.array([0.5, 0.5, 0.0])), \n", + " (r'$\\Gamma$', 2*np.pi*np.array([0.0, 0.0, 0.0])), \n", + " ]\n", + "\n", + "\n", + " ax_bs = plt.subplot(111)\n", + "\n", + " ax_bs.bsplot(chi_s_wk[(Idx(0), slice(None))], path)\n", + " ax_bs.bsplot(chi_c_wk[(Idx(0), slice(None))], path)\n", + "\n", + " ax_bs.set_ylabel(r'$\\chi(i\\nu_n=0, \\mathbf{k})$', rotation=0, ha='right')\n", + " ax_bs.text(0.62, 0.6, \"$\\chi^{s}$\", transform = ax_bs.transAxes, size=22, color='C0')\n", + " ax_bs.text(0.55, 0.18, \"$\\chi^{c}$\", transform = ax_bs.transAxes, size=22, color='C1')" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "nbsphinx": "hidden" + }, + "outputs": [], + "source": [ + "plt.style.use('notebook.mplstyle')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Solving the linearized Eliashberg equation in the random phase approximation limit\n", + "\n", + "In this notebook we will walk you through the steps of solving the linearized Eliashberg equation in the random phase approximation (RPA) limit. Make sure, that you have read the [theory](https://triqs.github.io/tprf/latest/theory/eliashberg.html) before reading further.\n", + "\n", + "The steps are\n", + " 1. Construct the charge- and spin-susceptibilties in RPA\n", + " 2. Construct the particle-particle vertex in RPA\n", + " 3. Construct the symmetrizing functions\n", + " 4. Solve the linearized Eliashberg equation\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1. Construct the charge- and spin-susceptibilties in RPA\n", + "\n", + "First we need a model and in this example we use the 1-band square lattice." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "from triqs_tprf.tight_binding import create_square_lattice\n", + "\n", + "square_lattice = create_square_lattice(norb=1, t=1.0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we need the non-interacting one-particle Green's function. For this we first create the dispersion relation on a mesh on the Brillouin zone." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "nk = 32\n", + "\n", + "e_k = square_lattice.on_mesh_brillouin_zone((nk, nk, 1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And then we solve the lattice dyson equation `lattice_dyson_g0_wk` for a specific fermionic Matsubara frequency mesh `MeshImFreq` to obtain the non-interacting one-particle Green's function `g0_wk`." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "from triqs.gf import MeshImFreq\n", + "from triqs_tprf.lattice import lattice_dyson_g0_wk\n", + "\n", + "wmesh = MeshImFreq(beta=10, S='Fermion', n_max=100)\n", + "g0_wk = lattice_dyson_g0_wk(mu=0, e_k=e_k, mesh=wmesh)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we solve for the charge- and spin-susceptibilties in RPA by first constructing the bare bubble $\\chi_0$ `imtime_bubble_chi0_wk`" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "╔╦╗╦═╗╦╔═╗ ╔═╗ ┌┬┐┌─┐┬─┐┌─┐\n", + " ║ ╠╦╝║║═╬╗╚═╗ │ ├─┘├┬┘├┤ \n", + " ╩ ╩╚═╩╚═╝╚╚═╝ ┴ ┴ ┴└─└ \n", + "Two-Particle Response Function tool-box \n", + "\n", + "beta = 10.0\n", + "nk = 1024\n", + "nw = 200\n", + "norb = 1\n", + "\n", + "Approx. Memory Utilization: 0.01 GB\n", + "\n", + "--> fourier_wk_to_wr\n", + "--> fourier_wr_to_tr\n", + "--> chi0_tr_from_grt_PH (bubble in tau & r)\n", + "--> chi_wr_from_chi_tr\n", + "--> chi_wk_from_chi_wr (r->k)\n" + ] + } + ], + "source": [ + "from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk\n", + "\n", + "chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=100)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and then solving the RPA equations `solve_rpa_PH` for a Hubbard $U$, a rank 4 numpy array." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from triqs_tprf.lattice import solve_rpa_PH\n", + "\n", + "U = 1.0 * np.ones(shape=(1, 1, 1, 1), dtype=np.complex)\n", + "\n", + "chi_c_wk = solve_rpa_PH(chi0_wk, -U) # Minus here for correct charge RPA equation\n", + "chi_s_wk = solve_rpa_PH(chi0_wk, U)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plotting this over a path through the high-symmetry points looks as follows." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "dark" + }, + "output_type": "display_data" + } + ], + "source": [ + "plot_chi(chi_s_wk, chi_c_wk)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2. Construct the particle-particle vertex in RPA\n", + "\n", + "Now we have all the ingredients to build the particle-particle vertex in the RPA limit. In this example we limit us to the singlet particle-particle vertex, which we construct by calling `gamma_PP_singlet`. For the 1-band case it is given by\n", + "\n", + "\\begin{align}\n", + "\\Gamma^{\\mathrm{singlet}}(i\\omega_n, \\mathbf{q})\n", + "=\n", + "3 U^2\\chi^{\\mathrm{s}}(i\\omega_n, \\mathbf{q}) - U^2\\chi^{\\mathrm{c}}(i\\omega_n, \\mathbf{q})\n", + "+ U\\,.\n", + "\\end{align}\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "from triqs_tprf.lattice import gamma_PP_singlet\n", + "\n", + "gamma_singlet = gamma_PP_singlet(chi_c_wk, chi_s_wk, U, U)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3. Construct the symmetrizing functions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By using the above $\\Gamma$ we must enforce the allowed $SPOT$ symmetries of the superconducting gap $\\Delta$.\n", + "Our 1-band model is by default even in orbital symmetry and by using the singlet $\\Gamma$ we are fixing the spin symmetry to odd. We are therefore left with two physical symmetry combinations.\n", + "\n", + "| Spin | Parity (Momentum) | Orbital | Time (Frequency) |\n", + "|:----:|:-----------------:|:-------:|:----------------:|\n", + "| odd | even | even | even |\n", + "| odd | odd | even | odd |\n", + "\n", + "We will solve for them individually, by constructing a symmetrizing function for each of them.\n", + "We do this by taking `enforce_symmetry` and using `functools.partial` to specifiy the symmetries that we want." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Frequency: Even, Momentum: Even" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "import functools\n", + "from triqs_tprf.symmetries import enforce_symmetry\n", + "\n", + "variables = [\"frequency\", \"momentum\"]\n", + "symmetries = [\"even\", \"even\"]\n", + "\n", + "symmetrize_freq_even_mom_even = functools.partial(enforce_symmetry, variables=variables, symmetries=symmetries)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Frequency: Odd, Momentum: Odd" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "symmetries = [\"odd\", \"odd\"]\n", + "\n", + "symmetrize_freq_odd_mom_odd = functools.partial(enforce_symmetry, variables=variables, symmetries=symmetries)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 4. Solve the linearized Eliashberg equation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we have everything that we need to solve the linearized Eliashberg equation. \n", + "We call the `solve_eliashberg` function with each of our `symmetrize_fct`s and solve for the first leading eigenvalue, gap pair (`k=1`)." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "from triqs_tprf.eliashberg import solve_eliashberg\n", + "\n", + "lambdas_freq_even_mom_even, deltas_freq_even_mom_even = solve_eliashberg(gamma_singlet, g0_wk, symmetrize_fct=symmetrize_freq_even_mom_even, k=1)\n", + "lambdas_freq_odd_mom_odd, deltas_freq_odd_mom_odd = solve_eliashberg(gamma_singlet, g0_wk, symmetrize_fct=symmetrize_freq_odd_mom_odd, k=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plotting them shows that all symmetries are correct and that the gap with even frequency and odd momentum has the higher $\\lambda$ and is therefore leading." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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0r1o/VXOd7cFwtFptTbharf2ZR4Lx5/9+VzB+b6Ra7dbV4Z5uU+rDYwB7TGwMxmfOCVd6NUa2B8h0hCvcxr0Y/lk8uypcWXffv1cH452t4T5z89rDfw8zOsK/m/pIdVvNuCnBeBqrboN4hVusKi3a1y2/xXeTMj3XagRJJE9pV+4kbSVIIiLVSgmSSL5y16FRgiQiUrWUIInkSyNIIiKjhhIkkTyl+a5kLCIiI54SJJF8aR0kEZFRQ1VsInnKXQdJRWwybNIUusLVSX23jfRWi1WxRUZGk8626CGSjnAlVmbNy8F4e6y32o33BOOFVqtt0xR+KTtou4nB+KwFM4PxCdtNDcZrm/rpS5Z76T2rdXW4h9q4JauC8WciVWyLl4Z7tKVXPhiO5674nzUjEq/fYV4wXjMh/LMASOuaIvFwL7s0VsWmXmwiVULrIImIjBpKkETypUnaIiKjhhIkkTylOQtFqtWIiEj1UoIkki9dYhMRGTWUIInkK3eStmZpi4hULSVIInlKNYIkIjJqqMxfJF99yvyVIMkwSTMkuWX+kbLtaJl/boLfHY8tH9AWLuUH6Fr9UjDe8ezjwfjyf4Qbrt539ZJg/PZIOf+88eFy+wP3Dpftb3PADsH4xDlbB+ONk8cH4zUN4fJ1gDR3fbSs9g3hn9+4bacH42OnPxuML/vXi8H4o8vDywjwp4eC4dhyBDMOjjS33W7n8P6Bmsnh74GucPl/Emlum9bURo/Re8PI33qJaQRJJF9aKFJEZNRQgiSSpz6tRpQfiYhULSVIIvnqUC82EZHRQgmSSJ4yGzb0DugSm4hI1RoVk7TNbDvgK8CxwDTgJeAqwJxza/N4/DTg7cB/AnsC2wLtwMPAL4BfOOcyOY+ZAyztZ7e/c86dVOj3IuWTWZ8zKVIJkohI1ar6BMnMdgLuAGYCVwOPAwcCpwPHmtmhzrlwl8AtTgR+iE+sbgaeA7YC3gH8DDjOzE50zoVeMRfjk7FcjxTx7UiZpK2t0Na7eadW0pZhk+kiaduU16ZJJtJ8tqsjvOtN4WqorrUro8doWxquPnvhlsXB+P3XPhmM37kmXK22YHK4Gmq/120XjG/z2vnB+MSdwtvXTgw3Yk3GjAvGybfaqoe69tZgvGnWumB87MwpwfiYKWPC+7k5XPX2+PMbgnGuCb/kRKvbDgifP0D9tjsF4zWTpgXjyZhwdWASaWKb5jaxjVRgllrVJ0jAD/DJ0Weccxd2B83sO8CZwP8Cpw6wjyeA44G/9BwpMrP/Ae4G3olPlq4MPPZB59yXB/MNSPn1ubwGGkESEaliVT0HyczmAscAy4CLcu52wCbg/WYWeduQ3dC5m5xz1+ZeRnPOrQB+lP3yiKE4Z6lMmVdD77KVIImIVKtqH0E6Knt7QyC52WBmt+MTqIOBG4s8Rve4dazEaRsz+zh+7tNq4F/OufBKXlKx0tz5R6ARJBGRKlbtCVL3heknIvc/iU+Q5lFEgmRmdcAHsl9eH9nsDdmPno9bBHzQOfdcP/teCCwM3LWg0POUwcusf7VvUAmSiEjVqupLbMCk7G3g1a1XfHKR+/8msAdwnXPubzn3NQNfBfYDpmQ/DsdP8j4CuHGAS3tzstvnfkzq5zFSIsFLbEqQRESqVrWPIA0kyd4W/EpnZp8BPoevint/7v3OuZXAl3LCt5jZMcBtwEHAR4DvRQ6xDPhnIL4AJUnDLnyJbfjPQ0apTBdJc+/3eX2aJ3fHO8PVal3RarVXgvHmpc9ET+eF2x4Nxu+7IfyY+9eFK6L2jVWrHTM3GN/2dbsH42N3DG9fO2VGMF4zbmIwTl2451pSRBVb7PeQRiq9aiaE36dvN2FsMF4fidf+NXzBJFbd1vWncHVbZ2ukRx+w1X7hPnP1284Jn1Osuq0pPEaQ5P4eVMVWEt3PKLGEYmLOdnkxs9Pwic1jwNHOuTX5PtY512lmP8MnSIcRSZCcc5cAlwSOvQg/kiQllmYybPjeBTRfcQVdywIltRpBEhGpWtWeIHUv1jEvcv8u2dvYHKU+zOwM4Hz8OkZHZ0eKCtX9lq3f6jkpr5Y//4UN3z4vvoESJBGRqlXtc5Buzt4eY2a9vlczmwAcCrQAd+azMzP7Aj45ehA4ssjkCHzVHEB8DFvKruXaa8t9CiIiUiaDHkHKTjTeCpgOjMGXsq/KrhFUVs65p83sBnyl2mnAhT3uNvwIzo+dc5sAzKwe2AnocM493XNfZnYOvl3JfcAxA11WM7ODgAecc+058aPwC1QC/LrY701KK9PSQttNN/e/kUaQRESqVsEJkpnVAm/GJx2vB3Zjy2Tnntu9CtwO3Ar8wTnXX1+yUvokvtXIBWZ2NPBv/PyfI/GX1s7qse222fufxVeRAWBmH8QnR1347+czZpZ7nGXZeUPdzgV2z84Zej4b24stazOd45y7Y3DfmpRK+113+fYi/VCrERGR6pV3gmRms4FP4Su2ZhBIinJMxjd3fRPwdTO7Gfipc+73RZ5rUbKjSPuzpVntm/A91S7AN6vNZ4L1jtnbWuCMyDb/pPek6l/hG9weABwH1AMvA78Hvu+cu7Ww70SGU/uDW3pKjVv4QWomT2bDhd+Hrh7VFEqQZJikHW10vvJC72Csiq0l3LOta334qW79088H4y/+K9xvDeC+28KPefjV8JuKg6eG+4nt+5ZdgvFtD9s7GG/cMdxzrXbKzGA8Vq2W1oar1dJYb7BgtH9JGu5xlkTOKRk7IRivicS3HhuuYqtragjGa//yWDAerW675t/BOEDHhnAV28xIdduYbbcJxmOVe0lD7+rGtKMtuF2pDZggmdkM4BzgY0D3T34xfnTo3uznq4C1QCtb1vyZg08ODsCP1hwNHGVmZwNnOeeGbYKHc245cEoe2y0jkPhle6l9ucBj/hz4eSGPkcrR8dCWxc7r99qLce9+F+NOWci6L55F63XXZe9RgiQiUq3yGUF6Bj9XZynwS+Ay51y4NbP3SvbjCeAGADNrxF+Wey++6etVZvZfzrnvDOLcRUqmffGWBKlh770AqJ0+naSux3ooGkESEala+SRIzwPfAH7jnCtqtSbnXBu+0/2VZrYz8N9sGY0SqShdL79MZoWvMUjGjKFu55233Jn0GGBUgiQiUrXySZB2c84N2SuBc+4p4CNmNtAcJpGyaH/o4c2f1++xB0ldj3+TXgnSMJ6UiIgMqwHXQXLOpWYWWZe9eEOZdIkMpdz5R71oBElEZFTIt4pthZldBVwK/E3JjVSz0PyjzZQgSRmkbS10vtBraTYy7eFeX23rNgbj65e9FIy/eM9zwfjdi+Pr4D61Mdyn69Bp4Wq1/d4arj7b/j/2D8brZ+8ajNdO2zp8Qo3hiq5MbXgmRxrrrZZExgxq+hlLyISr1WLPDkmsr1jkXGubwt9b0hj+Wc9sCPe3S2oj38M14V5sjy4P9+4DaL3u6WC8ZW1LMD5jr7XB+Litwz3aGnL6zKX9r7hSMvmupN0EvBv4C/C8mZ1rZuGugSIjWJqmvUeQchMklCCJiIwG+Y4gfRq//tGBwNbA54HPm9kD+LV/LnfOrSrJGYoMo8xLK8i84lvlJePHUzc3p0t4jxEkLRQpIlK98kqQnHMXAReZ2Tzgg8D7gB2AfYF9gPPM7Dr8JbhrnXOdJTpfkZJqX/zg5s/r99yTJHdoXZfYRERGhYJajTjnultznGVmR+CTpXcAE/DrGx0PrDGzy4BLnXP3Du3pipRWzxW0+8w/EhGRUaPoZrXOuUXAIjP7JL6lxgfwq2VPwzeGPc3MHsdfgvuNc+7FQZ+tSIl1LO45/6hvu4Ok1+IUGkESEalWRSdI3ZxzLcBvgd+a2Sz8XKWTgT2B1wDfxPdiu9E5d+xgjydSKmma0t5jgnbDgkA/KF1ikzLo2NTCqodW9Ip1tYYryTY8H+65tuLBcFXaXc+Hq5VebI3PlHh9pFpt/3e8Jhjf7ugDgvGGueFan5qpWwXjaX24oiutawzGqY30VotVq8Xi/YkUxMWksR5tmXB/uFh1W820cLwhUsU2sy68fbS67U8PhePAQ8+F/2Y23hru0Td3Vbi6bfr86cF407TeKwt1NG0DteG/uVIadILUk3NuBfAt4FtmtgD4KPBx/J/QG4byWCJDrWvZMtJXXwWgZsoUarffvu9GWihSRGRUGNIEqZuZHYy/5PYuAs1fRSpR++It84/q996LJAn86WoESURkVBiyBMnM5uAvr70f2CkbToAO/PpJvxyqY4mUQq8J2rkraHdTgiQiMioMKkHKtiB5F3606NBsuPsV5D58UnSZc271YI4jMhw6eo4gheYfgRIkEZFRouAEycxqgOPwSdFbgEa2JEUvAb8Gfumce2yoTlKk1NLW1t4tRhYsCG+oBElEZFTIO0Eys33xSdFJwIxsOAFagavxo0U3OOfCU/RFKlj74sXQ1gZA7Y47UrtVuIpGrUakHNrXt/LSw8t6xdrWtwW3Xbns1WD8/nXhhlZrO8JP2bFKNeinWu0NBwXjDXP3CMZrps4KxjMN48IHjlRipTWRl7JYvJhqtRJLM+GqwTRSxZbUhaveksj33DA3vP3MSJ+5Povk9rzvqsXB+OKl4b+91kfDjTZmv9wcjE/Ypvfvv32fqTClQqvYzOwRfMk+bHmFuAOfFP3OORfvaicyArTfedfmzxtfe3B8Q7UaEREZFfIdQdote/ss8Cv8JbRwO1+REajt9js2f954UPhdMOQsFKkESUSkauWbIF0KXJJdPVukqmQ2baLt7rs3f934ukPjG/fOkEp3UiIiUlb5NqtdWOLzECmbttvvgI4OAOp3243aWeF5EUBurxEREalSg14Hycy2Ao4AtgfGOue+Mth9igyn1htv2vx545FH5P9ADSCJiFStohMkM2sCzgc+lLOfr/TYZjLwDDAR2NE5t7zY44mUQtrVRetf/7r566ajj+r/ASrzlzLoaO7glcd6VwKtivRKW9bcEYy3Z8J/r8fMDFeM7RGpVAPY7j/ChQz1sd5qUwqrVkvrw/3EYlVpaU2kIVqh1WrDUd0W6cVG7HuIbh/7WYTjNbHqtl3CVXIz6sNxgNqGcEVc3TUPBuNLnlwbjD+7KlzFNj2nQrN9fgdMiZ5OyRT112BmdcB1wMeAduAmoE/NqXNuHfCT7HHeWfxpipRG+513kVnt1zGt2WomDQeEm2pupgRJRGRUKDZd/jD+stoSYA/n3BuA8AII8Pvs7ZuLPJZIyTRfeeXmz8ccd1y/a38ASpBEREaJYhOk9+NnYHzaOffsANsuBrqA8NirSJlkNmyg5ZprN3899p15DHIqQRIRGRWKTZB2xyc9iwba0DnXBawDphZ5LJGSaL7iStKWFgDqdp1P/T6R9iK9KEESERkNik2QmoDWbPKTj3H4liQiFSHt7GTjj3+y+etxJ59Mkk8Jf6/8SAmSiEi1KraK7SVgtplNd86Fm6xkmdmB+ITqqSKPJTLkmv9wBV3LfVFlMnkyY9/9rvweqEtsUgZJklDb0LvKaXxnuLpp3vhw9dG2sycF4zses2swPvOQ/aPnE6tWY+LMYDjTEO6jldaFq9WiVWmx3moxA80pzD1uGXu0JbFqtYg0U1g1XCbS0y2N9HSr32mv6LGnj50QjDdNmxiMT74p3LsttzKzW0dL7wrNmtryrD9X7F/Douzth/rbyMxqgK/j5yv9vchjiQypzKZNrP/2eZu/Hv+RD1Mzdmxej020kraIyKhQbIJ0Hv7V4WwzOz60gZm9Br8UwFH4pQC+V+SxRIbU+nP/j8yKFQDUzJzJ+I9/LP8H9xpBGuITExGRilFUguScexQ4AxgP/MnMnia7jJOZXWFmjwGPAG/Av4yc6px7bmhOWaR4rTfexKafX7z560lnn5X36BGgS2wSZWbqQzPKjJkwecCPdevWlfs0q1qSJJOTJFmXJMnqJEn6XPtLkqQmSZIrkiRJkyT5WSH7Lnolbefc981sOX5kaMced72jx+fP4ZcCuBaRMut47N+sOe1Tm79uPOooxrzj7YXtRL3YJO4RM/uic+6acp+IDK+zvviF6H1NTZFVwWVIpGm6LkmSC4BzgE8B38jZ5AL8QtV/Bj5eyL4H1YvNOXe1mV2LXzTyEAKLQ48AACAASURBVGBr/KjUy8C/gBudc+H18EWGUds997D6g6eQbtgAQO3WWzPlu9/Jr3ItRiNI0tsLwFVmdgfwBefc7eU+IRkeZ//PF8t9CqPd+cDpwOeSJLkwTdONAEmSnAWcBtwJvDtN03wr74EhaFbrnMvgW43cNNC2IsMtzWTYdOmvePWrX4VW3w0nmTCBaZf+ktpp0wrfoS6xSYRz7hgz+w/gXOAWM/sz8EXn3GOD3fe4WRPY8wO92+BkOsLvPRsmhPubTdxlh/D2c8I912qmbxs9n8yYcEVcWh++XJ3WhiulYr3P0toCX5qGqvqs2P0UWl0XUPCzSU2s6i1SrRapkkvqGsPbN4yPHjqJ/P4nbbV9MD5u9/Aaczs990QwvmnFml5fL2+ZwIZ+ivzSNF2bJMmFQHdCdG6SJKcAX8N3/Hhzmqbhxm/9KF9No0iJtd1zD6tOOJFXzzp7c3JUM2MG0//wO+p3izfi7JcSJOmHc+4fzrn9gJPxC+ouNrOLzSz8yiEiQ+U7wEbg80mSvAvfB/Yl4Ng0TVcXs8NBp73ZxrU74ydpR94meM65WwZ7vGKY2XbAV4BjgWn4H9pVgDnnwm2Gh2g/ZnYIcDZwMFvWg7oYuLCAhTYlT11r1tL69xtovux3tN9zT6/76ubPY9ovLqZu9uziD6AESfLgnLvMzK4APoF/V3uSmV0EfL2Q5xwRyU+apmuSJPk+8N/A74D1wHFpmi4rdp9FJ0hmthPwv8DxQHiMrrd0MMcrVvY87wBmAlcDjwMH4q9XHmtmhzrnBswui9mPmb0VuBK/ivjvgDXAW/DXSw8FThyK73G0StOUrhdfpOPhh+lY/BCtt95Gx4MP9k1camsZ/4lTmfjZM0ka8/lTzfsEhm5fUnWccx3ABWZ2DfAr4LPAR8zsXOC7zjl1FxAZWn/GJ0gA70vTNLxCZZ6KSljMbHfgFmAyvvlCK7AK35+t0vwAn9R8xjl3YXfQzL4DnIlP8k4d6v2Y2UTgp/ifyRHOuXuz8XPw87VOMLOTnHOXD+7b6y3t6qL9zrtoOOS1g5uAXCZpJkPa2kq6aROZdevIrF3rP9b4264XXqBz+fN0LV9O1/Llm3upBdXWMubtb2fiGZ+hbscd49sVosfPVK1GJJeZzQL2zX7sk73dAf88mQFWAAZ80sw+pYo3kaGRJMk2wG96hHbDJ0xFK3ZE51z8JbUlwEeB251zFfdqYWZzgWOAZcBFOXc74GPA+83sc865TUO8nxOAGcCl3ckRgHOu1czOBm7ED78PaYLU8sc/sfaMM2k44ACajjwCmppI6ur8kvtp2ucjDcSi20Dv+7q6SLu6oLOTtLMLurbc0tkZv6+jk7StjbSlZfNHpqWFtLVl81yhotXUUL9gAWPedBxjT3gntTNmDPpn2lMyCi6xpZkMdHZCJuN/95lMr4++sdRPAM1koKvLf53JQHesW5Js+ehuapck/measDn5TCZOpHbqyOttbWYv4d9Edf+RLAXuAr4P3APc55zbZGaz8R0G/pRNkn5YlhMWqRJJkkwGrgdmA18CvoCfi3RRmqbR1/aBFJsgvR5/yeydQ1GhUUJHZW9vyFbbbeac22Bmt+MTn4PxCctQ7qf7MdcH9ncL0AwcYmaNzrk+WYGZLQQWBh4bbTmftrez/rzvANB+zz195uBUo2TSJOp3242GPfegfp99aHr966iZMqWEB6yMUbk0TUnXryezeg1dq1eTWbOazOo1ZNauJd24kUxzM2lzM+mmTaTNzWQ2NZO2NENbO2lnJ2l7u09eO9p9wtrRAR0d/rar/APBjUcdycQvfIGGPSI9v8rAzPZ2zvU3ZH8PcHf29h7n3JrQRs65Z4H3mdl64IvAgAlS/Q67MOM9X+od7GoPbpt0FbaySibSr6yrv4quQqu9Sr19iQ30VqgsPdwix8zETjby1JXWhKve+ptRnGmMVDGO3ya8/VZ7hne0bzg8Jud5tvbyy+D55cFtkyRpwk972RP4SpqmX02SZCLwefwgxLfDRxlYsQlSBthQ4ckRwPzsbbiWEJ7EJzbz6D9BKmY/0cc45zrNbCm+ymUu8O/APucAh/dzTn2kra00HXE4my673I8AjFBJUxPJmDEkkydTM2VKj4/J1M7airrtd6B2h+2p2247ksmTh/dS4jCPIKWZDJ3PLKXj4YfoePQxOpcto+vZ5+h87jnSjRtLfvxyabvpZl654w5m3XMPtVNLmPAW5ioz26+fxCfYdqkft1DgwnUiskWSJLXAb4HDgJ+kaeqyd/0f8Engv5Ik+UExJf5QfIL0CHCQmY1xzvUzCaTsutPcVyP3d8cnl2A/gz32MuCfgfiCHvvupWbiRCZ/8xuMP/XjtFxzLZn160k7O/2IQFdX70sc3Zc5Ekhqavret3kbelwGyfmorfWX7+pqSWrroK6OpLYW6uoC99VCbR1JXa2/rzsJyv1obPTnU6mGIUHqWr2a1r//nbab/0nrbbeSrov9CZVQ9+8wSfzl2c0fCUnS+2uSGv8767lNTa3/vPtvJffSLfS4dNvjEm57B10vvQTAuPedXEnJEfjh+yvM7A35VqCa2fbOufBbXz+6rEINkeJdBLwdX03+ye5gmqavJEnyA/wo0qn4JQAKVmyCdAG+KuvD+OvrI1X3q91gX+mK2U+/j3HOXQJckhs3s0UMMLJUN2cOEz7z6QJORfJWwgSp7e672fiTn9L693/kNQKYjBlDzfTp1EybSs206dROm0rN1Kkk48eTjB1LzbhxJGPHkowbSzJmrP+8qdEnrvUNJPV1JPX10NDgY923dXVlneDfsWQJG753ARM+86mBNx5eV+Ordi/AL0bXLzM7FF/FOit0f7bc/8qhPEGR0SJJEsOPwN4KvCewSva38EnT/0uS5IdpmhY8mFNUguSc+4OZ7QecZ2aTgPOdc0UNYZVY91vv8AVTmJiz3VDuZ6iOLZWkBIlDx5IlvPqlL9N2223B+2umT6d+r71o2GN36ubPo26H2dTO3sEnQxUyJ2oo1c+fz9Qf5NZCVIT34+cXnWpmDzjnoo0vzewUfOVrZIKHiBQrSZJT8ZOxHwGOT9O0z5IZaZquTJLkh8Dn8InUdws9zmCa1f63mb2KX8r7bDNbhl84MSZ1zh1d7PGKtCR7Oy9y/y7Z29jcosHsZwmwf/Yx9/XcOLu45o5AJ/DMAMeWSjXIEaQ0k2HjD37oJ9a3955w27DffjS96ViajjiCuvnzqzIRGmmccxvN7G34idjfN7NHnXP/6rmNmSXAefj10RJ8M2+pUs3NlTguUP3SNP0R8KM8tvs8/jJbUYqa7GFmiZl9D/gq/kmgET8p+YgBPobbzdnbY8ys1/dqZhPwizW24BvZDfV+unvTHRvY32HAWOCOUAWbVLAhusSWtrWx9lOfZv03vrklOaqtZey7TmTmopuYcc1VTDj1VOp33VXJUQVxzi0BPoCv8bnSzDaX7WTXPvsrPjnqAD7snDuzLCcqIoNW7AjS6UD3JJebgH8AK6mwhSKdc0+b2Q34CrPTgAt73G3AOODH3WsXmVk9sBPQ4Zx7utj9ZF2BXy/qJDO7sMdCkU34UTfIo7xXKliRCVLa1sbqhafQdsutm2P1e+/FlPO/Q/38+f08UiqBc+5qM/sacA6+su31+AncV+PfKL4MvCN3dGkwnlrVzGeuebxXbNLYcB32dlPDDWN3mhKOz548Jhif1FgbPZ8x9eGkva4mHK+N1JhHNo/O5hxJbxWGaoZitGw/oivyvBR7uuqIHKCtM37gjR3hl/oVG8JLTzy5JrwU0WMvrg/G1zV39Pp661WbCP+VllaxCdLH8L//c5xzXx/C8ymFT+JbhFxgZkfjS+oPAo7EXxI7q8e222bvfxZfZl/sfnDOrTezj+ITpUVmdjm+1cjx+CfRK/AT3WUkGeRK2mmasu6ss3slR+M+8H4mffUrfoK0VAQzOxN4EHgw1DvNOeey8zCPw6/Wux++IvU+4G3OuReG83xFZOgV+4w8Bz9aVFTp3HDKjv7sz5Yms2/Cz5W6AN9kNrimyVDsxzl3lZkdjk+e3smWZrWfBS6oxNXHpX+DXUl70y9/SfNlWxZPn3DmGUz43Gd1Ga3ynEd2EMDMlgMP4BOmB/BJ03PAe/GTto/CD25chr+sph5rIlWg2ARpFTBhpDwRZNchOSWP7ZbRzyhuvvvJeczt+GRKqsEgEpmOp57m1a98bfPXY97xDiVHles6YG/8qPIO2Y/NC0Ga2Tp8wvQMvkjj18CHnHMjd4VWEeml2ATpOuCjZra7c+7RoTwhkYpW5AhSmqa8+j9nQZufk1+/xx5M+b9vKjmqUM65NwOY2VR809m98Yu0LgB2xfeiPJItU03eB7zLzB4HFvf4eMg598rwnr2IDIViE6Qv499N/cjM3uSc2zB0pyRSwYpMkNpuXkTb7bf7L2prmfKd80jGlGPaoRQie+n8Rnq0IjKzBmAPeidNe+HXPNsr+3FydvOUQSynIiLlU+w/7jzgf4DzgaVm9iPgYfpfBwnn3C1FHk+kMhSRIKVpyvpvb+mXOO5976V+992G+sxkmDjn2oH7sx+bmdmO9E6a9gG2H4pjrnu1lZtvWdYrlkRKwOrqw6u3TN9mYjB+9N5bB+MH7xDvwLT9pKZgfHx9uPKtsS5S3RYZQK2NfG+FrktTzhHaQos4MgNv0ktXpPqsK3LY9sgdbZ3hI69pjV8tXrIqXJX2j3+vDMYfeGhFML72xfD2NXW911c9blYzY8J/ciVVbIK0iC1Dywm+I/VA9E5KRr4iEqT2O/5Fx+KH/BdNjUw484wSnJiUm3NuKbAU3xcKgGynAREZgYpNWJ5j6JZ5EBk5ikiQNl588ebPx514IrUzZw71WUmFcs6plZDICFVsL7Y5Q3weIiNDzxH7PBKkrpUrffPZrHEf+UgJTkpERIZaUa1GREavwuY0NF/5R+jyq842HHQg9TvvVIqTEhGRIaYESaRI+UzCbLn22s2fj333u0p5OiIiMoQGvMRmZnOdc0PacT7b8HW77Gq0IiNHAXOQOpcv3zI5u76eMW98YwlPTKpZmqZ05VQbZTo7gtuuX78qGF+zPLzv9avDHelf2X/b6PkcMW9GMD5v2rhgfFwm/F68KVLdVhf514pVvdXEqtUi/6PDUdxW6EL7mcgDYlVpsSq29ki8pSMcX9Uc7p/2eKRSDeCaB14Mxh+++9lgfOVjtwfjdU3jg/Hxs+b0+jrNlKfNaz5zkB43s8uAr2c7WRct2wz2FOALwC/xbTtERozerUb637b1+r9t/rzx9a+jZnK8bFpERCpLPgnS3cD7gfeZ2a3A5cAVzrnV+RzAzBLgCOAk4B3AVGATfpVZkZGl11vP/jOk1kWLNn8+5phjSnM+IiJSEgMmSM6515nZ8cDXgcOBw4CLzOxJfOfqh/C92dYC7fiO1lOAHYH98YuljcPPbu0ALgK+quX3ZUTK8xJbpqWFtn/dufnrxqOOLOVZiYjIEMurzN85d42ZXYvvYv8R4M3A/OzHe/p5aPeryTPAxcAvnHP9rrYtUtHyTJDa77prc9+1unnzqNs2Pp9DREQqT97rIDnnUuCvwF+zDRyPBA4FDgS2BqYDjcAa/IjSEuB24Dbn3L1DfN4i5ZFngtRr9Oj1ryvlGYmISAkUu1DkGuDK7IfI6JHvCNKdd23+vPHgg0t5RjIK1DfWMX3bCb1imc7w39/GceEmyOteCpexPf/wQ8H4oo545VB7pH9X5/zwKvG7TBsbjE9oDPdua6oNV73VRRamibRuI7KbsvaBiBSZFdxbrTNWrRb53azcFK56XLJqYzB+9f3hSjWAh+8I12u9/MitwXjD+CnB+JQ5e4Tjs3pvX9+wCT9DZ3hpHSSRQuSxknampYX2xVtqEBoOOrDEJyUiIkNNCZJIQQYeQepYvBg6/Ludul12oXbatOE4MRERGUJKkEQK0eMSW+wKW/uDPUaP9t2n1GckIiIloARJpABJHkvwdvS4vFa/996lPB0RESkRJUgixYoMIbU/tGXSa8MCJUgiIiNRUVVsIqPWACtpZ9aupWtZth9RfT31u+46POclVW1sUx2v2a73XLZY1dMr69vC+5jUGIy//MzzwfiKxx+Nns9tkWPHKqu6dg1Xt+00JVzdNqkp/NLUEGnGVh95q18buQw+DK3YooVy0Sq22BuuSBlbW6SK8ZVNhfVW+/ODkb5qkUo1iFerjZm2TTC+9W4HBOMzd5gUjM/KqXoc+3I9hP+sS0ojSCKFGKDMv+foUf1uryFpDL8oiYhIZVOCJFKIARKkjp4TtPfaazjOSERESmDYEiQzmzhcxxIpmUJGkDT/SERkxCrpHCQzS4A3Ah8Ejsc3rRUZuQZKkHqOIKmCTURkxCpJgmRmu+OTovcBs/Bz4sq4uLvIEOlnJe2ul18ms2KF36ypibpddhnGExMRkaE0ZAmSmU0D3otPjLpXxxuOYgGR4dPPCFL7Qw9v/rx+zz1J6lQkKkNjwph6tttxaq9YrOppXXO4Z9UL08MVY4+NbwjGn39ifPR8XnkqXOF0ZzAar7g7cv6MYHxOpLpt2pj6YDxW3VYXadIW7dEWUdPPS1km8t4/tpBs7GfREW6hRmu0t1q4rOvJ1c3B+LUPhKvVHrvzifD+H7s9fELAxG3nBeM77LMgGN957tRgfJdZE4LxaTl/k83r6+gqQxXboJ7BzawOeAs+KTouu7/uv6QlwGXANcD9gzmOSOWIr6Td0XP+kSZoi4iMaEUlSGa2Pz4pOgmYypZXjeeBy4HLnHMPZLfVvCOpHv2MIHX0GEFq2FsJkojISJZ3gmRm2wAn4xOj7tXvEmA1cAU+KbplyM9QpIIkkQQpTdPeFWxKkERERrS8EiQzux44Gr8sQAJsAq4Gfgvc4JzrLNkZilSSSC+2zIoVZFau9JuMG0fd3LnDeVYiIjLE8h1BOgZfhXY3cD5wrXOupWRnJTIibBlB6jV6tOceJDVag1VEZCQrdA7S/sDHgQlmdqVzbl0JzkmkcvUYQWr5459Y3dbOxM+eQcfiHg1qNUFbhlhTXQ1zJo/Ja9vWieGqp+0jj58Vid8xLlzdBvDsv8MtdFY981Qwfk9kP7GKrtfPmx6Mx34GUyLVbWPra4Px2shIcKTojWJWqYlVGUaK0tjQFr4Qs6o53FvtiUhvtb89vCIYX3LXk8H4K4+Haw+nzA1XpAHM3fc1wfgBu4arEufPCq8TPTXyexuT01zvybpawt9taeWbIL0dP/foP4EjgSOAi7KX3i4HrtaIkowKOU+srX/5C61/+xu1s2Ztjmn+kYjIyJdXguScuxq42sym4hd//CCwL3517LcAzWZ2NT5Zul5zkqRqhd5hdnbS9fyWjuiNBx40fOcjIiIlUdAlNufcGuBC4EIz2w1YiE+YtsYvEvkeYJ2ZdVe1LRrSsy2CmR0CnA0cDDQBTwEXAxc657ry3McuwDvwbVN2AbYC1uLXRfuuc+7mwGMWAr/oZ7efcM79KP/vRCpCZGi+W/0+C6jdZuthOhkRESmVoheKdM49Bvw/M/tv/CTuhfgRpSnAR4CPmNlL+Gq3sjCztwJXAq3A74A1+BGv84FDgRPz3NVXgXcDjwHXZfczH//9Hm9mpzvnLog89mrgwUD83jyPLZVkgARpzHHHDdOJiIhIKQ26F4JzLgNcD1xvZhPxi0d+ADgE2AY4dbDHKEb2XH4KdAFHOOfuzcbPAW4CTjCzk5xzl+exu+uBc7sXv+xxjMOBvwPfMrM/OOdeCjz2KufcJYP4VqSixBOk2tk7MPakdw/juYiISKkMabMo59x64CfAT8xsJ/yo0snA7KE8Tp5OAGYAl3YnR9lzbDWzs4EbgU/g5031K5bgOOf+aWaLgDfgE8IrB3/aUtECI0hjTzyBsSeeSMOBB5DUh6syRAajobaGrSeEK8dydXSFq6eam8IzCiY2hV8GJo+N/y3fHqk+ejTS5CxW3XZvZ/hcW9rD53popLpth0h129Smwqrb6iM93foTq1aL/R42tseq1cI99Jas3BiM3/Loy8H4E/c8HoyveSrc8WvqzvsG4/MO2DUYBzhs962C8fkzw/37pkf+lsY3hP/2cn8Pz9XVVHQVW8Gcc08D5wDnmNmR+FGl4XRU9vb6wH23AM3AIWbW6JwbTBu87r/q2MT0BWZ2Bn7+0wvAzc655yPbbpadw7QwtL8izlGGSBJIkBoPP4zGQw8pw9mIiEipDEu78ewk5j4TmUtsfva2T6ti51ynmS0FdgfmAv8u5gBmNhu/wngzPukKOT3n6y4z+xlwhnOutZ/dzwEOL+a8pIQCCVLNxEllOBERESmlYUmQyqT7VevVyP3d8cnF7NzMGoHfAI3A/3POrc3ZZCnwaeAGfBPfScDrgG/gF9uciK/8i1kG/DMQX8CW702GWyBBSiaGF0ETEZGRq6ITJDNbRmHzl37jnDs5z227X+kKXiLVzGqBX+Er4X4HfDt3G+fcP+md4DQDfzCzO4HFwHvM7Fzn3OLQMbLzni4JHHsRGlkqn9AI0iQlSCIi1abSG0Y9DSwp4OPFHo/tHiGKjbZMzNkuL9nk6Nf4JQJ+D5zsnMs7yXLOLccvFQBwWCHHlgoQmMNZoxEkEZGqU9EjSM65owfx8CX43nHzgPt63mFmdcCO+InVz+S7w+zjfotPjn4LfCDfxSZzvJK9HVfEY6XCJJN0xVNKqzZJGN8QrrzKFWlvxvjG8ONj8Qn9HG9c5L4xkfj9deHqsFh120Nd4YZlr7aEK70O2SXSu23q2GA8VrnXFKnC60+siq2lI/w9rIl8D0tWrA/G73n8lWD8mfvDU2fXLXs4GJ+x68HB+PyDdgnG37jnrGAcYN708EvX9LHh/n0TGsM/77rIjzu3V16sd16pVfoI0mDclL09NnDfYcBY4I58K9jMrAG4Ap8cXQq8v8jkCKC7F0XeyZlUiNx/1Pp6kqam8pyLiIiUTDUnSFcAq4CTzGz/7qCZNQFfy375w54PMLNJZrarmW2dE28E/gS8Ffg5cEp2gcwoM3t9IJaY2ReB12bPLbQEgVSynASpZuLEYOm/iIiMbBV9iW0wnHPrzeyj+ERpkZldjm8Rcjx+CYAr8BOse3o7vn/aL+m9BtGPgDfhk5oXgC+ZWe4hF+X0nrvFzJ4A7sk+ZhJ+Uvce+Anb78surCkjSU4ylEyYUKYTERGRUqraBAnAOXdVth3IWcA72dKs9rPABQVMrt4xezsd+FI/2y3q8fm3gQPxC1ZOBTLAc8BFwHecc7q8NiLlJEhjwiv4iojIyFbVCRKAc+52/OhPPtteQqC03jl3RBHH/a9CHyMjQO4IUm1+E2dFRGRkqfoESWQo9ZlvVKcESUqvNoExOSU/mQKXcOvKhOfK1deE42P6+dtujNzXGKkCq40c457I/l95akkw3tEarqlp3dQejO82Z0owvm2kui3Wf66/Kqr2SMXd6o3hc3pyxYZg/Kln1gTjzz3wYDC+4aVwBeDM3Q4Nxnc7eF4w/pZ9tgnGd5kW/hkBzBwX7gvYFClLq49Vq0X+LnJ/3JHNSq6aJ2mLDL0+/7lKkEREqpESJJFC5F5i0wiSiEhVUoIkUojcoV7NQRIRqUpKkEQK0WeStqbxiYhUIyVIIoXInYNURGsCERGpfHp2FxkMjSCJiFQlPbuLFKLPJTa9x5DSS5JQY8/Cap/TyJ9qrPy/ria+jEBdTbgpaazZa32B5f93Ro678onHgvGlrRuD8eaN2wXjz84Kr4A/Y2K4fD12ngAt7eGWnCtWNwfjK597NRh/6bHwogctq18Mxrfao083KwD2PGR+MP7mBeFy/l0jjWdnjAv/jgEaI82HG2rD8dgyCbEfa25YZf4iI0LuOkh6jyEiUo2UIIkUQusgiYiMCkqQRAqQu5K2LrGJiFQnPbuLFKJPqxFdYhMRqUZKkEQKoUtsIiKjgt7+ihQiJz9SqxEZDkkC9ZEKocHqiuw20ncUiDe4ra0Jv6TU14YrpWpfs1Xk2OH93xGJr3j80WD8xcdbg/HmV7cPxldPbgrGayJVWwDtLZ3B+NoVa8PHeOr+8H42hrcvtFrtrfuGq9XmTx8fjM8cF27Qm9scuafY7yf2JxqrAsy3Oq2fXsElpREkkUL0WShSCZKISDVSgiRSiD6TtJUgiYhUIyVIIoXQCJKIyKigBEmkEEqQRERGBSVIIoOgS2wiItVJVWwiBdEIkgy/hCRaOZSvNNJaLfYnnIm3YiO2PmptTaTnWqQMabeZ4cqqukg5VEOksuq2+vA3seKpZ4LxdS8tD8ZbN00PxmvqwpVeAK3rVwXjG1csC8Yzne3B+Db7HhOM73ng7GD8+H0K6602fWy4t9qY+sjPup+/t1hVWqyKrabAMrTczZMC+w4OFY0giRRCl9hEREYFJUgiBejbakQJkohINVKCJFIItRoRERkVlCCJFCL32nhkzoWIiIxsenYXKYRGkERERgU9u4sUos8kbb3HkNJLiFeCFbSTgDRS3tbf8WIz72JVTLEKvFhPt91mhCuxJjSEjzxjYriH2o3Txgbjq15cH4x3dmSC8bSfkr76pnAl3qTt5gXjU7aZGYzvs9esYPw/XhPefn6kWm1qU/hlvTFSAdgQ+aX11/ovVsUWU+izZJ+5ngU+fqjo2V2kEH0maes9hohINVKCJFIIlfmLiIwKSpBECqEESURkVFCCJFIQrYMkIjIaKEESGQwlSCIiVUkzTEUKkFtdoQRJhkXSf1XR4PZd+I5jNV2xqrRYEVhDbfiOWH+w8fXhyq1tJoSr2PbbdlIw/vTa5mD8+TXh+KvNHcE4QFtnuPJt8thw/7bdtpkYjO8yNfy9zZoQ7qE2PtJ/rrGusIrB2K+/mKrJQbYL3KzPbspUxqYRJJFCqNWIiMiooARJpBC572TqlCCJiFQjJUgihcgdQapRKWd+UAAAELhJREFUgiQiUo2qfg6SmR0CnA0cDDQBTwEXAxc657ry3MccYGk/m/zOOXdS5LEfBE4DdgO6gAeAbzvn/pzntyCVpE+rESVIIiLVqKoTJDN7K3Al0Ar8DlgDvAU4HzgUOLHAXS4GrgrEH4kc/9vA54DngZ8CDcBJwLVm9mnn3PcLPL6UmyZpy/DaGWDlypVcfvll5T6X4kUmaccme6eRezLh+dB0RtqltEYmULdEWoqM6Qy/Z67vircayUSOXRdpQ7R6efg5oyUy6frxaCuQwiZd1xQ46bqoedElmky9cuXK7k93Ls0Rwqo2QTKzifikpAs4wjl3bzZ+DnATcIKZneScu7yA3T7onPtynsc/BJ8cPQ0c4Jxbm41/C7gP+LaZ/dk5t6yA40u5qdWIDK/xAO1tbTy/fHm5z6XqRXvMDeExOjaF468O4TGqWLjxXYlU87P7CcAM4NLu5AjAOddqZmcDNwKfAApJkApxavb2f7uTo+zxl5nZRcA5wCmAK9HxpRTUrFaG11JgR2AjfnqAyGi0Mz456m+qy5Cr5gTpqOzt9YH7bgGagUPMrNE515bnPrcxs48D04DVwL+ccw8Vcfy/4hOko1CCNMLkJkjV/C8k5eac26fc5yAyWlXzs/v87O0TuXc45zrNbCmwOzAX+Hee+3xD9mMzM1sEfNA591yP2DhgW2Cjc+6lwH6ezN7Oix3IzBYCCwN3LcjzXKUUtA6SiMioUM3XB7qXUI1d2u2OT85jX83AV4H9gCnZj8OBm4EjgBuzSdFQHntO9hi5H+GlYWVY9F1Ju5r/hURERq+KHkEys2XA7AIe8hvn3Ml5btv9ShcvT8hyzq0EvpQTvsXMjgFuAw4CPgJ8L98TzePYy4B/BuILUJJUPrlVGrrEJiJSlSr92f1pfIl+vl7s8Xn3KE0smZiYs13BspfqfoZPkA5jS4I00LEHGmHCOXcJcEluPHtJ7/DCz1ZKIdEIksiIZ2Z/Bv4T+Lxz7rxyn49UhopOkJxzRw/i4UuA/fHzfO7reYeZ1eErQzqBZwZxDIBXsrebL7E55zaZ2QvAtma2dWAe0i7Z2z7zo6TC9VkosqL/hUQkP91zOx8s61lIRanmt783ZW+PDdx3GDAWuKOACraYg7O3uYlWf8c/LmcbGSnUakSkqpjZNHxRDShBkh6qOUG6AlgFnGRm+3cHzawJ+Fr2yx/2fICZTTKzXc1s65z4QWbWkHsAMzsKODP75a9z7v5R9vYsM5vS4zFz8K1H2oBfFPg9Sbmp1YhIteleSmG5c251Wc9EKkrVXh9wzq03s4/iE6VFZnY5vtXI8fglAK7Atx/p6e34pOWX9C6xPxfYPTv/5/lsbC+2rHV0jnPujpzj32Fm3wE+CzxkZlfgW428G5gKfFqraI9AajUiUm32zt4+UNazkIpTtQkSgHPuKjM7HDgLeCdbmtV+FrjAOTdgBVvWr/DJ0wH4y2P1wMvA74HvO+dujRz/c2b2EPAp4GNABrgf+Jaa1Y5QWgdJpNpE5x+Z2QTgUuBtwHPA25xzSqRGiSSNNNqTytRdxTZ79mwWLlxY5rMZfTpfeIGXDzx489db/et26nbYoYxnNKqVqDWmjCZm9jCwB/B259xVPeLz8c3Jd8V3XzjBOfdKeC9Sjap5DpJICegSm0i1MLNGfAIEPUaQzOytwN3Z+34M/IeSo9Gnqi+xiQy13JW0dYlNZETbA/86uC7bSDwBvozvldkJnOqc+3EZz0/KSAmSSCH6rKStBElkBOueoP2gmU0CfoNfMHIl8E7n3G1lOzMpOyVIIoXoU8WmfyGREax7gnYbcA9+Ed/78ZOxl5ftrKQi6NldpBB9LrFpGp/ICNadIL0xe3sT8GbnXEuZzkcqiJ7dRQZDrUZERrK9sre/yd7uB6gsVQCNIIkUpk+rEb3HEBmJzGwuvnF4B/Ah/IDBe4BrzOwg59y6wGO2xjdRv8o5994e8QOBRcAfnXMnD8PpyzDQs7tIIdSsVqRadE/Qftw51w58GN/YfB7wezPrU4GRbTz+I+DdZjYPwMxmA9cA9+ITLakSSpBECqFWIyLVonv+0WKA7Lyjt+G7JLwBOC/yuHOBVuB/zGwi8GdgPX6hyfaSnrEMKyVIIoXIWXlel9hERqxeCRKAc+554B1AO3C6mX0490HOuZfxjc7fB1wHbA28SY1uq4+e3UUKkcmU+wxEZGj0SZDANxoHPpH98gdm9rrAY8/Dv34eiF8S4KmSnaWUjRIkkUJ0KUESGenMbDJbqtUeyr3fOXcxcAHQAPwxO8+op7Pwr5+1wNoSnqqUkWaYihQgTZUgiYx02Qq1fpsdO+dOB07PjZvZGcBpwJmAw7cmOXHoz1LKTSNIIgVIVLUmMmqZ2Vvwl9e+4Zz7LvA94J1mtnf/j5SRSAmSSAFqt9qKxiOPAGDc+7XcichoYWb7ApcBV+IvsYFPkDYCVq7zktJRgiRSoGmX/pKtbr2FSd/4erlPRUSGgZltB1wLPAJ8wDmXAjjn1gLfB95qZvuV8RSlBJI0p2xZKpuZLQIOnz17NgsXLizz2YiUVb9zSEREBkMjSCIiIiI5lCCJiIiI5FCCJCIiIpJDCZKIiIhIDiVIIiIiIjmUIImIiIjk+P/t3WuMXGUdx/FvDVCk0HKJpFC1lCLgpRdDSWlBwIqAVzBWbYyKRsVLQUUsYiT++atNjJSoCGiiwcZLwosmlkiCQeVSoCiBgEaBcq9a6IsqQa3QAq4vnjMynu5sd5adnZ2Z7ydpnp4z55l95tmT7G+ec87zGJAkSZJqDEiSJEk1LizVe44A2Lp1K2vXru1yU6Tu2bx5803APRHxuW63RVL/MSD1nn0BduzYwebNm7vdFqmbTup2AyT1LwNS73kUmENZIPGhFscsBGYATwH3TFC7Bon923mj7WP7X1JHuBZbH2qs1wbcHBEnd7c1/cf+7Tz7WFK3eZO2JElSjQFJkiSpxoAkSZJUY0CSJEmq8Sm2/rQWuAl4rKut6F9rsX87bS32saQu8ik2SZKkGi+xSZIk1RiQJEmSagxIkiRJNd6k3UMyc0/g05RlGF4PvAbYE/h4RPxwN3XPAlZWdZ4H7gbWRMS1LY5/KXAhsAKYDfyDctNsRMR94/F5ek1mvhz4KnA6cBDwBLAeyIh4spttm2wyczllJuyFwAJgP+BnEfGBEeosBS4CjgP2piylcxXw3Yh4vkWdts5rSRotR5B6yzTg28CHgZnA1tFUysw1lKeCDgF+APwUmAf8IjPPGeb4qcCvgK9QgtF3gF8D7wLuzMzFL/Jz9JzMnAvcBXwEuAP4FvAI8Fng9sw8qIvNm4wuAs6hBKQtuzs4M88ANgAnAj8HrgD2ovTz1S3qtHVeS1I7DEi95d/AW4FDI2Im5dv1iKpv5ecDDwPzI+K8iFgJHAP8HViTmYfVqn0eOB5YByyOiC9GxPuB5cA+wFWZOWjnzpXAwcBnIuLMiLgwIpZR/oAfBazuausmn/OAI4HpwKdGOjAzp1MCzvPAyRHx0YhYRQlXtwPLM3NFrc5YzmtJGrVB+yPX0yJiZ0RcFxFPtFHtk1W5uvkyUEQ8RvmWPpUyKgJAZk5pqnNBRPynqc41wC2UyxknjelD9KDMPBw4lTInzxW1lwPYDnwwM6dNcNMmrYi4MSIejIjRzCOyHHgZcHVE3Nn0Hs9QRqJg15DV1nktSe0yIPW/ZVX5y2Feu652DMBc4JXAAxHx6Cjr9LvGZ72+OTACRMQ/gdsoI2vHTXTD+sRI5+gGysjp0urS72jqDOI5KmmcGZD6WDWiMQv4V4tRpwer8simfUdV5QMt3na4Ov3OPumslv0bEc8Bj1IeKDkcxnxeS1JbDEj9bUZVPtXi9cb+/V9knX5nn3RWu/3r70NSx/mY/wTLzMcoj82P1oiPRo+TdtabmTKGOv3OPumssfavvw9JY2ZAmngPA8+0cfzjL+JnNb5Jz2jx+nDfxHdXZ/owdfqdfdJZ7fbvWM5rSWqLAWmCRcSbJvBnbc/MLcCszDxkmPs1XlWVzfd+bKrKVvdvDFen39knnbUJWETp37uaX8jMPYA5wHOUeafGel5LUlu8B6n/3VCVpw/z2ltqx0AZ4fozcGRmzhllnX53Y1WeWp//KTP3o8wZ9TTw24luWJ8Y6Rw9kfKE4MaI2DHKOoN4jkoaZwak/vf9qvxyZh7Q2FlNorcS2AH8qLG/mremUeebzYGgmu34DcC9wM0dbfUkEhEPA9cDh1H6rFlSZjj/cURsn+Cm9Yt1wDZgRWYuauzMzL2Br1eb36vVaeu8lqR2TRka8j7GXpKZFwJHV5uNda428sKjzbfW12XLzEsps2P/lfLHaC/gfZT1xM6NiMtrx0+lfPteCtwJ/IYyN9J7gJ3Asoj43bh/uEmsWmpkI2U27WuA+4DFwBspl3KWRsTfutfCySUzzwTOrDZnAqdRLpHdUu3bFhFfqB2/jnJ/3tWU2bDfSZkCYB3w3vqkk+2e15LUDkeQes/pwFnVvwXVvqVN+06oV4iI8ynrt20FzgY+BPwJeMdwf0SqSxmnUBZm3Z+ybMSbKQuzHjto4Qj+N4q0iLL212LKMhdzgcuAJYajXSzkhXPytGrf4U37ljcfHBHrKbOzbwDeDZwLPEsJQCuGm5G73fNaktrhCJIkSVKNI0iSJEk1BiRJkqQaA5IkSVKNAUmSJKnGgCRJklRjQJIkSaoxIEmSJNUYkCRJkmoMSJIkSTV7dLsB0mSRmdcCbwNWRcSabrdHktQ9jiBJL5hflX/oaiskSV1nQJKAzJwGbAc2Ab/vcnMkSV3mYrWSJEk1jiBJkiTVeJO2BGTmeuAM4EsR8Y1q393AQmB1RFxUO/544FZgKzA7InZOcJMlSR3kCJJUNG7Qbr7/aEtVzqofHBG3AXcDM4FTO9s0SdJEMyBp4GXmdOCwarM5ID1elbsEpMrGqjyhA82SJHWRAUkqo0dTgG0R8XjT/pYjSJW/VOWcTjVMktQdBiQJFlRl/fH+3Y0gTa1K7+WTpD5jQJJaB6TGCNKMap6kuiVVeX9HWiVJ6hoDkrT7ESSojSJl5mzglGrzmg61S5LUJQYkDbTMfAnwumqzvsTIlqb/1y+zXU65tLYhIu7oUPMkSV3ivRMadEcA+wDPAvfWXtsG7AT2oikgZeYngLcDzwAr62+YmdcBBwIfA1YDJwNPA1dGRI77J5AkjTtHkDToGpfX7q9P9hgRQ8AT1eYsgMxcAlxW7Ts7Iv44zHvOB6YB11NC1yrgQeDizFw2vs2XJHWCI0gadK3uP2rYAswGDs3MVwPrKSNKF0TET+oHZ+aBwKGUUaljIuKRav96yqzbi4AbxvUTSJLGnSNIGnS7C0iNG7WXUILNwUBGxCUtjm/MyL26EY4qO6rSJUkkqQc4gqRBN5oRJIBjq/JrEXHxCO/XCEjra/uPrspNbbVOktQVBiQNrMw8AHhFtVl/gq2hEZCGgFURcelu3nYe8GREPFTbv7AqWwUxSdIkYkDSwIqIJylLjIx0zCVAq8tpw5nP8CFoAbsuZSJJmqS8B0kaJ5k5BXgtcM8wLy/A0SNJ6hkGJGn8zKU83v9/AakKTvMwIElSzzAgSeNnXlXWR5DmAvvS+j4nSdIkM2VoaKjbbZAkSZpUHEGSJEmqMSBJkiTVGJAkSZJqDEiSJEk1BiRJkqQaA5IkSVKNAUmSJKnGgCRJklTzXx7Ikv3GvB4eAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "dark" + }, + "output_type": "display_data" + } + ], + "source": [ + "plot_delta(deltas_freq_odd_mom_odd[0], lambdas_freq_odd_mom_odd[0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "---" + ] + } + ], + "metadata": { + "celltoolbar": "Edit Metadata", + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} From afd990874f161d5d636d7f775a46a46e47acf18a Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 19 Aug 2020 17:33:06 +0200 Subject: [PATCH 086/121] [eli] use almost_equal instead of equal --- test/python/eliashberg/preprocessing_gamma.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/test/python/eliashberg/preprocessing_gamma.py b/test/python/eliashberg/preprocessing_gamma.py index 30db755e2..ecdb072fb 100644 --- a/test/python/eliashberg/preprocessing_gamma.py +++ b/test/python/eliashberg/preprocessing_gamma.py @@ -67,8 +67,8 @@ def test_preprocess_gamma_for_fft_benchmark(gamma, p): np.testing.assert_equal(gamma.data, p_benchmark.gamma.data) gamma_dyn_tr, gamma_const_r = preprocess_gamma_for_fft(gamma) - np.testing.assert_equal(gamma_dyn_tr.data, p_benchmark.gamma_dyn_tr.data) - np.testing.assert_equal(gamma_const_r.data, p_benchmark.gamma_const_r.data) + np.testing.assert_almost_equal(gamma_dyn_tr.data, p_benchmark.gamma_dyn_tr.data) + np.testing.assert_almost_equal(gamma_const_r.data, p_benchmark.gamma_const_r.data) if __name__ == '__main__': From 2fc3421039dd81a1eca3784585f9714622a86a45 Mon Sep 17 00:00:00 2001 From: Stefan Date: Thu, 20 Aug 2020 07:07:05 +0200 Subject: [PATCH 087/121] [eli] use all_close with atol --- test/python/eliashberg/preprocessing_gamma.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/test/python/eliashberg/preprocessing_gamma.py b/test/python/eliashberg/preprocessing_gamma.py index ecdb072fb..46c920f68 100644 --- a/test/python/eliashberg/preprocessing_gamma.py +++ b/test/python/eliashberg/preprocessing_gamma.py @@ -64,11 +64,11 @@ def test_preprocess_gamma_for_fft_benchmark(gamma, p): model_parameters_to_test = ['dim', 'norb', 't', 'mu', 'beta', 'U'] assert_parameter_collection_not_equal_model_parameters(p, p_benchmark, model_parameters_to_test) - np.testing.assert_equal(gamma.data, p_benchmark.gamma.data) + np.testing.assert_allclose(gamma.data, p_benchmark.gamma.data, atol=1e-10) gamma_dyn_tr, gamma_const_r = preprocess_gamma_for_fft(gamma) - np.testing.assert_almost_equal(gamma_dyn_tr.data, p_benchmark.gamma_dyn_tr.data) - np.testing.assert_almost_equal(gamma_const_r.data, p_benchmark.gamma_const_r.data) + np.testing.assert_allclose(gamma_dyn_tr.data, p_benchmark.gamma_dyn_tr.data, atol=1e-10) + np.testing.assert_allclose(gamma_const_r.data, p_benchmark.gamma_const_r.data, atol=1e-10) if __name__ == '__main__': From fafc6e2026473a97aa5dfff99ee0872c69ce31c8 Mon Sep 17 00:00:00 2001 From: Stefan Date: Thu, 20 Aug 2020 07:38:33 +0200 Subject: [PATCH 088/121] [eli] add exception handeling for older numpy --- test/python/eliashberg/product_summation_vs_fft.py | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/test/python/eliashberg/product_summation_vs_fft.py b/test/python/eliashberg/product_summation_vs_fft.py index f1bf85cda..097b74836 100644 --- a/test/python/eliashberg/product_summation_vs_fft.py +++ b/test/python/eliashberg/product_summation_vs_fft.py @@ -51,7 +51,10 @@ def print_diff(diff): for i in range(i_max): for j in range(j_max): - s += np.format_float_scientific(diff[i,j], precision=2, pad_left=3) + try: + s += np.format_float_scientific(diff[i,j], precision=2, pad_left=3) + except AttributeError: + s += str(diff[i,j]) s += "\t" s += "\n" s += dashes From a270b16e5d14411abcfacfef04c06cdca7f7cf59 Mon Sep 17 00:00:00 2001 From: Nils Wentzell Date: Tue, 8 Sep 2020 11:55:04 -0400 Subject: [PATCH 089/121] Add matplotlib to requirements.txt --- requirements.txt | 1 + 1 file changed, 1 insertion(+) diff --git a/requirements.txt b/requirements.txt index 21ccef9e3..2f137363c 100644 --- a/requirements.txt +++ b/requirements.txt @@ -1 +1,2 @@ # Required python packages for this application (these should also be added to Dockerfile for Jenkins) +matplotlib From 72d708d93ab8ffa1cbb1586636dbe01c78f84f32 Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 25 Sep 2020 09:44:28 +0200 Subject: [PATCH 090/121] [eli] use FFT instead of SUM for test That FFT and SUM yield the same result is covered by a different test. 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zMke+3G<*R3{z~reWvuXne&BED1B!rbJL&_{?`_nc97pNVFZt9L)bKv=lm}Vp4;lur z-eDm6h@w@WM}0(Euj=0q%Y44;b(#8#8mP>x34UYiFo!Ei? z=JyeUp`Uq^`=j%Qze{~kTJLCGm8&$<6Maz)PXUkpmiwdUyh5Ni3`8GQw1j(6AC-PD zS+B0PmX~;qroO6%$ARZRLf=(6{U-XWBI*MAu;OBQ&wYO`8cF*_SVEhNRGeHueOV3f z0#7@_{ne&)HNNvobJ~HXokMQp+T{rTg zzH%2H)f;_hCHwq#=$C|}4=pBCnNlAbe#0tPE2(w8AN8d*JP~Ym5PfUKt3?mJ7x%G6 z;2V3Xk4@*@LHYl5mv3F%Kz(fuuLHmK4*K4Tb#^-RX?~B;ACH?_PknIATd}&|i_X>M zQ(s)e=#z`S2hcZHj#t(||HB{Xql;fMBdL#0-&f?OidQ8c{~+qCYd93VXBPVI%C<2p zp!aP;A6`7Y_L%zc^m{eWI{k_~?$g=Sm)G!2@X~$g+bh?N|AgLk1p4@5Q!@Jdr0-F- zz()# Date: Fri, 25 Sep 2020 10:05:40 +0200 Subject: [PATCH 091/121] [eli] reduce number of symmetries checked The test 'symmetrize_gf' does already test the functionality of the 'enforce_symmetry' function. Therefore we now only test if 'solve_eliashberg' actually uses this function and applies it correctly for two different cases. Speed up from 8 sec to 2 sec. --- test/python/eliashberg/symmetrize_delta.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/test/python/eliashberg/symmetrize_delta.py b/test/python/eliashberg/symmetrize_delta.py index 1548158b1..72c88767b 100644 --- a/test/python/eliashberg/symmetrize_delta.py +++ b/test/python/eliashberg/symmetrize_delta.py @@ -26,9 +26,9 @@ # ---------------------------------------------------------------------- -def test_symmetry_of_symmetry_enforced_deltas(g0_wk, gamma): +def test_symmetry_constraint_of_solve_eliashberg(g0_wk, gamma): variables = ["frequency", "momentum", "orbital"] - all_symmetries = list(itertools.product(["even", "odd"], repeat=3)) + all_symmetries = [('even', 'odd', 'even'), ('odd', 'even', 'even')] for symmetries in all_symmetries: symmetrize_fct = functools.partial(enforce_symmetry, @@ -92,4 +92,4 @@ def plot_delta(delta): g0_wk = eliashberg_ingredients.g0_wk gamma = eliashberg_ingredients.gamma - test_symmetry_of_symmetry_enforced_deltas(g0_wk, gamma) + test_symmetry_constraint_of_solve_eliashberg(g0_wk, gamma) From 0cf3789a8c8eee829feec68b14bef15b15ce91b7 Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 25 Sep 2020 10:18:18 +0200 Subject: [PATCH 092/121] [eli] change model parameter for speed up Speed up from 5 sec to 2 sec. --- test/python/eliashberg/eigenvalue_solver.py | 47 ++++++++++++--------- 1 file changed, 27 insertions(+), 20 deletions(-) diff --git a/test/python/eliashberg/eigenvalue_solver.py b/test/python/eliashberg/eigenvalue_solver.py index 120b2e56e..8c9073d59 100644 --- a/test/python/eliashberg/eigenvalue_solver.py +++ b/test/python/eliashberg/eigenvalue_solver.py @@ -23,35 +23,42 @@ # ---------------------------------------------------------------------- + def test_equality_of_eigenvalue_solvers(g0_wk, gamma): initial_delta = semi_random_initial_delta(g0_wk, seed=1337) - Es_PM, eigen_modes_PM = solve_eliashberg(gamma, g0_wk, product="FFT", solver="PM", initial_delta=initial_delta) - Es_IRAM, eigen_modes_IRAM = solve_eliashberg(gamma, g0_wk, product="FFT", solver="IRAM", initial_delta=initial_delta) + Es_PM, eigen_modes_PM = solve_eliashberg( + gamma, g0_wk, product="FFT", solver="PM", initial_delta=initial_delta + ) + Es_IRAM, eigen_modes_IRAM = solve_eliashberg( + gamma, g0_wk, product="FFT", solver="IRAM", initial_delta=initial_delta, k=1 + ) np.testing.assert_allclose(Es_PM[0], Es_IRAM[0]) - assert allclose_by_scalar_multiplication(eigen_modes_PM[0], eigen_modes_IRAM[0]),\ - "Eigenvectors are not the same." + assert allclose_by_scalar_multiplication( + eigen_modes_PM[0], eigen_modes_IRAM[0] + ), "Eigenvectors are not the same." + + print("Both solvers yield the same results.") + - print('Both solvers yield the same results.') -#================================================================================ +# ================================================================================ -if __name__ == '__main__': +if __name__ == "__main__": p = ParameterCollection( - dim = 1, - norb = 1, - t = 1.0, - mu = 0.0, - beta = 5, - U = 1.0, - Up = 0.8, - J = 0.1, - Jp = 0.1, - nk = 4, - nw = 200, - solver = 'PM', - ) + dim=1, + norb=1, + t=1.0, + mu=0.0, + beta=5, + U=1.0, + Up=0.0, + J=0.0, + Jp=0.0, + nk=2, + nw=200, + ) eliashberg_ingredients = create_eliashberg_ingredients(p) g0_wk = eliashberg_ingredients.g0_wk gamma = eliashberg_ingredients.gamma From 214e5b178bbc4be804461e22459c8f18e181462b Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 25 Sep 2020 10:41:15 +0200 Subject: [PATCH 093/121] [eli] don't solve eliashberg but use mocks Speed up from 5 sec to 1 sec. --- .../solve_eliashberg_functionality.py | 26 +++++++++++++------ 1 file changed, 18 insertions(+), 8 deletions(-) diff --git a/test/python/eliashberg/solve_eliashberg_functionality.py b/test/python/eliashberg/solve_eliashberg_functionality.py index a90173314..1629ef787 100644 --- a/test/python/eliashberg/solve_eliashberg_functionality.py +++ b/test/python/eliashberg/solve_eliashberg_functionality.py @@ -8,7 +8,9 @@ from triqs_tprf.eliashberg import solve_eliashberg -def test_no_initial_delta_input(g0_wk, gamma): +@patch("triqs_tprf.eliashberg.implicitly_restarted_arnoldi_method") +def test_no_initial_delta_input(patched_solver, g0_wk, gamma): + patched_solver.return_value = [0.0], [g0_wk.data.flatten()] with patch("triqs_tprf.eliashberg.semi_random_initial_delta") as patched: patched.return_value = g0_wk @@ -17,7 +19,9 @@ def test_no_initial_delta_input(g0_wk, gamma): patched.assert_called() -def test_initial_delta_input(g0_wk, gamma): +@patch("triqs_tprf.eliashberg.implicitly_restarted_arnoldi_method") +def test_initial_delta_input(patched_solver, g0_wk, gamma): + patched_solver.return_value = [0.0], [g0_wk.data.flatten()] with patch("triqs_tprf.eliashberg.semi_random_initial_delta") as patched: patched.return_value = g0_wk @@ -122,7 +126,10 @@ def test_wrong_input_for_solver(g0_wk, gamma): assert str(e) == expected_message -def test_call_symmetrize_function(g0_wk, gamma): +@patch("triqs_tprf.eliashberg.eliashberg_product_fft") +def test_call_symmetrize_function(patched_product, g0_wk, gamma): + patched_product.return_value = g0_wk + symmetrize_fct = MagicMock() symmetrize_fct.return_value = g0_wk @@ -140,7 +147,10 @@ def test_invalid_symmetrize_function(g0_wk, gamma): assert str(e) == "'int' object has no attribute 'data'" -def test_k_input(g0_wk, gamma): +@patch("triqs_tprf.eliashberg.eliashberg_product_fft") +def test_k_input(patched_product, g0_wk, gamma): + patched_product.return_value = g0_wk + for k_input in [1, 3]: Es, evs = solve_eliashberg(gamma, g0_wk, k=k_input) assert len(Es) == k_input @@ -166,8 +176,8 @@ def test_k_input(g0_wk, gamma): g0_wk = eliashberg_ingredients.g0_wk gamma = eliashberg_ingredients.gamma - test_no_initial_delta_input(g0_wk, gamma) - test_initial_delta_input(g0_wk, gamma) + test_no_initial_delta_input(g0_wk=g0_wk, gamma=gamma) + test_initial_delta_input(g0_wk=g0_wk, gamma=gamma) test_tol_used_in_IRAM(g0_wk, gamma) test_tol_used_in_PM(g0_wk, gamma) test_call_eliashberg_product_fft(g0_wk, gamma) @@ -179,6 +189,6 @@ def test_k_input(g0_wk, gamma): test_wrong_input_for_product(g0_wk, gamma) test_wrong_input_for_solver(g0_wk, gamma) - test_call_symmetrize_function(g0_wk, gamma) + test_call_symmetrize_function(g0_wk=g0_wk, gamma=gamma) test_invalid_symmetrize_function(g0_wk, gamma) - test_k_input(g0_wk, gamma) + test_k_input(g0_wk=g0_wk, gamma=gamma) From 3cf6eba603cc62a62d88c62c5b90f863d6021645 Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 25 Sep 2020 10:47:34 +0200 Subject: [PATCH 094/121] [eli] reduce temperature and number of frequencies Speed up from 5 sec to 1 sec. --- test/python/eliashberg/product_summation_vs_fft.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/test/python/eliashberg/product_summation_vs_fft.py b/test/python/eliashberg/product_summation_vs_fft.py index 097b74836..8da0636e9 100644 --- a/test/python/eliashberg/product_summation_vs_fft.py +++ b/test/python/eliashberg/product_summation_vs_fft.py @@ -144,13 +144,13 @@ def plot_output(g0_wk, gamma): t12 = 0.1, t21 = 0.1, mu = 0.0, - beta = 5, + beta = 1, U = 1.0, Up = 0.8, J = 0.1, Jp = 0.1, nk = 3, - nw = 150, + nw = 30, atol = 1e-8, ) From a03cd395d7d9f4db224650f8404e964391fbe756 Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 25 Sep 2020 11:37:02 +0200 Subject: [PATCH 095/121] [eli] rename tests to regression test --- test/python/eliashberg/CMakeLists.txt | 4 ++-- ....tar.gz => eliashberg_benchmark_one_band.tar.gz} | Bin ...mplementation.py => regression_test_one_band.py} | 4 ++-- ...tion_two_band.py => regression_test_two_band.py} | 0 4 files changed, 4 insertions(+), 4 deletions(-) rename test/python/eliashberg/{eliashberg_benchmark.tar.gz => eliashberg_benchmark_one_band.tar.gz} (100%) rename test/python/eliashberg/{previous_implementation.py => regression_test_one_band.py} (96%) rename test/python/eliashberg/{previous_implementation_two_band.py => regression_test_two_band.py} (100%) diff --git a/test/python/eliashberg/CMakeLists.txt b/test/python/eliashberg/CMakeLists.txt index 5c32dca6c..0d5a31cd8 100644 --- a/test/python/eliashberg/CMakeLists.txt +++ b/test/python/eliashberg/CMakeLists.txt @@ -9,7 +9,7 @@ add_python_test(solve_eliashberg_functionality ${PREFIX}) add_python_test(semi_random_initial_delta ${PREFIX}) add_python_test(product_summation_vs_fft ${PREFIX}) add_python_test(eigenvalue_solver ${PREFIX}) -add_python_test(previous_implementation ${PREFIX}) -add_python_test(previous_implementation_two_band ${PREFIX}) +add_python_test(regression_test_one_band ${PREFIX}) +add_python_test(regression_test_two_band ${PREFIX}) add_python_test(fft_product_constant_vs_full ${PREFIX}) add_python_test(symmetrize_delta ${PREFIX}) diff --git a/test/python/eliashberg/eliashberg_benchmark.tar.gz b/test/python/eliashberg/eliashberg_benchmark_one_band.tar.gz similarity index 100% rename from test/python/eliashberg/eliashberg_benchmark.tar.gz rename to test/python/eliashberg/eliashberg_benchmark_one_band.tar.gz diff --git a/test/python/eliashberg/previous_implementation.py b/test/python/eliashberg/regression_test_one_band.py similarity index 96% rename from test/python/eliashberg/previous_implementation.py rename to test/python/eliashberg/regression_test_one_band.py index 98b4d6ffd..bbdd88ee5 100644 --- a/test/python/eliashberg/previous_implementation.py +++ b/test/python/eliashberg/regression_test_one_band.py @@ -61,8 +61,8 @@ def test_solve_eliashberg(g0_wk, gamma, expected_E, expected_eigen_mode): if __name__ == "__main__": p = ParameterCollection( - benchmark_filename = "./eliashberg_benchmark.tar.gz", - filename = 'eliashberg_benchmark_new.tar.gz', + benchmark_filename = "./eliashberg_benchmark_one_band.tar.gz", + filename = 'eliashberg_benchmark_one_band_new.tar.gz', dim = 2, norb = 1, t = 1.0, diff --git a/test/python/eliashberg/previous_implementation_two_band.py b/test/python/eliashberg/regression_test_two_band.py similarity index 100% rename from test/python/eliashberg/previous_implementation_two_band.py rename to test/python/eliashberg/regression_test_two_band.py From 0662371a48980e4623468852c85534f24a6eb90d Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 25 Sep 2020 11:50:31 +0200 Subject: [PATCH 096/121] [eli] add author header for tests --- .../compare_general_rpa_to_matrix_rpa.py | 4 +- test/python/eliashberg/eigenvalue_solver.py | 2 +- .../fft_product_constant_vs_full.py | 3 +- test/python/eliashberg/gamma_creation.py | 57 +++++++++++-------- test/python/eliashberg/preprocessing_gamma.py | 1 + .../eliashberg/product_summation_vs_fft.py | 3 +- .../eliashberg/regression_test_one_band.py | 4 +- .../eliashberg/regression_test_two_band.py | 4 +- .../eliashberg/semi_random_initial_delta.py | 1 + .../solve_eliashberg_functionality.py | 1 + test/python/eliashberg/symmetrize_delta.py | 4 +- test/python/symmetrize_gf.py | 4 +- 12 files changed, 57 insertions(+), 31 deletions(-) diff --git a/test/python/compare_general_rpa_to_matrix_rpa.py b/test/python/compare_general_rpa_to_matrix_rpa.py index 564c5f9e2..d58ad8b2e 100644 --- a/test/python/compare_general_rpa_to_matrix_rpa.py +++ b/test/python/compare_general_rpa_to_matrix_rpa.py @@ -1,7 +1,9 @@ # ---------------------------------------------------------------------- """ Comparison of the general RPA formalism and the matrix RPA formalism -for the spin- and charge-susceptibility. """ +for the spin- and charge-susceptibility. + +Author: Stefan Käser (2020) stefan.kaeser7@gmail.com """ # ---------------------------------------------------------------------- diff --git a/test/python/eliashberg/eigenvalue_solver.py b/test/python/eliashberg/eigenvalue_solver.py index 8c9073d59..6861cef73 100644 --- a/test/python/eliashberg/eigenvalue_solver.py +++ b/test/python/eliashberg/eigenvalue_solver.py @@ -3,7 +3,7 @@ """ Compare the output of the implemented eigenvalue solver: The Power Method and the Implicitly Restarted Arnoldi Method. -""" +Author: Stefan Käser (2020) stefan.kaeser7@gmail.com """ # ---------------------------------------------------------------------- diff --git a/test/python/eliashberg/fft_product_constant_vs_full.py b/test/python/eliashberg/fft_product_constant_vs_full.py index da85350c6..29d51d08f 100644 --- a/test/python/eliashberg/fft_product_constant_vs_full.py +++ b/test/python/eliashberg/fft_product_constant_vs_full.py @@ -8,7 +8,8 @@ is constant in momentum space. This also tests the function 'split_into_dynamic_wk_and_constant_k', to see if the split is done correctly. -""" + +Author: Stefan Käser (2020) stefan.kaeser7@gmail.com """ # ---------------------------------------------------------------------- diff --git a/test/python/eliashberg/gamma_creation.py b/test/python/eliashberg/gamma_creation.py index 43893bf08..04fa7b88f 100644 --- a/test/python/eliashberg/gamma_creation.py +++ b/test/python/eliashberg/gamma_creation.py @@ -1,3 +1,4 @@ +""" Author: Stefan Käser (2020) stefan.kaeser7@gmail.com """ import numpy as np from triqs_tprf.ParameterCollection import ParameterCollection @@ -6,59 +7,69 @@ from triqs_tprf.lattice import gamma_PP_spin_charge, gamma_PP_singlet, gamma_PP_triplet + def test_gamma_PP_spin_charge_mesh_types(chi_c, chi_s, U_c, U_s): gamma = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, 0.0, 0.0) assert type(gamma.mesh) == MeshProduct - assert type(gamma.mesh[0]) == MeshImFreq - assert type(gamma.mesh[1]) == MeshBrillouinZone + assert type(gamma.mesh[0]) == MeshImFreq + assert type(gamma.mesh[1]) == MeshBrillouinZone + def test_gamma_PP_spin_charge_zero_input(chi_c, chi_s, U_c, U_s): - gamma = gamma_PP_spin_charge(0.0*chi_c, 0.0*chi_s, 0.0*U_c, 0.0*U_s, 0.0, 0.0) + gamma = gamma_PP_spin_charge( + 0.0 * chi_c, 0.0 * chi_s, 0.0 * U_c, 0.0 * U_s, 0.0, 0.0 + ) np.testing.assert_equal(gamma.data, 0) + def test_gamma_PP_spin_charge_only_constant(chi_c, chi_s, U_c, U_s): gamma = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, 0.0, 0.0) - np.testing.assert_equal(gamma.data[0, 0], 0.5*(U_c + U_s)) + np.testing.assert_equal(gamma.data[0, 0], 0.5 * (U_c + U_s)) + def test_gamma_PP_singlet_mesh_type(chi_c, chi_s, U_c, U_s): gamma_singlet = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) assert type(gamma_singlet.mesh) == MeshProduct - assert type(gamma_singlet.mesh[0]) == MeshImFreq - assert type(gamma_singlet.mesh[1]) == MeshBrillouinZone + assert type(gamma_singlet.mesh[0]) == MeshImFreq + assert type(gamma_singlet.mesh[1]) == MeshBrillouinZone + def test_gamma_PP_singlet_value(chi_c, chi_s, U_c, U_s): gamma = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, -1, 3) gamma_singlet = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) np.testing.assert_equal(gamma.data, gamma_singlet.data) + def test_gamma_PP_triplet_mesh_type(chi_c, chi_s, U_c, U_s): gamma_triplet = gamma_PP_triplet(chi_c, chi_s, U_c, U_s) assert type(gamma_triplet.mesh) == MeshProduct - assert type(gamma_triplet.mesh[0]) == MeshImFreq - assert type(gamma_triplet.mesh[1]) == MeshBrillouinZone + assert type(gamma_triplet.mesh[0]) == MeshImFreq + assert type(gamma_triplet.mesh[1]) == MeshBrillouinZone + def test_gamma_PP_triplet_value(chi_c, chi_s, U_c, U_s): gamma = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, -1, -1) gamma_triplet = gamma_PP_triplet(chi_c, chi_s, U_c, U_s) np.testing.assert_equal(gamma.data, gamma_triplet.data) + if __name__ == "__main__": p = ParameterCollection( - dim = 2, - norb = 2, - t1 = 1.0, - t2 = 0.5, - t12 = 0.1, - t21 = 0.1, - mu = 0.1, - beta = 1, - U = 1.0, - Up = 0.8, - J = 0.1, - Jp = 0.1, - nk = 3, - nw = 50, - ) + dim=2, + norb=2, + t1=1.0, + t2=0.5, + t12=0.1, + t21=0.1, + mu=0.1, + beta=1, + U=1.0, + Up=0.8, + J=0.1, + Jp=0.1, + nk=3, + nw=50, + ) eliashberg_ingredients = create_eliashberg_ingredients(p) chi_c = eliashberg_ingredients.chi_c diff --git a/test/python/eliashberg/preprocessing_gamma.py b/test/python/eliashberg/preprocessing_gamma.py index 46c920f68..76f66bdfc 100644 --- a/test/python/eliashberg/preprocessing_gamma.py +++ b/test/python/eliashberg/preprocessing_gamma.py @@ -1,3 +1,4 @@ +""" Author: Stefan Käser (2020) stefan.kaeser7@gmail.com """ import numpy as np from triqs.gf import MeshProduct, MeshImFreq, MeshBrillouinZone, MeshImTime, MeshCyclicLattice diff --git a/test/python/eliashberg/product_summation_vs_fft.py b/test/python/eliashberg/product_summation_vs_fft.py index 8da0636e9..969c20cc8 100644 --- a/test/python/eliashberg/product_summation_vs_fft.py +++ b/test/python/eliashberg/product_summation_vs_fft.py @@ -2,7 +2,8 @@ """ Compare the summation implementation of the linearized Eliashberg product and the one using Fourier transformations. -""" + +Author: Stefan Käser (2020) stefan.kaeser7@gmail.com """ # ---------------------------------------------------------------------- diff --git a/test/python/eliashberg/regression_test_one_band.py b/test/python/eliashberg/regression_test_one_band.py index bbdd88ee5..52cfcc7be 100644 --- a/test/python/eliashberg/regression_test_one_band.py +++ b/test/python/eliashberg/regression_test_one_band.py @@ -3,7 +3,9 @@ """ Goes through the steps of solving the linearized Eliashberg equation for singlet pairing in RPA limit in model with two orbitals, saves the results and compares to previously established -benchmark data. """ +benchmark data. + +Author: Stefan Käser (2020) stefan.kaeser7@gmail.com """ # ---------------------------------------------------------------------- diff --git a/test/python/eliashberg/regression_test_two_band.py b/test/python/eliashberg/regression_test_two_band.py index 1c6709340..67aded9fa 100644 --- a/test/python/eliashberg/regression_test_two_band.py +++ b/test/python/eliashberg/regression_test_two_band.py @@ -3,7 +3,9 @@ """ Goes through the steps of solving the linearized Eliashberg equation for singlet pairing in RPA limit in model with two orbitals, saves the results and compares to previously established -benchmark data. """ +benchmark data. + +Author: Stefan Käser (2020) stefan.kaeser7@gmail.com """ # ---------------------------------------------------------------------- diff --git a/test/python/eliashberg/semi_random_initial_delta.py b/test/python/eliashberg/semi_random_initial_delta.py index b754ab1a1..205ebdd27 100644 --- a/test/python/eliashberg/semi_random_initial_delta.py +++ b/test/python/eliashberg/semi_random_initial_delta.py @@ -1,3 +1,4 @@ +""" Author: Stefan Käser (2020) stefan.kaeser7@gmail.com """ import numpy as np from triqs_tprf.ParameterCollection import ParameterCollection diff --git a/test/python/eliashberg/solve_eliashberg_functionality.py b/test/python/eliashberg/solve_eliashberg_functionality.py index 1629ef787..a2a833b71 100644 --- a/test/python/eliashberg/solve_eliashberg_functionality.py +++ b/test/python/eliashberg/solve_eliashberg_functionality.py @@ -1,3 +1,4 @@ +""" Author: Stefan Käser (2020) stefan.kaeser7@gmail.com """ from unittest.mock import patch, MagicMock import numpy as np diff --git a/test/python/eliashberg/symmetrize_delta.py b/test/python/eliashberg/symmetrize_delta.py index 72c88767b..56b7ca310 100644 --- a/test/python/eliashberg/symmetrize_delta.py +++ b/test/python/eliashberg/symmetrize_delta.py @@ -1,7 +1,9 @@ # ---------------------------------------------------------------------- """ Test the symmetrizing feature of the solve_eliashberg function -""" + +Author: Stefan Käser (2020) stefan.kaeser7@gmail.com """ + # ---------------------------------------------------------------------- import itertools diff --git a/test/python/symmetrize_gf.py b/test/python/symmetrize_gf.py index 16529c807..31f61e3a2 100644 --- a/test/python/symmetrize_gf.py +++ b/test/python/symmetrize_gf.py @@ -2,7 +2,9 @@ """ Symmetrize a randomly filled Green's function in frequency, momentum, and orbital and test if it was done proberly. -""" + +Author: Stefan Käser (2020) stefan.kaeser7@gmail.com """ + # ---------------------------------------------------------------------- import itertools From 01414402695cda0b19933573ac716cd641cc7330 Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 25 Sep 2020 11:54:54 +0200 Subject: [PATCH 097/121] [eli] delete old test files --- test/python/eliashberg.py | 130 ---------------------------------- test/python/eliashberg_fft.py | 107 ---------------------------- 2 files changed, 237 deletions(-) delete mode 100644 test/python/eliashberg.py delete mode 100644 test/python/eliashberg_fft.py diff --git a/test/python/eliashberg.py b/test/python/eliashberg.py deleted file mode 100644 index 701edff46..000000000 --- a/test/python/eliashberg.py +++ /dev/null @@ -1,130 +0,0 @@ - -# ---------------------------------------------------------------------- - -""" Goes through the steps of solving the linearized Eliashberg equation for singlet pairing in -RPA limit, saves the results and compares to previously established benchmark data. """ - -# ---------------------------------------------------------------------- - -import itertools - -# ---------------------------------------------------------------------- - -import numpy as np - -# ---------------------------------------------------------------------- - -from triqs.gf import MeshImFreq - -from triqs_tprf.ParameterCollection import ParameterCollection -from triqs_tprf.tight_binding import TBLattice -from triqs_tprf.lattice import lattice_dyson_g0_wk -from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk -from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors -from triqs_tprf.lattice import solve_rpa_PH -from triqs_tprf.lattice import gamma_PP_singlet -from triqs_tprf.lattice import eliashberg_product -from triqs_tprf.eliashberg import solve_eliashberg - -# ---------------------------------------------------------------------- - -from triqs_tprf.utilities import write_TarGZ_HDFArchive, read_TarGZ_HDFArchive, show_version_info -import triqs_tprf.version as version - -# ---------------------------------------------------------------------- - -p = ParameterCollection( - filename = 'eliashberg_benchmark_new.tar.gz', - dim = 2, - norbs = 1, - t = 1.0, - mu = 0.0, - beta = 1, - U = 1.0, - nk = 2, - nw = 100, - version_info = version.info, - ) - -# -- Setup model, RPA susceptibilities and spin/charge interaction - -full_units = [(1, 0, 0), (0, 1, 0), (0, 0, 1)] -all_nn_hoppings = list(itertools.product([-1, 0, 1], repeat=p.dim)) -non_diagonal_hoppings = [ele for ele in all_nn_hoppings if sum(np.abs(ele)) == 1] - -t = -p.t * np.eye(p.norbs) - -H = TBLattice( - units = full_units[:p.dim], - hopping = {hop : t for hop in non_diagonal_hoppings}, - orbital_positions = [(0,0,0)]*p.norbs, - ) - -e_k = H.on_mesh_brillouin_zone(n_k=[p.nk]*p.dim + [1]*(3-p.dim)) - -# A bigger w-mesh is needed to construct a Gamma with a twice as big w-mesh than GF -big_factor = 2.0 - -wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nw) -wmesh_big = MeshImFreq(beta=p.beta, S='Fermion', n_max=int(big_factor*p.nw)) - -g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh) -g0_wk_big = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh_big) - -chi0_wk = imtime_bubble_chi0_wk(g0_wk_big, nw=p.nw) -chi0_wk_big = imtime_bubble_chi0_wk(g0_wk_big, nw=int(big_factor*p.nw)+1) - -U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norbs, p.U, 0, 0, 0) - -chi_s = solve_rpa_PH(chi0_wk, U_s) -chi_c = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation -chi_s_big = solve_rpa_PH(chi0_wk_big, U_s) -chi_c_big = solve_rpa_PH(chi0_wk_big, -U_c) # Minus for correct charge rpa equation - -# -- The output of the following three functions shall be tested - -gamma = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) -gamma_big = gamma_PP_singlet(chi_c_big, chi_s_big, U_c, U_s) -next_delta = eliashberg_product(gamma_big, g0_wk, g0_wk) -E, eigen_modes = solve_eliashberg(gamma_big, g0_wk) - -# -- Save results - -p.gamma = gamma -p.next_delta = next_delta -p.E = E[0] -p.eigen_mode = eigen_modes[0] - -write_TarGZ_HDFArchive(p.filename, p=p) - -# -- Load benchmark data - -filename = './eliashberg_benchmark.tar.gz' -p_benchmark = read_TarGZ_HDFArchive(filename)['p'] - -# -- Check if the benchmark data was calculated for the same model, -# -- otherwise a comparison does not make sense. - -model_parameters = ['dim', 'norbs', 't', 'mu', 'beta', 'U'] - -for model_parameter in model_parameters: - run_time, benchmark = p[model_parameter], p_benchmark[model_parameter] - if run_time != benchmark: - error = 'The model of the benchmark and the one used now are not the same.\n' - error += '\t\tNow: {0} = {1}, benchmark: {0} = {2}.'.format(model_parameter, run_time, - benchmark) - raise AssertionError(error) - -# -- Compare the results. Raise an error if the are not the same within a tolerance. - -print('\nThe benchmark data was obtained with %s.'%show_version_info(p_benchmark.version_info)) - -np.testing.assert_allclose(p_benchmark.gamma.data, p.gamma.data) -np.testing.assert_allclose(p_benchmark.next_delta.data, p.next_delta.data, atol=1e-7) -np.testing.assert_allclose(p_benchmark.E, p.E) -try: - np.testing.assert_allclose(p_benchmark.eigen_mode.data, p.eigen_mode.data, atol=1e-6) -except AssertionError: - np.testing.assert_allclose(-p_benchmark.eigen_mode.data, p.eigen_mode.data, atol=1e-6) - -print('\nThis (new) version with %s yields the same results!'%show_version_info(p.version_info)) diff --git a/test/python/eliashberg_fft.py b/test/python/eliashberg_fft.py deleted file mode 100644 index db43bf43c..000000000 --- a/test/python/eliashberg_fft.py +++ /dev/null @@ -1,107 +0,0 @@ -# ---------------------------------------------------------------------- - -""" Compare the naive implementation of the linearized Eliashberg product -and the one using Fourier transformations. -This test is quite computational intensive, because of the inefficiency of -the naive implementations. In the future the Fourier transformation -implementation will subsitute the naive one. -""" - -# ---------------------------------------------------------------------- - -import itertools - -# ---------------------------------------------------------------------- - -import numpy as np - -# ---------------------------------------------------------------------- - -from triqs_tprf.ParameterCollection import ParameterCollection -from triqs.gf import Gf, MeshImFreq - -from triqs_tprf.tight_binding import TBLattice - -from triqs_tprf.lattice import lattice_dyson_g0_wk, solve_rpa_PH -from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk -from triqs_tprf.lattice import gamma_PP_singlet -from triqs_tprf.lattice import eliashberg_product, eliashberg_product_fft -from triqs_tprf.lattice import split_into_dynamic_wk_and_constant_k, dynamic_and_constant_to_tr -from triqs_tprf.eliashberg import solve_eliashberg, solve_eliashberg_fft -from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors - -# ---------------------------------------------------------------------- - -p = ParameterCollection( - dim = 1, - norbs = 1, - t = 1.0, - mu = 0.0, - beta = 5, - U = 1.0, - nk = 4, - nw = 500, - ) - -# -- Setup model, RPA susceptibilities and spin/charge interaction - -full_units = [(1, 0, 0), (0, 1, 0), (0, 0, 1)] -all_nn_hoppings = list(itertools.product([-1, 0, 1], repeat=p.dim)) -non_diagonal_hoppings = [ele for ele in all_nn_hoppings if sum(np.abs(ele)) == 1] - -t = -p.t * np.eye(p.norbs) - -H = TBLattice( - units = full_units[:p.dim], - hopping = {hop : t for hop in non_diagonal_hoppings}, - orbital_positions = [(0,0,0)]*p.norbs, - ) - -e_k = H.on_mesh_brillouin_zone(n_k=[p.nk]*p.dim + [1]*(3-p.dim)) - -# A bigger w-mesh is needed to construct a Gamma with a twice as big w-mesh than GF -big_factor = 2.0 - -wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nw) -wmesh_big = MeshImFreq(beta=p.beta, S='Fermion', n_max=int(big_factor*p.nw)) - -g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh) -g0_wk_big = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh_big) - -chi0_wk_big = imtime_bubble_chi0_wk(g0_wk_big, nw=int(big_factor*p.nw)+1) - -U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norbs, p.U, 0, 0, 0) - -chi_s_big = solve_rpa_PH(chi0_wk_big, U_s) -chi_c_big = solve_rpa_PH(chi0_wk_big, -U_c) # Minus for correct charge rpa equation - -gamma_big = gamma_PP_singlet(chi_c_big, chi_s_big, U_c, U_s) - -# -- Preprocess gamma for the FFT implementation - -gamma_dyn_wk, gamma_const_k = split_into_dynamic_wk_and_constant_k(gamma_big) -gamma_dyn_tr, gamma_const_r = dynamic_and_constant_to_tr(gamma_dyn_wk, gamma_const_k) - -# -- Test the Eliashberg equation - -next_delta = eliashberg_product(gamma_big, g0_wk, g0_wk) -next_delta_fft = eliashberg_product_fft(gamma_dyn_tr, gamma_const_r, g0_wk, g0_wk) - -np.testing.assert_allclose(next_delta.data, next_delta_fft.data, atol=1e-7) - -Es, eigen_modes = solve_eliashberg(gamma_big, g0_wk) -Es_fft, eigen_modes_fft = solve_eliashberg_fft(gamma_big, g0_wk) - -E = Es[0] -eigen_mode = eigen_modes[0] -E_fft = Es_fft[0] -eigen_mode_fft = eigen_modes_fft[0] - -np.testing.assert_allclose(E, E_fft, atol=1e-7) - -try: - np.testing.assert_allclose(eigen_mode.data, eigen_mode_fft.data, atol=1e-7) -except AssertionError: - np.testing.assert_allclose(-eigen_mode.data, eigen_mode_fft.data, atol=1e-7) - -print('\nSame results for both implementations of the linearized Eliashberg equation.') From 8039fb8015738fac844cbc0c15c0e7f97fea87ae Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 25 Sep 2020 12:19:01 +0200 Subject: [PATCH 098/121] [eli] add copyright and author to python files --- python/triqs_tprf/ParameterCollection.py | 3 +++ python/triqs_tprf/eliashberg.py | 10 +++++----- python/triqs_tprf/matrix_rpa.py | 24 ++++++++++++++++++++++++ python/triqs_tprf/plotting_tools.py | 24 ++++++++++++++++++++++++ python/triqs_tprf/rpa_tensor.py | 5 +++-- python/triqs_tprf/symmetries.py | 24 ++++++++++++++++++++++++ python/triqs_tprf/tight_binding.py | 3 ++- python/triqs_tprf/utilities.py | 5 ++--- 8 files changed, 87 insertions(+), 11 deletions(-) diff --git a/python/triqs_tprf/ParameterCollection.py b/python/triqs_tprf/ParameterCollection.py index 96f69de92..e75085feb 100644 --- a/python/triqs_tprf/ParameterCollection.py +++ b/python/triqs_tprf/ParameterCollection.py @@ -1,9 +1,12 @@ +# -*- coding: utf-8 -*- ################################################################################ # # TPRF: Two-Particle Response Function (TPRF) Toolbox for TRIQS # # Copyright (C) 2017 by Hugo U.R. Strand +# Copyright (C) 2019 by S.Käser +# Author: H. U.R. Strand, S. Käser # # TPRF is free software: you can redistribute it and/or modify it under the # terms of the GNU General Public License as published by the Free Software diff --git a/python/triqs_tprf/eliashberg.py b/python/triqs_tprf/eliashberg.py index 621f3ade2..d83eb2a6f 100644 --- a/python/triqs_tprf/eliashberg.py +++ b/python/triqs_tprf/eliashberg.py @@ -2,23 +2,23 @@ ################################################################################ # -# TRIQS: a Toolbox for Research in Interacting Quantum Systems +# TPRF: Two-Particle Response Function (TPRF) Toolbox for TRIQS # # Copyright (C) 2019, The Simons Foundation and S. Käser -# Authors: H. U.R. Strand, S. Käser +# Author: H. U.R. Strand, S. Käser # -# TRIQS is free software: you can redistribute it and/or modify it under the +# TPRF is free software: you can redistribute it and/or modify it under the # terms of the GNU General Public License as published by the Free Software # Foundation, either version 3 of the License, or (at your option) any later # version. # -# TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY +# TPRF is distributed in the hope that it will be useful, but WITHOUT ANY # WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS # FOR A PARTICULAR PURPOSE. See the GNU General Public License for more # details. # # You should have received a copy of the GNU General Public License along with -# TRIQS. If not, see . +# TPRF. If not, see . # ################################################################################ diff --git a/python/triqs_tprf/matrix_rpa.py b/python/triqs_tprf/matrix_rpa.py index 0e13238fb..672c7ddb3 100644 --- a/python/triqs_tprf/matrix_rpa.py +++ b/python/triqs_tprf/matrix_rpa.py @@ -1,3 +1,27 @@ +# -*- coding: utf-8 -*- + +################################################################################ +# +# TPRF: Two-Particle Response Function (TPRF) Toolbox for TRIQS +# +# Copyright (C) 2019, S. Käser +# Author: S. Käser +# +# TPRF is free software: you can redistribute it and/or modify it under the +# terms of the GNU General Public License as published by the Free Software +# Foundation, either version 3 of the License, or (at your option) any later +# version. +# +# TPRF is distributed in the hope that it will be useful, but WITHOUT ANY +# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS +# FOR A PARTICULAR PURPOSE. See the GNU General Public License for more +# details. +# +# You should have received a copy of the GNU General Public License along with +# TPRF. If not, see . +# +################################################################################ + # ---------------------------------------------------------------------- """ This set of functions implements the matrix RPA as preseneted in mutliple papers. diff --git a/python/triqs_tprf/plotting_tools.py b/python/triqs_tprf/plotting_tools.py index eb69b86ca..902f7f69a 100644 --- a/python/triqs_tprf/plotting_tools.py +++ b/python/triqs_tprf/plotting_tools.py @@ -1,3 +1,27 @@ +# -*- coding: utf-8 -*- + +################################################################################ +# +# TPRF: Two-Particle Response Function (TPRF) Toolbox for TRIQS +# +# Copyright (C) 2019, S. Käser +# Author: S. Käser +# +# TPRF is free software: you can redistribute it and/or modify it under the +# terms of the GNU General Public License as published by the Free Software +# Foundation, either version 3 of the License, or (at your option) any later +# version. +# +# TPRF is distributed in the hope that it will be useful, but WITHOUT ANY +# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS +# FOR A PARTICULAR PURPOSE. See the GNU General Public License for more +# details. +# +# You should have received a copy of the GNU General Public License along with +# TPRF. If not, see . +# +################################################################################ + import itertools import types diff --git a/python/triqs_tprf/rpa_tensor.py b/python/triqs_tprf/rpa_tensor.py index 4f6e95c46..962429387 100644 --- a/python/triqs_tprf/rpa_tensor.py +++ b/python/triqs_tprf/rpa_tensor.py @@ -1,10 +1,11 @@ +# -*- coding: utf-8 -*- ################################################################################ # # TPRF: Two-Particle Response Function (TPRF) Toolbox for TRIQS # -# Copyright (C) 2018 by The Simons Foundation -# Author: H. U.R. Strand +# Copyright (C) 2019, The Simons Foundation and S. Käser +# Author: H. U.R. Strand, S. Käser # # TPRF is free software: you can redistribute it and/or modify it under the # terms of the GNU General Public License as published by the Free Software diff --git a/python/triqs_tprf/symmetries.py b/python/triqs_tprf/symmetries.py index 07e22d6f0..939faf38d 100644 --- a/python/triqs_tprf/symmetries.py +++ b/python/triqs_tprf/symmetries.py @@ -1,3 +1,27 @@ +# -*- coding: utf-8 -*- + +################################################################################ +# +# TPRF: Two-Particle Response Function (TPRF) Toolbox for TRIQS +# +# Copyright (C) 2019, S. Käser +# Author: S. Käser +# +# TPRF is free software: you can redistribute it and/or modify it under the +# terms of the GNU General Public License as published by the Free Software +# Foundation, either version 3 of the License, or (at your option) any later +# version. +# +# TPRF is distributed in the hope that it will be useful, but WITHOUT ANY +# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS +# FOR A PARTICULAR PURPOSE. See the GNU General Public License for more +# details. +# +# You should have received a copy of the GNU General Public License along with +# TPRF. If not, see . +# +################################################################################ + import numpy as np def enforce_symmetry(gf, variables, symmetries): diff --git a/python/triqs_tprf/tight_binding.py b/python/triqs_tprf/tight_binding.py index 5f77a24bf..4f38d88cb 100644 --- a/python/triqs_tprf/tight_binding.py +++ b/python/triqs_tprf/tight_binding.py @@ -4,7 +4,8 @@ # # Copyright (C) 2011 by M. Ferrero, O. Parcollet # Copyright (C) 2018 The Simons Foundation -# Author: Hugo U. R. Strand +# Copyright (C) 2019, S. Käser +# Author: Hugo U. R. Strand, S. Käser # # TRIQS is free software: you can redistribute it and/or modify it under the # terms of the GNU General Public License as published by the Free Software diff --git a/python/triqs_tprf/utilities.py b/python/triqs_tprf/utilities.py index f8a70ed43..21aacfb71 100644 --- a/python/triqs_tprf/utilities.py +++ b/python/triqs_tprf/utilities.py @@ -4,9 +4,8 @@ # # TPRF: Two-Particle Response Function (TPRF) Toolbox for TRIQS # -# Copyright (C) 2019 S. Käser -# Copyright (C) 2019 by The Simons Foundation -# Author: H. U.R. Strand +# Copyright (C) 2019, The Simons Foundation and S. Käser +# Author: H. U.R. Strand, S. Käser # # TPRF is free software: you can redistribute it and/or modify it under the # terms of the GNU General Public License as published by the Free Software From b646c7c797df5ab8ca63a73f862eeb08b4a005f6 Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 25 Sep 2020 12:31:45 +0200 Subject: [PATCH 099/121] [eli] add myself to the about section --- doc/about.rst | 1 + 1 file changed, 1 insertion(+) diff --git a/doc/about.rst b/doc/about.rst index 9d2e75243..d3a0a2cd4 100644 --- a/doc/about.rst +++ b/doc/about.rst @@ -4,6 +4,7 @@ Authors ======= TPRF has been written by Hugo U.R. Strand with TRIQS-library support from N. Wentzell and O. Parcollet. +The Eliashberg section was contributed by Stefan Käser with support from H. U.R. Strand, N. Wentzell, O. Parcollet and P. Dumitrescu. License ======= From b04b6482620973337dc167cab084f0e83fc04abf Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 25 Sep 2020 12:40:20 +0200 Subject: [PATCH 100/121] [eli] set me as first author --- c++/triqs_tprf/lattice/eliashberg.cpp | 2 +- c++/triqs_tprf/lattice/eliashberg.hpp | 2 +- python/triqs_tprf/eliashberg.py | 2 +- 3 files changed, 3 insertions(+), 3 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index e4b487216..3d2ff3c34 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -3,7 +3,7 @@ * TRIQS: a Toolbox for Research in Interacting Quantum Systems * * Copyright (C) 2019, The Simons Foundation and S. Käser - * Authors: H. U.R. Strand, S. Käser + * Authors: S. Käser, H. U.R. Strand * * TRIQS is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software diff --git a/c++/triqs_tprf/lattice/eliashberg.hpp b/c++/triqs_tprf/lattice/eliashberg.hpp index 34740333d..470a54754 100644 --- a/c++/triqs_tprf/lattice/eliashberg.hpp +++ b/c++/triqs_tprf/lattice/eliashberg.hpp @@ -3,7 +3,7 @@ * TRIQS: a Toolbox for Research in Interacting Quantum Systems * * Copyright (C) 2019, The Simons Foundation and S. Käser - * Authors: H. U.R. Strand, S. Käser + * Authors: S. Käser, H. U.R. Strand * * TRIQS is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software diff --git a/python/triqs_tprf/eliashberg.py b/python/triqs_tprf/eliashberg.py index d83eb2a6f..0ea0210a6 100644 --- a/python/triqs_tprf/eliashberg.py +++ b/python/triqs_tprf/eliashberg.py @@ -5,7 +5,7 @@ # TPRF: Two-Particle Response Function (TPRF) Toolbox for TRIQS # # Copyright (C) 2019, The Simons Foundation and S. Käser -# Author: H. U.R. Strand, S. Käser +# Author: S. Käser, H. U.R. Strand # # TPRF is free software: you can redistribute it and/or modify it under the # terms of the GNU General Public License as published by the Free Software From 30988444e6c9b1ce00bf61b4bac67711615b66f0 Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 25 Sep 2020 12:52:22 +0200 Subject: [PATCH 101/121] remove Dummy files --- python/triqs_tprf/Dummy.py | 30 ------------------------------ test/python/Dummy.out.h5 | Bin 4584 -> 0 bytes test/python/Dummy.py | 19 ------------------- 3 files changed, 49 deletions(-) delete mode 100644 python/triqs_tprf/Dummy.py delete mode 100644 test/python/Dummy.out.h5 delete mode 100644 test/python/Dummy.py diff --git a/python/triqs_tprf/Dummy.py b/python/triqs_tprf/Dummy.py deleted file mode 100644 index 12eee2e6f..000000000 --- a/python/triqs_tprf/Dummy.py +++ /dev/null @@ -1,30 +0,0 @@ -################################################################################ -# -# TRIQS: a Toolbox for Research in Interacting Quantum Systems -# -# Copyright (C) 2017 by Hugo U.R. Strand -# -# TRIQS is free software: you can redistribute it and/or modify it under the -# terms of the GNU General Public License as published by the Free Software -# Foundation, either version 3 of the License, or (at your option) any later -# version. -# -# TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY -# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS -# FOR A PARTICULAR PURPOSE. See the GNU General Public License for more -# details. -# -# You should have received a copy of the GNU General Public License along with -# TRIQS. If not, see . -# -################################################################################ - -version = "@PROJECT_VERSION@" -triqs_hash = "@TRIQS_GIT_HASH@" -@PROJECT_NAME@_hash = "@PROJECT_GIT_HASH@" - -def show_version(): - print("\nYou are using @PROJECT_NAME@ version %s\n"%version) - -def show_git_hash(): - print("\nYou are using @PROJECT_NAME@ git hash %s based on triqs git hash %s\n"%("@PROJECT_GIT_HASH@", triqs_hash)) diff --git a/test/python/Dummy.out.h5 b/test/python/Dummy.out.h5 deleted file mode 100644 index 92664816cecba05f16c8684b435c2fca492e0931..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 4584 zcmeHLeNa?Y6n_f=JA8i?4rb6`<_D4j(Hh!stpyhpWY<+eoe24GCtM)en1w+_P$FoR zK`Jx^0uo9GO(aEH1(8^l76gmZC3ZJHc5&Dx4IN0d{djMt;h#ol94F(wnS0JX=e%?8 z{oQlVJMVqWW(C_>yIT{6i%ut=BOHw^)jT9GwUbFg^(p;(Bts)<9!YD>Obm@M+ypU; zlsl3Br`z$kK|zGxlJZYc@-aeTVdChNV21v$5MT$bj4&)Xl3XRrSf4Onb)Z03FA|R(Qz@t z7*asRF_SWQM7l0~Ez6LBskrkrH#wmEvdKPw+B_a{m}lOcMpzp2fT=OOsZ2XaqnVJT z@(xAK^?HNG$rB{@Ov2xW@PA0+ZK0PM^k!yeMhA4#pE->|ZWXmtCTN{WF9u_mn~S3e zLS#}rr8eVY{Bl9tEzswOEZEi7h-F7I=-u;1Fjq^rUEU+dpOe9u+NwpxXMZ&NS(QUq zwR_xk5MENJ2aEQi`u;(y{@qSD z?A%qhNjETHcSXjWP~qF;IJ?eb1)S@eR3%H*s3;75^M$?<_-xaNuAU#n{`DPK4zjf< z>1V&Pd-F-KCLD9WUfT_kYn1Qp)u-W}b(f*)?ME~3+6G3F8s7`s>jl3IVN0leS-9i} z$SSstr?lOG&l&Nm$of$b{nd9;g-S@rG?Q~P2yqqU&W3ke2vj+3Lzi{j=mqRs+cfm)j zM8Z^~<=cWTl*|?v+kDV~sm#(9Y3~mqVp9Z8Z>>fL+d(#wEJLOuRkr1n3}Hq7-Wg#! 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R. Strand" Date: Sun, 4 Oct 2020 15:16:15 +0200 Subject: [PATCH 104/121] [eli] move note section in Eli theory doc --- doc/theory/eliashberg.rst | 22 +++++++++++----------- 1 file changed, 11 insertions(+), 11 deletions(-) diff --git a/doc/theory/eliashberg.rst b/doc/theory/eliashberg.rst index 35dec1345..5376bb396 100644 --- a/doc/theory/eliashberg.rst +++ b/doc/theory/eliashberg.rst @@ -3,12 +3,6 @@ Linearized Eliashberg Equation ============================== -.. note:: - The following is restricted to :math:`SU(2)` symmetric systems. - All indices are purely orbital and superconducting gaps :math:`\Delta` and - particle-particle vertices :math:`\Gamma` are restricted to the singlet/triplet - channel, shown by the superscripts s/t respectively. - The linearized Eliashberg equation is a generalization of the linearized Bardeen-Cooper-Schrieffer (BCS) gap equation to frequency dependent gaps. It can be used to determine the critical (inverse) temperature @@ -31,11 +25,17 @@ frequency and momentum :math:`\mathbf{k}`, :math:`\Gamma^{\mathrm{s/t}}` is the irreducible particle-particle vertex and :math:`G` is the one-particle Green's function. -Note, that the bosonic Matsubara frequency and momentum in the particle-particle vertex -is set to zero. -This is because we are interested in Cooper-pairs which have a zero -transfered momentum-frequency in a scattering process. - +.. note:: + The bosonic Matsubara frequency and momentum in the particle-particle vertex is set to zero. + This is because we are interested in Cooper-pairs which have a zero + transfered momentum-frequency in a scattering process. + +.. note:: + The current implementation is restricted to :math:`SU(2)` symmetric systems. + All indices are purely orbital and superconducting gaps :math:`\Delta` and + particle-particle vertices :math:`\Gamma` are restricted to the singlet/triplet + channel, shown by the superscripts s/t respectively. + Deriving the linearized Eliashberg equation from the normal state ----------------------------------------------------------------- From 3e1c85a5208974336bf3726faa8d0b3260113479 Mon Sep 17 00:00:00 2001 From: "Hugo U. R. Strand" Date: Sun, 4 Oct 2020 15:31:38 +0200 Subject: [PATCH 105/121] [pkg] Readme update --- README.md | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) diff --git a/README.md b/README.md index d0e39ba33..ad9bc7329 100644 --- a/README.md +++ b/README.md @@ -1,12 +1,13 @@ # *TPRF*: the Two-Particle Response Function tool box for TRIQS -Copyright (C) 2017, H. U.R. Strand +Copyright (C) 2017-2020, H. U.R. Strand Copyright (C) 2018-2019, The Simons Foundation -TPRF is a TRIQS application containing various tools for working with -two particle response functions. +Copyright (C) 2019-2020, S. Käser + +TPRF is a two-particle response function tool box based on the TRIQS library For more information see the Documentation https://triqs.github.io/tprf From 217e983b7c77375b54081641c86bb0be45d85978 Mon Sep 17 00:00:00 2001 From: "Hugo U. R. Strand" Date: Sun, 4 Oct 2020 15:33:16 +0200 Subject: [PATCH 106/121] [pkg] revert desc in readme --- README.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/README.md b/README.md index ad9bc7329..e5a4a9bb4 100644 --- a/README.md +++ b/README.md @@ -7,7 +7,8 @@ Copyright (C) 2018-2019, The Simons Foundation Copyright (C) 2019-2020, S. Käser -TPRF is a two-particle response function tool box based on the TRIQS library +TPRF is a TRIQS application containing various tools for working with +two particle response functions. For more information see the Documentation https://triqs.github.io/tprf From a485fd9f5a97da0759c6d09f67847ea1e3881360 Mon Sep 17 00:00:00 2001 From: Stefan Date: Tue, 6 Oct 2020 13:05:56 +0200 Subject: [PATCH 107/121] [eli] solve factor 1/2 inconsistency --- doc/theory/eliashberg.rst | 33 ++++++++++++++------------------- 1 file changed, 14 insertions(+), 19 deletions(-) diff --git a/doc/theory/eliashberg.rst b/doc/theory/eliashberg.rst index 5376bb396..ecaf4bc4c 100644 --- a/doc/theory/eliashberg.rst +++ b/doc/theory/eliashberg.rst @@ -39,16 +39,9 @@ and :math:`G` is the one-particle Green's function. Deriving the linearized Eliashberg equation from the normal state ----------------------------------------------------------------- -Generally speaking a transition from the normal state to the superconducting -one occurs when the particle-particle susceptibility diverges. - -.. math:: - \mathbf{\chi}^{\mathrm{s/t}} = [\mathbf{1}-\mathbf{\Gamma}^{\mathrm{s/t}} - \mathbf{\chi}^{(0),{PP}}]^{-1} - \mathbf{\chi}^{(0),{PP}} - -This is the case when the largest eigenvalue of -:math:`\mathbf{\Gamma^{\mathrm{s/t}}} \mathbf{\chi}^{(0),{PP}}` becomes unity. +Generally speaking a transition from the normal state to a singlet/triplet +superconducting one occurs when the largest eigenvalue of +:math:`\frac{1}{2}\mathbf{\Gamma^{\mathrm{s/t}}} \mathbf{\chi}^{(0),{PP}}` becomes unity. For a largest eigenvalues that is smaller than :math:`1` we are still in the normal state, but we can calculate the corresponding eigenvectors :math:`\Delta^{\mathrm{s/t}}`. @@ -57,7 +50,7 @@ This corresponds to the following eigenvalue equation .. math:: \lambda\Delta^{\mathrm{s/t}}_{\bar{a}\bar{b}}(K) = - \frac{1}{N_{\mathbf{k}}^2 \beta^2}\sum_{K', K''} + \frac{1}{2N_{\mathbf{k}}^2 \beta^2}\sum_{K', K''} \Gamma^{\mathrm{s/t}}_{c\bar{a}d\bar{b}}(Q=0, K, K') \chi^{(0),{PP}}_{\bar{e}d\bar{f}c}(Q=0, K', K'') \Delta^{\mathrm{s/t}}_{\bar{e}\bar{f}}(K')\,, @@ -67,9 +60,9 @@ which we can write like Eq. :eq:`linearized_eliashberg_1` with the definiton of :math:`\chi^{(0),{PP}}` .. math:: - \chi^{(0),{PP}}_{\bar{a}b\bar{c}d}(Q, K, K') + \chi^{(0),{PP}}_{\bar{a}b\bar{c}d}(Q=0, K, K') = - -\frac{N_{\mathbf{k}} \beta}{2} + -N_{\mathbf{k}} \beta G_{d\bar{a}}(K)G_{b\bar{c}}(-K')\delta_{K, K'}\,, :label: chi_0_pp @@ -83,12 +76,14 @@ as :label: linearized_eliashberg_3 .. note:: - There is an inconsistency with a factor of :math:`\frac{1}{2}` with - Eq. :eq:`chi_0_pp` and Eq. :eq:`bare_pp_sus_def`. - As there is no bare particle-particle bubble implementation yet, - and the Eliashberg implementation is self-consistent, - we don't have any problems. - But for future implementations this needs to be addressed. + Our definiton of :math:`\chi^{(0),{PP}}` is different from [#bickers]_ + and [#nourafkan]_. This stems from the fact, that due to the indistinguishability + of the particles in the particle-particle channel doublecounting diagrams in the + Bethe-Salpeter equation (BSE) must be avoided. + We do this by defining the particle-particle BSE with a factor of + :math:`\frac{1}{2}`, see :ref:`vertex` Eq. :eq:`BSE_PP`. + In [#bickers]_ and [#nourafkan]_ the particle-particle BSE is defined without this + factor and they include it in their definiton of :math:`\chi^{(0),{PP}}`. This equation is valid for :math:`\lambda \leq 1` and yields eigenvectors, which correspond to superconducting gap functions From 2152fc47666128f3fcd3c2e56182f1abc42efb4c Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 20 Jan 2021 16:24:39 +0100 Subject: [PATCH 108/121] [eli] update theory --- doc/theory/eliashberg.rst | 336 ++++++++++++++++++++++++++++---------- 1 file changed, 246 insertions(+), 90 deletions(-) diff --git a/doc/theory/eliashberg.rst b/doc/theory/eliashberg.rst index ecaf4bc4c..aa1afb7ae 100644 --- a/doc/theory/eliashberg.rst +++ b/doc/theory/eliashberg.rst @@ -15,7 +15,7 @@ It is given by .. math:: \Delta^{\mathrm{s/t}}_{\bar{a}\bar{b}}(K)= -\frac{1}{2 N_{\mathbf{k}}\beta_\mathrm{c}}\sum_{K'} \Gamma^{\mathrm{s/t}}_{c\bar{a}d\bar{b}}(Q=0, K, K') - G_{c\bar{e}}(K')G_{d\bar{f}}(-K') + G_{c\bar{f}}(K')G_{d\bar{e}}(-K') \Delta^{\mathrm{s/t}}_{\bar{e}\bar{f}}(K')\,. :label: linearized_eliashberg_1 @@ -28,20 +28,60 @@ and :math:`G` is the one-particle Green's function. .. note:: The bosonic Matsubara frequency and momentum in the particle-particle vertex is set to zero. This is because we are interested in Cooper-pairs which have a zero - transfered momentum-frequency in a scattering process. + transfered momentum-frequency in a scattering process [#nourafkan]_. .. note:: The current implementation is restricted to :math:`SU(2)` symmetric systems. All indices are purely orbital and superconducting gaps :math:`\Delta` and particle-particle vertices :math:`\Gamma` are restricted to the singlet/triplet channel, shown by the superscripts s/t respectively. + But note, that the equations still hold for the spin-dependent case and + one would soley need to implement the spin-dependent particle-particle vertex + to use them. Deriving the linearized Eliashberg equation from the normal state ----------------------------------------------------------------- -Generally speaking a transition from the normal state to a singlet/triplet -superconducting one occurs when the largest eigenvalue of -:math:`\frac{1}{2}\mathbf{\Gamma^{\mathrm{s/t}}} \mathbf{\chi}^{(0),{PP}}` becomes unity. +The singlet and triplet susceptibilties are given by + +.. math:: + \chi^{\mathrm{s}} + = + - + \chi^{(0), \mathrm{PP}} + + + \frac{1}{2} + \chi^{(0), \mathrm{PP}} + \mathbf{\Gamma}^{\mathrm{s}} + \left[ + - + \chi^{\mathrm{s}} + + + \chi^{(0), \mathrm{PP}} + \right] + \,, + +and + +.. math:: + \chi^{\mathrm{t}} + = + \chi^{(0), \mathrm{PP}} + + + \frac{1}{2} + \chi^{(0), \mathrm{PP}} + \mathbf{\Gamma}^{\mathrm{t}} + \left[ + \chi^{\mathrm{t}} + + + \chi^{(0), \mathrm{PP}} + \right] + \,. + +A transition from the normal state to a singlet/triplet superconducting one occurs +when the susceptibilties diverge. +This is the case, when the largest eigenvalue of +:math:`\mp \frac{1}{2}\mathbf{\Gamma^{\mathrm{s/t}}} \mathbf{\chi}^{(0),{PP}}` becomes unity. For a largest eigenvalues that is smaller than :math:`1` we are still in the normal state, but we can calculate the corresponding eigenvectors :math:`\Delta^{\mathrm{s/t}}`. @@ -52,11 +92,15 @@ This corresponds to the following eigenvalue equation = \frac{1}{2N_{\mathbf{k}}^2 \beta^2}\sum_{K', K''} \Gamma^{\mathrm{s/t}}_{c\bar{a}d\bar{b}}(Q=0, K, K') - \chi^{(0),{PP}}_{\bar{e}d\bar{f}c}(Q=0, K', K'') - \Delta^{\mathrm{s/t}}_{\bar{e}\bar{f}}(K')\,, + \chi^{(0),{PP}}_{\bar{f}d\bar{e}c}(Q=0, K', K'') + \Delta^{\mathrm{s/t}}_{\bar{e}\bar{f}}(K')\,. :label: linearized_eliashberg_2 + \,, + +where we incorporate the minus sign of the singlet channel in our definition of the +singlet irreducible vertex to only keep track of one version of the Eliashberg equation. -which we can write like Eq. :eq:`linearized_eliashberg_1` with the definiton +We can write this like Eq. :eq:`linearized_eliashberg_1` by using the definiton of :math:`\chi^{(0),{PP}}` .. math:: @@ -66,12 +110,12 @@ of :math:`\chi^{(0),{PP}}` G_{d\bar{a}}(K)G_{b\bar{c}}(-K')\delta_{K, K'}\,, :label: chi_0_pp -as +which yields .. math:: \lambda\Delta^{\mathrm{s/t}}_{\bar{a}\bar{b}}(K)= -\frac{1}{2 N_{\mathbf{k}}\beta}\sum_{K'} \Gamma^{\mathrm{s/t}}_{c\bar{a}d\bar{b}}(Q=0, K, K') - G_{c\bar{e}}(K')G_{d\bar{f}}(-K') + G_{c\bar{f}}(K')G_{d\bar{e}}(-K') \Delta^{\mathrm{s/t}}_{\bar{e}\bar{f}}(K')\,. :label: linearized_eliashberg_3 @@ -195,75 +239,74 @@ Random phase approximation for the irreducible particle-particle vertex The irreducible particle-particle vertex is given by the parquet equation, which can be expressed in terms of the fully irreducible vertex :math:`\Lambda` -and the channel reducible vertex-ladder functions :math:`\Phi`. +and the channel reducible vertex ladder functions :math:`\Phi`. It is given in the singlet channel by .. math:: - \Gamma^{\mathrm{s}}_{a\bar{b}c\bar{d}}(Q=0, K, K') - \equiv & - \frac{3}{2} - \left[ - \Phi^{\mathrm{m}}_{a\bar{b}c\bar{d}}(K-K') - + - \Phi^{\mathrm{m}}_{c\bar{b}a\bar{d}}(K+K') - \right] - \\&- - \frac{1}{2} - \left[ - \Phi^{\mathrm{d}}_{a\bar{b}c\bar{d}}(K-K') - + - \Phi^{\mathrm{d}}_{c\bar{b}a\bar{d}}(K+K') - \right] + \Gamma^{\text{s}}_{a\overline{b}c\overline{d}}(Q, K, K') =& + - + \Lambda^{\text{s}}_{a\overline{b}c\overline{d}}(Q, K, K') + - \Lambda^{\mathrm{s}}_{a\bar{b}c\bar{d}}\,, - :label: singlet_gamma - -and in the triplet channel by - -.. math:: - \Gamma^{\mathrm{t}}_{a\bar{b}c\bar{d}}(Q=0, K, K') - \equiv & - -\frac{1}{2} \left[ - \Phi^{\mathrm{m}}_{a\bar{b}c\bar{d}}(K-K') + \frac{3}{2} + \Phi^{\text{m}}_{a\overline{b}c\overline{d}} - - \Phi^{\mathrm{m}}_{c\bar{b}a\bar{d}}(K+K') - \right] - \\&- \frac{1}{2} + \Phi^{\text{d}}_{a\overline{b}c\overline{d}} + \right](Q-K-K', K, K') + \\ + &+ \left[ - \Phi^{\mathrm{d}}_{a\bar{b}c\bar{d}}(K-K') + \frac{3}{2} + \Phi^{\text{m}}_{c\overline{b}a\overline{d}} - - \Phi^{\mathrm{d}}_{c\bar{b}a\bar{d}}(K+K') - \right] - + - \Lambda^{\mathrm{t}}_{a\bar{b}c\bar{d}}\,, - :label: triplet_gamma + \frac{1}{2} + \Phi^{\text{d}}_{c\overline{b}a\overline{d}} + \right](K-K', Q-K, K') + :label: singlet_gamma_no_approx +and in the triplet channel by -where the vertex-ladder functions are given by +.. math:: + \Gamma^{\text{t}}_{a\overline{b}c\overline{d}}(Q, K, K') =& + \Lambda^{\text{t}}_{a\overline{b}c\overline{d}}(Q, K, K') + + + \left[ + \frac{1}{2} + \Phi^{\text{m}}_{a\overline{b}c\overline{d}} + + + \frac{1}{2} + \Phi^{\text{d}}_{a\overline{b}c\overline{d}} + \right](Q-K-K', K, K') + \\ + &+ + \left[ + - + \frac{1}{2} + \Phi^{\text{m}}_{c\overline{b}a\overline{d}} + - + \frac{1}{2} + \Phi^{\text{d}}_{c\overline{b}a\overline{d}} + \right](K-K', Q-K, K') + \,, + :label: triplet_gamma_no_approx + +with the spin diagonalized reducible vertex ladder functions given by .. math:: - \Phi^{\text{d/m}}_{a\overline{b}c\overline{d}}(Q) + \Phi^{\text{d/m}}_{a\overline{b}c\overline{d}}(Q, K, K') = - \Lambda^{\text{d/m}} \chi^{\text{d/m}}(Q) \Lambda^{\text{d/m}}\,. - + \frac{1}{(N_\mathbf{k}\beta)^2} + \sum_{K'', K'''} + \Gamma^{\text{d/m}}(Q, K, K'') \chi^{\text{d/m}}(Q, K'', K''') \Gamma^{\text{d/m}}(Q, K''', K') + \,. Note, that the superscripts :math:`\mathrm{d/m}` indicate the density/magnetic channel. Now, in the random phase approximation (RPA) the susceptibilities :math:`\chi^{\text{d/m}}` are approximated by the RPA bubble susceptibility, -and the vertices are approximated by - -.. math:: - \Lambda^{\text{d/m}} \approx U^{\mathrm{d/m}}\,, - -and - -.. math:: - \Lambda^{\text{s/t}} \approx \frac{1}{2}(U^{\mathrm{d}} + U^{\mathrm{m}})\,. - -Here :math:`U^{\mathrm{d/m}}` is the bare local Kanamori interaction given by +and all vertices are substituted by the local and static bare Kanamori interaction :math:`U^{\mathrm{d/m}}`, +given by .. math:: U^{\mathrm{d/m}}_{a\bar{b}c\bar{d}} = @@ -276,45 +319,145 @@ Here :math:`U^{\mathrm{d/m}}` is the bare local Kanamori interaction given by \end{cases}\,, with the Hubbard interaction :math:`U` and the Hund's :math:`J`. +The reducible ladder vertices then beceome only dependent on one bosonic Frequence and +momentum pair :math:`Q` + +.. math:: + \Phi^{\text{d/m}}_{a\overline{b}c\overline{d}}(Q) + &\approx + \frac{1}{(N_\mathbf{k}\beta)^2} + \sum_{K'', K'''} + \overline{U}^{\text{d/m}}\chi^{\text{d/m}}(Q, K'', K''') \overline{U}^{\text{d/m}} + \\ + &\approx + \overline{U}^{\mathrm{d/m}} + \chi^{\text{d/m}}(Q) \overline{U}^{\mathrm{d/m}} + \,, -Note, that in both singlet :eq:`singlet_gamma` and -triplet :eq:`triplet_gamma` a density and magnetic -:math:`\Phi` term appears twice. -Once without an index flip and a dependence on :math:`K-K'`, -:math:`\Phi_{a\overline{b}c\overline{d}}(K-K')`, -and another time with an index flip and a dependence on :math:`K+K'`, -:math:`\Phi_{c\overline{b}a\overline{d}}(K+K')`. -Inside the linearized Eliashberg equation :eq:`linearized_eliashberg_3` -the :math:`\Phi_{c\overline{b}a\overline{d}}(K+K')` term -picks up a sign which depends on the frequency, momentum and orbital -symmetry of the gap :math:`\Delta^{\mathrm{s/t}}`. -For all allowed singlet combinations it is positive and for all allowed triplet ones -negative. Therefore Eq. :eq:`singlet_gamma` and Eq. :eq:`triplet_gamma` become +and the fully irreducible vertices become .. math:: - \Gamma^{\text{s}}_{a\overline{b}c\overline{d}}(Q=0, K, K') \equiv - 3 - \Phi^{\text{m}}_{a\overline{b}c\overline{d}}(K-K') + \Lambda^{\mathrm{s}} + \approx - - \Phi^{\text{d}}_{a\overline{b}c\overline{d}}(K-K') - + - \Lambda^{\text{s}}_{a\overline{b}c\overline{d}} + \frac{1}{2}U^{\mathrm{d}} + - + \frac{3}{2}U^{\mathrm{m}} \,, - :label: singlet_gamma_2 .. math:: - \Gamma^{\text{t}}_{a\overline{b}c\overline{d}}(Q=0, K, K') \equiv + \Lambda^{\mathrm{t}} + \approx - - \Phi^{\text{m}}_{a\overline{b}c\overline{d}}(K-K') - - - \Phi^{\text{d}}_{a\overline{b}c\overline{d}}(K-K') + \frac{1}{2}U^{\mathrm{d}} + - \Lambda^{\text{t}}_{a\overline{b}c\overline{d}} + \frac{1}{2}U^{\mathrm{m}} + \,. + +In this approximation the irreducible singlet/triplet vertex for :math:`Q=0` takes the form + +.. math:: + \Gamma^{\text{s}}_{a\overline{b}c\overline{d}}(Q=0, K, K') =& + \frac{1}{2}U_{a\overline{b}c\overline{d}}^{\mathrm{d}} + + + \frac{3}{2}U_{a\overline{b}c\overline{d}}^{\mathrm{m}} + + + \left[ + \frac{3}{2} + \Phi^{\text{m}}_{a\overline{b}c\overline{d}} + - + \frac{1}{2} + \Phi^{\text{d}}_{a\overline{b}c\overline{d}} + \right](-K-K') + \\ + &+ + \left[ + \frac{3}{2} + \Phi^{\text{m}}_{c\overline{b}a\overline{d}} + - + \frac{1}{2} + \Phi^{\text{d}}_{c\overline{b}a\overline{d}} + \right](K-K') + \,, + :label: singlet_gamma + +and + +.. math:: + \Gamma^{\text{t}}_{a\overline{b}c\overline{d}}(Q=0, K, K') =& + - + \frac{1}{2}U_{a\overline{b}c\overline{d}}^{\mathrm{d}} + + + \frac{1}{2}U_{a\overline{b}c\overline{d}}^{\mathrm{m}} + + + \left[ + \frac{1}{2} + \Phi^{\text{m}}_{a\overline{b}c\overline{d}} + + + \frac{1}{2} + \Phi^{\text{d}}_{a\overline{b}c\overline{d}} + \right](-K-K') + \\ + &+ + \left[ + - + \frac{1}{2} + \Phi^{\text{m}}_{c\overline{b}a\overline{d}} + - + \frac{1}{2} + \Phi^{\text{d}}_{c\overline{b}a\overline{d}} + \right](K-K') \,. + :label: triplet_gamma + +Note, that in both the singlet :eq:`singlet_gamma` and the triplet vertex +:eq:`triplet_gamma` the density and magnetic ladder vertices +:math:`\Phi^{\text{d/m}}` appear twice. Once with an index flip and with a :math:`K-K'` +dependence, :math:`\Phi_{c\overline{b}a\overline{d}}(K-K')`, and once without an index flip +and a :math:`-K-K'` dependence, :math:`\Phi_{a\overline{b}c\overline{d}}(-K-K')`. +In the linearized Eliashberg equation :eq:`linearized_eliashberg_3` those two terms can be +transformed into each other by abiding the frequency, momentum and orbital +symmetry of the gap. +For example :math:`\Phi_{a\overline{b}c\overline{d}}(-K-K')` transforms into +:math:`\pm\Phi_{c\overline{b}a\overline{d}}(K'-K)=\pm\Phi^*_{c\overline{b}a\overline{d}}(K-K')` +for a singlet/triplet gap. +We can therefore write Eq. :eq:`singlet_gamma` and :eq:`triplet_gamma` as + +.. math:: + \Gamma^{\text{s}}_{a\overline{b}c\overline{d}}(Q=0, K, K') \equiv + \frac{1}{2}U_{a\overline{b}c\overline{d}}^{\mathrm{d}} + + + \frac{3}{2}U_{a\overline{b}c\overline{d}}^{\mathrm{m}} + + + \Re + \left[ + 3 + \Phi^{\text{m}}_{c\overline{b}a\overline{d}}(K-K') + - + \Phi^{\text{d}}_{c\overline{b}a\overline{d}}(K-K') + \right] + \,, + :label: singlet_gamma_2 + +.. math:: + \Gamma^{\text{t}}_{a\overline{b}c\overline{d}}(Q=0, K, K') \equiv + - + \frac{1}{2}U_{a\overline{b}c\overline{d}}^{\mathrm{d}} + + + \frac{1}{2}U_{a\overline{b}c\overline{d}}^{\mathrm{m}} + + + \Re + \left[ + - + \Phi^{\text{m}}_{c\overline{b}a\overline{d}}(K-K') + - + \Phi^{\text{d}}_{c\overline{b}a\overline{d}}(K-K') + \right] + \,. :label: triplet_gamma_2 -Note, that this simplification is only allowed, if the solutions of :math:`\Delta^{\mathrm{s/t}}` -are restricted to the allowed symmetries, otherwise unphysical solution can occur. +Note, that this simplification is only allowed if the solutions of :math:`\Delta^{\mathrm{s/t}}` +are restricted to the allowed symmetries, otherwise unphysical solutions can occur. Also note, that the RPA particle-particle vertices in Eq. :eq:`singlet_gamma_2` and :eq:`triplet_gamma_2` only depend on the difference between the two fermionic Matsubara frequencies, i.e. a bosonic Matsubara frequency and one momentum. @@ -324,7 +467,7 @@ We can therefore write the linearized Eliashberg equation .. math:: \lambda\Delta^{\mathrm{s/t}}_{\bar{a}\bar{b}}(K)= -\frac{1}{2 N_{\mathbf{k}}\beta}\sum_{K'} \Gamma^{\mathrm{s/t}}_{c\bar{a}d\bar{b}}(K-K') - G_{c\bar{e}}(K')G_{d\bar{f}}(-K') + G_{c\bar{f}}(K')G_{d\bar{e}}(-K') \Delta^{\mathrm{s/t}}_{\bar{e}\bar{f}}(K')\,, :label: linearized_eliashberg_5 @@ -337,12 +480,25 @@ This allows us to get rid of the summation by using the convolution theorem \mathcal{F}\left[\Delta_{\bar{a}\bar{b}}^{\mathrm{s/t}}(K)\right]= -\frac{1}{2} \mathcal{F}\left[\Gamma_{c\bar{a}d\bar{b}}^{\mathrm{s/t}}(K-K')\right] \mathcal{F}\left[ - G_{c\bar{e}}(K')G_{d\bar{f}}(-K') + G_{c\bar{f}}(K')G_{d\bar{e}}(-K') \Delta_{\bar{e}\bar{f}}^{\mathrm{s/t}}(K') \right]\,, :label: linearized_eliashberg_5 -making the calculation computationaly more efficient. +making the calculation computationaly more efficient for large numbers of frequencies +and momenta. +But note, that for small numbers of frequencies and/or momenta using the sum +instead of the convolution theorem can be more effecient. + +.. note:: + It is possible to expand the current implementation of the Eliashberg equation to + also allow for irreducible vertices to be explicitly dependent on two fermionic + frequency and momenta pairs. + For an idea on how to tackle such a task see the following draft + `here `_ + and + `here `_. + .. rubric:: References From 3ff26ea8e971386fe398bd269932f19518cfd6a0 Mon Sep 17 00:00:00 2001 From: Stefan Date: Thu, 21 Jan 2021 11:08:23 +0100 Subject: [PATCH 109/121] [eli] adjust indices ordering in eli product --- c++/triqs_tprf/lattice/eliashberg.cpp | 20 ++++++++++---------- 1 file changed, 10 insertions(+), 10 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index 3d2ff3c34..187d3c5ff 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -53,10 +53,10 @@ g_wk_t eliashberg_g_delta_g_product(g_wk_vt g_wk, g_wk_vt delta_wk) { for (unsigned int idx = 0; idx < meshes_mpi.size(); idx++){ auto &[w, k] = meshes_mpi(idx); - for (auto [A, B] : F_wk.target_indices()) - for (auto [c, d] : delta_wk.target_indices()) - F_wk[w, k](A, B) += - g_wk[w, k](A, c) * g_wk[-w, -k](B, d) * delta_wk[w, k](c, d); + for (auto [d, c] : F_wk.target_indices()) + for (auto [e, f] : delta_wk.target_indices()) + F_wk[w, k](d, c) += + g_wk[w, k](c, f) * g_wk[-w, -k](d, e) * delta_wk[w, k](e, f); } return F_wk; @@ -83,9 +83,9 @@ g_wk_t eliashberg_product(chi_wk_vt Gamma_pp, g_wk_vt g_wk, for (const auto [w, k] : delta_wk.mesh()) for (const auto [n, q] : delta_wk.mesh()) - for (auto [A, a, B, b] : Gamma_pp.target_indices()) + for (auto [c, a, d, b] : Gamma_pp.target_indices()) delta_wk_out[w, k](a, b) += - -0.5 * Gamma_pp(w-n, k - q)(A, a, B, b) * F_wk[n, q](A, B); + -0.5 * Gamma_pp(w-n, k - q)(c, a, d, b) * F_wk[n, q](d, c); delta_wk_out /= (wmesh.domain().beta * kmesh.size()); @@ -133,8 +133,8 @@ e_r_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, g_tr_t F_tr for (const auto r : std::get<1>(F_tr.mesh())) { auto F_t = F_tr[_, r]; - for (auto [A, a, B, b] : Gamma_pp_const_r.target_indices()) - delta_r_out[r](a, b) += -0.5 * Gamma_pp_const_r[r](A, a, B, b) * F_t(0)(A, B); + for (auto [c, a, d, b] : Gamma_pp_const_r.target_indices()) + delta_r_out[r](a, b) += -0.5 * Gamma_pp_const_r[r](c, a, d, b) * F_t(0)(d, c); } return delta_r_out; @@ -163,8 +163,8 @@ g_tr_t eliashberg_dynamic_gamma_f_product(chi_tr_vt Gamma_pp_dyn_tr, g_tr_vt F_t for (unsigned int idx = 0; idx < meshes_mpi.size(); idx++){ auto &[t, r] = meshes_mpi(idx); - for (auto [A, a, B, b] : Gamma_pp_dyn_tr.target_indices()) - delta_tr_out[t, r](a, b) += -0.5 * Gamma_pp_dyn_tr[t, r](A, a, B, b) * F_tr[t, r](A, B); + for (auto [c, a, d, b] : Gamma_pp_dyn_tr.target_indices()) + delta_tr_out[t, r](a, b) += -0.5 * Gamma_pp_dyn_tr[t, r](c, a, d, b) * F_tr[t, r](d, c); } return delta_tr_out; From 2b1541991ef5d65d4b2d5dff25a19955c3059347 Mon Sep 17 00:00:00 2001 From: Stefan Date: Thu, 21 Jan 2021 14:57:33 +0100 Subject: [PATCH 110/121] [eli] add function to construct phi --- c++/triqs_tprf/lattice/eliashberg.cpp | 35 +++++++++++++++++++++++++++ c++/triqs_tprf/lattice/eliashberg.hpp | 27 +++++++++++++++++++++ python/triqs_tprf/lattice_desc.py | 29 ++++++++++++++++++++-- 3 files changed, 89 insertions(+), 2 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index 187d3c5ff..1caa24009 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -270,4 +270,39 @@ chi_wk_t gamma_PP_triplet(chi_wk_vt chi_c, chi_wk_vt chi_s, \ return Gamma_pp_wk; } +chi_wk_t construct_phi_wk(chi_wk_vt chi, array_view, 4> U) { + + using scalar_t = chi_wk_t::scalar_t; + + size_t nb = chi.target_shape()[0]; + + auto phi_wk = make_gf(chi); + phi_wk *= 0; + + // PH grouping of the vertex, from cc+cc+, permuting the last two indices. + auto U_matrix = make_matrix_view(group_indices_view(U, {0, 1}, {3, 2})); + + auto meshes_mpi = mpi_view(phi_wk.mesh()); + +#pragma omp parallel for + for (unsigned int idx = 0; idx < meshes_mpi.size(); idx++){ + auto &[w, k] = meshes_mpi(idx); + + array phi_arr{nb, nb, nb, nb, memory_layout_t<4>{0, 1, 2, 3}}; + array chi_arr{chi[w, k], memory_layout_t<4>{0, 1, 2, 3}}; + + // PH grouping of the vertex, from cc+cc+, permuting the last two indices. + auto phi_matrix = make_matrix_view(group_indices_view(phi_arr, {0, 1}, {3, 2})); + // PH grouping of the susceptibilites, from c+cc+c, permuting the last two indices. + auto chi_matrix = make_matrix_view(group_indices_view(chi_arr, {0, 1}, {3, 2})); + + phi_matrix = U_matrix * chi_matrix * U_matrix; + + phi_wk[w, k] = phi_arr; + } + phi_wk = mpi::all_reduce(phi_wk); + + return phi_wk; +} + } // namespace triqs_tprf diff --git a/c++/triqs_tprf/lattice/eliashberg.hpp b/c++/triqs_tprf/lattice/eliashberg.hpp index 470a54754..b4372cc67 100644 --- a/c++/triqs_tprf/lattice/eliashberg.hpp +++ b/c++/triqs_tprf/lattice/eliashberg.hpp @@ -229,4 +229,31 @@ namespace triqs_tprf { chi_wk_t gamma_PP_triplet(chi_wk_vt chi_c, chi_wk_vt chi_s, array_view, 4> U_c, array_view, 4> U_s); chi_wk_t gamma_PP_spin_charge(chi_wk_vt chi_c, chi_wk_vt chi_s, array_view, 4> U_c, array_view, 4> U_s, double charge_factor, double spin_factor); + + /** Computes reducible ladder vertex for the approximation of a local and static vertex. + + In this approximation the reducible ladder vertex in density/magnetic channel are given by + + .. math:: + \Phi^{\text{d/m}}_{a\overline{b}c\overline{d}}(Q) + &\approx + \frac{1}{(N_\mathbf{k}\beta)^2} + \sum_{K'', K'''} + \overline{U}^{\text{d/m}}\chi^{\text{d/m}}(Q, K'', K''') \overline{U}^{\text{d/m}} + \\ + &\approx + \overline{U}^{\mathrm{d/m}} + \chi^{\text{d/m}}(Q) \overline{U}^{\mathrm{d/m}} + \,, + + where all products are particle-hole products. + The reducible ladder vertex in then only dependent on one bosonic frequency and momentum. + It can then be used in [REF] to construct the irreducible singlet/triplet vertex. + + @param chi density/magnetuc susceptibility :math:`\chi^{\mathrm{d/m}}_{\bar{a}b\bar{c}d}(i\omega_n,\mathbf{q})` + @param U density/magnetic local and static vertex :math:`U^{\mathrm{d/m}}_{a\bar{b}c\bar{d}}` + @return The reducible ladder vertex in the density/magnetic channel :math:`\Phi^{\mathrm{d/m}}(i\omega_n,\mathbf{q})` + + */ + chi_wk_t construct_phi_wk(chi_wk_vt chi, array_view, 4> U); } diff --git a/python/triqs_tprf/lattice_desc.py b/python/triqs_tprf/lattice_desc.py index fb4d6f7f9..9e18c1dfe 100644 --- a/python/triqs_tprf/lattice_desc.py +++ b/python/triqs_tprf/lattice_desc.py @@ -568,9 +568,32 @@ module.add_function ("triqs_tprf::g_wk_t triqs_tprf::eliashberg_g_delta_g_product (triqs_tprf::g_wk_vt g_wk, triqs_tprf::g_wk_vt delta_wk)", doc = r"""""") -module.add_function ("std::tuple triqs_tprf::split_into_dynamic_wk_and_constant_k (triqs_tprf::chi_wk_vt Gamma_pp)", doc = r"""""") +module.add_function ("std::tuple triqs_tprf::split_into_dynamic_wk_and_constant_k (triqs_tprf::chi_wk_vt Gamma_pp)", doc = r"""Split Gamma in dynamic and constant part by tail fitting -module.add_function ("std::tuple triqs_tprf::dynamic_and_constant_to_tr (triqs_tprf::chi_wk_vt Gamma_pp_dyn_wk, triqs_tprf::chi_k_vt Gamma_pp_const_k)", doc = r"""""") +Parameters +---------- +Gamma_pp + : particle-particle pairing vertex :math:`\Gamma(i\omega_n, \mathbf{k})`. + +Returns +------- +out + Tuple of Gamma_pp_dyn_wk, the dynamic part of Gamma, which converges to zero for :math:`\omega_n \rightarrow \infty`, and Gamma_pp_const_k, the part of Gamma that is constant in Matsubara frequency space :math:`\Gamma(\mathbf{k})`.""") + +module.add_function ("std::tuple triqs_tprf::dynamic_and_constant_to_tr (triqs_tprf::chi_wk_vt Gamma_pp_dyn_wk, triqs_tprf::chi_k_vt Gamma_pp_const_k)", doc = r"""Fourier transform Gamma parts to imaginary time and real-space + +Parameters +---------- +Gamma_pp_dyn_wk + : The dynamic part of Gamma, which converges to zero for :math:`\omega_n \rightarrow \infty`. + +Gamma_pp_const_k + : The part of Gamma that is constant in Matsubara frequency space :math:`\Gamma(\mathbf{k})`. + +Returns +------- +out + Tuple of Gamma_pp_dyn_tr, the dynamic part of Gamma, which converges to zero for :math:`\omega_n \rightarrow \infty`, but now in :math:`\tau`-space, Gamma_pp_const_r, the constant part of Gamma in real-space.""") module.add_function ("triqs_tprf::e_r_t triqs_tprf::eliashberg_constant_gamma_f_product (triqs_tprf::chi_r_vt Gamma_pp_const_r, triqs_tprf::g_tr_t F_tr)", doc = r"""""") @@ -658,6 +681,8 @@ module.add_function ("triqs_tprf::chi_wk_t triqs_tprf::gamma_PP_spin_charge (triqs_tprf::chi_wk_vt chi_c, triqs_tprf::chi_wk_vt chi_s, array_view, 4> U_c, array_view, 4> U_s, double charge_factor, double spin_factor)", doc = r"""""") +module.add_function ("triqs_tprf::chi_wk_t triqs_tprf::construct_phi_wk (triqs_tprf::chi_wk_vt chi, array_view, 4> U)", doc = r"""""") + module.add_function ("array, 6> triqs_tprf::cluster_mesh_fourier_interpolation (array k_vecs, triqs_tprf::chi_wr_cvt chi)", doc = r"""""") module.add_function ("triqs_tprf::chi_tr_t triqs_tprf::chi0_tr_from_grt_PH (triqs_tprf::g_tr_cvt g_tr)", doc = r"""Generalized susceptibility imaginary time bubble in the particle-hole channel :math:`\chi^{(0)}_{\bar{a}b\bar{c}d}(\tau, \mathbf{r})` From baace7d985384ab28eb0a18edbf8b4d60bb91e1a Mon Sep 17 00:00:00 2001 From: Stefan Date: Thu, 21 Jan 2021 15:27:06 +0100 Subject: [PATCH 111/121] [eli] add new functions for singlet/triplet vertex --- python/triqs_tprf/eliashberg.py | 210 ++++++++++++++++++++++++++------ 1 file changed, 174 insertions(+), 36 deletions(-) diff --git a/python/triqs_tprf/eliashberg.py b/python/triqs_tprf/eliashberg.py index 0ea0210a6..be1e17363 100644 --- a/python/triqs_tprf/eliashberg.py +++ b/python/triqs_tprf/eliashberg.py @@ -33,10 +33,22 @@ from .lattice import eliashberg_product from .lattice import eliashberg_product_fft, eliashberg_product_fft_constant from .lattice import split_into_dynamic_wk_and_constant_k, dynamic_and_constant_to_tr +from .lattice import construct_phi_wk + # ---------------------------------------------------------------------- -def solve_eliashberg(Gamma_pp_wk, g_wk, initial_delta=None, Gamma_pp_const_k=None, - tol=1e-10, product='FFT', solver='IRAM', symmetrize_fct=lambda x : x, k=6): + +def solve_eliashberg( + Gamma_pp_wk, + g_wk, + initial_delta=None, + Gamma_pp_const_k=None, + tol=1e-10, + product="FFT", + solver="IRAM", + symmetrize_fct=lambda x: x, + k=6, +): r""" Solve the linearized Eliashberg equation Returns the biggest eigenvalues and corresponding eigenvectors of the linearized Eliashberg @@ -117,23 +129,32 @@ def from_wk_to_x(delta_wk): delta_x = delta_wk.data.copy().flatten() return delta_x - if product == 'FFT': + if product == "FFT": - Gamma_pp_dyn_tr, Gamma_pp_const_r = preprocess_gamma_for_fft(Gamma_pp_wk, Gamma_pp_const_k) + Gamma_pp_dyn_tr, Gamma_pp_const_r = preprocess_gamma_for_fft( + Gamma_pp_wk, Gamma_pp_const_k + ) - if np.allclose(Gamma_pp_dyn_tr.data, 0): # -- If dynamic part is zero reduced calculation - eli_prod = functools.partial(eliashberg_product_fft_constant, Gamma_pp_const_r, g_wk) + if np.allclose( + Gamma_pp_dyn_tr.data, 0 + ): # -- If dynamic part is zero reduced calculation + eli_prod = functools.partial( + eliashberg_product_fft_constant, Gamma_pp_const_r, g_wk + ) else: - eli_prod = functools.partial(eliashberg_product_fft, - Gamma_pp_dyn_tr, Gamma_pp_const_r, g_wk) + eli_prod = functools.partial( + eliashberg_product_fft, Gamma_pp_dyn_tr, Gamma_pp_const_r, g_wk + ) - elif product == 'SUM': + elif product == "SUM": eli_prod = functools.partial(eliashberg_product, Gamma_pp_wk, g_wk) else: - raise NotImplementedError('There is no implementation of the eliashberg product' - ' called %s.'%product) + raise NotImplementedError( + "There is no implementation of the eliashberg product" + " called %s." % product + ) def matvec(delta_x): delta_wk = from_x_to_wk(delta_x) @@ -146,20 +167,23 @@ def matvec(delta_x): initial_delta = semi_random_initial_delta(g_wk) initial_delta = from_wk_to_x(initial_delta) - if solver == 'PM': + if solver == "PM": es, evs = power_method_LR(matvec, initial_delta, tol=tol) es, evs = [es], [evs] - elif solver == 'IRAM': - es, evs = implicitly_restarted_arnoldi_method(matvec, initial_delta, k=k, tol=tol) + elif solver == "IRAM": + es, evs = implicitly_restarted_arnoldi_method( + matvec, initial_delta, k=k, tol=tol + ) else: - raise NotImplementedError('There is no solver called %s.'%solver) + raise NotImplementedError("There is no solver called %s." % solver) eigen_modes = [from_x_to_wk(ele) for ele in evs] return es, eigen_modes + def preprocess_gamma_for_fft(Gamma_pp_wk, Gamma_pp_const_k=None): r""" Prepare Gamma to be used with the FFT implementation @@ -186,22 +210,26 @@ def preprocess_gamma_for_fft(Gamma_pp_wk, Gamma_pp_const_k=None): # -- Determine the dynamic and constant part via a tail fit # -- (This is done even if the constant term is given to get the specific Gf types) - Gamma_pp_dyn_wk_fit, Gamma_pp_const_k_fit = split_into_dynamic_wk_and_constant_k(Gamma_pp_wk) + Gamma_pp_dyn_wk_fit, Gamma_pp_const_k_fit = split_into_dynamic_wk_and_constant_k( + Gamma_pp_wk + ) # -- Use a constant term if explicitly given const_type = type(Gamma_pp_const_k) if (const_type == float) or (const_type == np.ndarray): Gamma_pp_const_k_fit.data[:] = Gamma_pp_const_k Gamma_pp_dyn_wk_fit.data[:] = Gamma_pp_wk.data - Gamma_pp_const_k - elif (const_type == Gf): + elif const_type == Gf: Gamma_pp_const_k_fit[:] = Gamma_pp_const_k.data Gamma_pp_dyn_wk_fit.data[:] = Gamma_pp_wk.data - Gamma_pp_const_k.data # -- FFT dynamic and constant term to (tau, real) or (real) - Gamma_pp_dyn_tr, Gamma_pp_const_r = dynamic_and_constant_to_tr(Gamma_pp_dyn_wk_fit, - Gamma_pp_const_k_fit) + Gamma_pp_dyn_tr, Gamma_pp_const_r = dynamic_and_constant_to_tr( + Gamma_pp_dyn_wk_fit, Gamma_pp_const_k_fit + ) return Gamma_pp_dyn_tr, Gamma_pp_const_r + def semi_random_initial_delta(g_wk, nr_factor=0.5, seed=None): r"""Create a delta based on the GF with random elements @@ -233,17 +261,18 @@ def semi_random_initial_delta(g_wk, nr_factor=0.5, seed=None): delta = g_wk.copy() shape = delta.data.shape - delta.data[:] = delta.data.real # Pure real delta is sufficient w/o magnetic field + delta.data[:] = delta.data.real # Pure real delta is sufficient w/o magnetic field random_data = np.random.random(shape[1:]) freq_data = np.mean(np.abs(delta.data), axis=tuple(range(len(shape))[1:])) - not_randomized = int(nr_factor*shape[0] / 2.) - start, stop = not_randomized, shape[0]-not_randomized - freq_data[start:stop] *= np.random.random(stop-start) + not_randomized = int(nr_factor * shape[0] / 2.0) + start, stop = not_randomized, shape[0] - not_randomized + freq_data[start:stop] *= np.random.random(stop - start) delta.data[:] = np.tensordot(freq_data, random_data, axes=0) return delta + def implicitly_restarted_arnoldi_method(matvec, init, tol=1e-10, k=6): """Find the eigenvalue with the largest real value via the Implicitly Restarted Arnoldi Method @@ -275,11 +304,12 @@ def implicitly_restarted_arnoldi_method(matvec, init, tol=1e-10, k=6): """ N = init.shape[0] linop = LinearOperator(matvec=matvec, dtype=np.complex, shape=(N, N)) - Es, U = eigs(linop, k=k, which='LR', tol=tol, v0=init) + Es, U = eigs(linop, k=k, which="LR", tol=tol, v0=init) Es = Es.real - + return list(Es), list(U.T) + def power_method_LR(matvec, init, tol=1e-10, max_it=1e5): """Find the eigenvalue with the largest real value via the power method @@ -304,17 +334,17 @@ def power_method_LR(matvec, init, tol=1e-10, max_it=1e5): """ def iteration(v_k, offset=0.0): - v_k1 = matvec(v_k) - offset*v_k + v_k1 = matvec(v_k) - offset * v_k v_k1_norm = np.linalg.norm(v_k1) v_k1 = v_k1 / v_k1_norm - return v_k1_norm+offset, v_k1 + return v_k1_norm + offset, v_k1 def power_method(init, offset=0.0, tol=tol, max_it=max_it): norm, v_k = iteration(init, offset) it = 1 while True: norm, new_v_k = iteration(v_k, offset) - + # -- Convergence criterion add = np.max(np.abs(v_k + new_v_k)) diff = np.max(np.abs(v_k - new_v_k)) @@ -325,7 +355,7 @@ def power_method(init, offset=0.0, tol=tol, max_it=max_it): v_k = new_v_k it += 1 if it > max_it: - raise AssertionError('Did not converge.') + raise AssertionError("Did not converge.") return norm, v_k # Find eigenvalue with maximum magnitude @@ -334,14 +364,15 @@ def power_method(init, offset=0.0, tol=tol, max_it=max_it): # Check sign of found eigenvalue _, v_k_test = iteration(v_k) - add = np.sum(np.abs(v_k + v_k_test)) # small if sign of E is negative - diff = np.sum(np.abs(v_k - v_k_test)) # small if sign of E is positive + add = np.sum(np.abs(v_k + v_k_test)) # small if sign of E is negative + diff = np.sum(np.abs(v_k - v_k_test)) # small if sign of E is positive # -- Return eigenvalue with largest real part - if diff > add: # The eigenvalue with the largest magnitude is negative + if diff > add: # The eigenvalue with the largest magnitude is negative norm, v_k = power_method(init, offset=-norm, tol=tol) return norm, v_k + def allclose_by_scalar_multiplication(delta_1, delta_2, atol=1e-10): """Test if two eigenvectors are equal if multiplied by a scalar @@ -366,17 +397,124 @@ def allclose_by_scalar_multiplication(delta_1, delta_2, atol=1e-10): """ delta_1_arr = delta_1.data.flatten() delta_2_arr = delta_2.data.flatten() - + # Remove numerical zeroes delta_1_arr = delta_1_arr[np.abs(delta_1_arr) > 1e-7] delta_2_arr = delta_2_arr[np.abs(delta_2_arr) > 1e-7] try: division_of_deltas = np.divide(delta_1_arr, delta_2_arr) - except ValueError: # Arrays do not contain the same # of zeroes and are therefore not equal - return False + except ValueError: # Arrays do not contain the same # of zeroes and are therefore not equal + return False # Check if elements share common scalar factor - have_common_scalar_factor = np.allclose(division_of_deltas, division_of_deltas[0], atol=atol) + have_common_scalar_factor = np.allclose( + division_of_deltas, division_of_deltas[0], atol=atol + ) return have_common_scalar_factor + + +def construct_gamma_singlet_rpa(U_d, U_m, phi_d_wk, phi_m_wk): + r"""Construct the irreducible singlet vertex in the RPA limit + + The irreducible singlet vertex in the random phase approximation limit for a + symmetrized calculations of the Eliashberg equation is given by + + .. math:: + \Gamma^{\text{s}}_{a\overline{b}c\overline{d}}(Q=0, K, K') \equiv + \frac{1}{2}U_{a\overline{b}c\overline{d}}^{\mathrm{d}} + + + \frac{3}{2}U_{a\overline{b}c\overline{d}}^{\mathrm{m}} + + + \Re + \left[ + 3 + \Phi^{\text{m}}_{c\overline{b}a\overline{d}}(K-K') + - + \Phi^{\text{d}}_{c\overline{b}a\overline{d}}(K-K') + \right] + \,. + + Parameters + ---------- + U_d : np.ndarray, + The local static interaction in the density channel. + U_m : np.ndarray, + The local static interaction in the magnetic channel. + phi_d_wk : Gf, + The reducible ladder vertex in the density channel + `:math:\Phi^{\mathrm{d}}(i\omega_n, \mathbf{q})`. The mesh attribute of the Gf + must be a MeshProduct with the components (MeshImFreq, MeshBrillouinZone). + phi_m_wk : Gf, + The reducible ladder vertex in the magnetic channel + `:math:\Phi^{\mathrm{m}}(i\omega_n, \mathbf{q})`. The mesh attribute of the Gf + must be a MeshProduct with the components (MeshImFreq, MeshBrillouinZone). + + Returns + ------- + gamma_singlet : Gf, + The irreducible singlet vertex in the RPA limit for a symmetrized + calculation of the Eliashberg equation + :math:`\Gamma^{\mathrm{s}}(i\omega_n,\mathbf{q}). + """ + gamma_singlet = 0.0 * phi_d_wk.copy() + + gamma_singlet.data[:] = 3 * phi_m_wk.data.real + phi_d_wk.data.real + gamma_singlet.data[:] = gamma_singlet.data.transpose([0, 1, 4, 3, 2, 5]) + + gamma_singlet.data[:] += 0.5 * U_d + 1.5 * U_m + return gamma_singlet + + +def construct_gamma_triplet_rpa(U_d, U_m, phi_d_wk, phi_m_wk): + r"""Construct the irreducible triplet vertex in the RPA limit + + The irreducible triplet vertex in the random phase approximation limit for a + symmetrized calculations of the Eliashberg equation is given by + + .. math:: + \Gamma^{\text{t}}_{a\overline{b}c\overline{d}}(Q=0, K, K') \equiv + - + \frac{1}{2}U_{a\overline{b}c\overline{d}}^{\mathrm{d}} + + + \frac{1}{2}U_{a\overline{b}c\overline{d}}^{\mathrm{m}} + + + \Re + \left[ + - + \Phi^{\text{m}}_{c\overline{b}a\overline{d}}(K-K') + - + \Phi^{\text{d}}_{c\overline{b}a\overline{d}}(K-K') + \right] + \,. + + Parameters + ---------- + U_d : np.ndarray, + The local static interaction in the density channel. + U_m : np.ndarray, + The local static interaction in the magnetic channel. + phi_d_wk : Gf, + The reducible ladder vertex in the density channel + `:math:\Phi^{\mathrm{d}}(i\omega_n, \mathbf{q})`. The mesh attribute of the Gf + must be a MeshProduct with the components (MeshImFreq, MeshBrillouinZone). + phi_m_wk : Gf, + The reducible ladder vertex in the magnetic channel + `:math:\Phi^{\mathrm{m}}(i\omega_n, \mathbf{q})`. The mesh attribute of the Gf + must be a MeshProduct with the components (MeshImFreq, MeshBrillouinZone). + + Returns + ------- + gamma_triplet : Gf, + The irreducible triplet vertex in the RPA limit for a symmetrized + calculation of the Eliashberg equation + :math:`\Gamma^{\mathrm{t}}(i\omega_n,\mathbf{q}). + """ + gamma_triplet = 0.0 * phi_d_wk.copy() + + gamma_triplet.data[:] = -phi_m_wk.data.real - phi_d_wk.data.real + gamma_triplet.data[:] = gamma_triplet.data.transpose([0, 1, 4, 3, 2, 5]) + + gamma_triplet.data[:] += -0.5 * U_d + 0.5 * U_m + return gamma_triplet From 16eab59e244bcd4049d12ec18f80faf05256cf5f Mon Sep 17 00:00:00 2001 From: Stefan Date: Thu, 21 Jan 2021 16:02:04 +0100 Subject: [PATCH 112/121] [eli] add documentation for phi creation function --- c++/triqs_tprf/lattice/eliashberg.hpp | 18 ++++++++++-------- doc/reference/cpp_reference.rst | 1 + 2 files changed, 11 insertions(+), 8 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.hpp b/c++/triqs_tprf/lattice/eliashberg.hpp index b4372cc67..2df4eccda 100644 --- a/c++/triqs_tprf/lattice/eliashberg.hpp +++ b/c++/triqs_tprf/lattice/eliashberg.hpp @@ -243,16 +243,18 @@ namespace triqs_tprf { \\ &\approx \overline{U}^{\mathrm{d/m}} - \chi^{\text{d/m}}(Q) \overline{U}^{\mathrm{d/m}} - \,, + \chi^{\text{d/m}}(Q) \overline{U}^{\mathrm{d/m}}\,, - where all products are particle-hole products. - The reducible ladder vertex in then only dependent on one bosonic frequency and momentum. - It can then be used in [REF] to construct the irreducible singlet/triplet vertex. - @param chi density/magnetuc susceptibility :math:`\chi^{\mathrm{d/m}}_{\bar{a}b\bar{c}d}(i\omega_n,\mathbf{q})` - @param U density/magnetic local and static vertex :math:`U^{\mathrm{d/m}}_{a\bar{b}c\bar{d}}` - @return The reducible ladder vertex in the density/magnetic channel :math:`\Phi^{\mathrm{d/m}}(i\omega_n,\mathbf{q})` + where all products are particle-hole products. + The reducible ladder vertex in then only dependent on one bosonic frequency and momentum. + It can then be used in :meth:`triqs_tprf.eliashberg.construct_gamma_singlet_rpa` + or :meth:`triqs_tprf.eliashberg.construct_gamma_triplet_rpa` to construct the + irreducible singlet/triplet vertex. + + @param chi density/magnetic susceptibility :math:`\chi^{\mathrm{d/m}}_{\bar{a}b\bar{c}d}(i\omega_n,\mathbf{q})` + @param U density/magnetic local and static vertex :math:`U^{\mathrm{d/m}}_{a\bar{b}c\bar{d}}` + @return The reducible ladder vertex in the density/magnetic channel :math:`\Phi^{\mathrm{d/m}}(i\omega_n,\mathbf{q})` */ chi_wk_t construct_phi_wk(chi_wk_vt chi, array_view, 4> U); diff --git a/doc/reference/cpp_reference.rst b/doc/reference/cpp_reference.rst index f51c7db49..81b7f8825 100644 --- a/doc/reference/cpp_reference.rst +++ b/doc/reference/cpp_reference.rst @@ -109,6 +109,7 @@ Linearized Eliashberg equation /cpp2rst_generated/triqs_tprf/dynamic_and_constant_to_tr /cpp2rst_generated/triqs_tprf/gamma_PP_singlet /cpp2rst_generated/triqs_tprf/gamma_PP_triplet + /cpp2rst_generated/triqs_tprf/construct_phi_wk Hubbard atom analytic response functions ======================================== From d1227e8abb8833b7b94d5f06c3200620c4812e80 Mon Sep 17 00:00:00 2001 From: Stefan Date: Thu, 21 Jan 2021 16:02:36 +0100 Subject: [PATCH 113/121] [eli] add doc for singlet/triplet vertex function --- doc/reference/python_reference.rst | 2 ++ python/triqs_tprf/eliashberg.py | 16 ++++++++++------ 2 files changed, 12 insertions(+), 6 deletions(-) diff --git a/doc/reference/python_reference.rst b/doc/reference/python_reference.rst index a6f9ca87f..5c7b217d3 100644 --- a/doc/reference/python_reference.rst +++ b/doc/reference/python_reference.rst @@ -52,6 +52,8 @@ Linearized Eliashberg equation .. autofunction:: triqs_tprf.eliashberg.semi_random_initial_delta .. autofunction:: triqs_tprf.eliashberg.power_method_LR .. autofunction:: triqs_tprf.eliashberg.implicitly_restarted_arnoldi_method +.. autofunction:: triqs_tprf.eliashberg.construct_gamma_singlet_rpa +.. autofunction:: triqs_tprf.eliashberg.construct_gamma_triplet_rpa Hubbard atom analytic response functions ======================================== diff --git a/python/triqs_tprf/eliashberg.py b/python/triqs_tprf/eliashberg.py index be1e17363..edc46d881 100644 --- a/python/triqs_tprf/eliashberg.py +++ b/python/triqs_tprf/eliashberg.py @@ -436,6 +436,8 @@ def construct_gamma_singlet_rpa(U_d, U_m, phi_d_wk, phi_m_wk): \right] \,. + For more details see :ref:`eliashberg`. + Parameters ---------- U_d : np.ndarray, @@ -444,11 +446,11 @@ def construct_gamma_singlet_rpa(U_d, U_m, phi_d_wk, phi_m_wk): The local static interaction in the magnetic channel. phi_d_wk : Gf, The reducible ladder vertex in the density channel - `:math:\Phi^{\mathrm{d}}(i\omega_n, \mathbf{q})`. The mesh attribute of the Gf + :math:`\Phi^{\mathrm{d}}(i\omega_n, \mathbf{q})`. The mesh attribute of the Gf must be a MeshProduct with the components (MeshImFreq, MeshBrillouinZone). phi_m_wk : Gf, The reducible ladder vertex in the magnetic channel - `:math:\Phi^{\mathrm{m}}(i\omega_n, \mathbf{q})`. The mesh attribute of the Gf + :math:`\Phi^{\mathrm{m}}(i\omega_n, \mathbf{q})`. The mesh attribute of the Gf must be a MeshProduct with the components (MeshImFreq, MeshBrillouinZone). Returns @@ -456,7 +458,7 @@ def construct_gamma_singlet_rpa(U_d, U_m, phi_d_wk, phi_m_wk): gamma_singlet : Gf, The irreducible singlet vertex in the RPA limit for a symmetrized calculation of the Eliashberg equation - :math:`\Gamma^{\mathrm{s}}(i\omega_n,\mathbf{q}). + :math:`\Gamma^{\mathrm{s}}(i\omega_n,\mathbf{q})`. """ gamma_singlet = 0.0 * phi_d_wk.copy() @@ -489,6 +491,8 @@ def construct_gamma_triplet_rpa(U_d, U_m, phi_d_wk, phi_m_wk): \right] \,. + For more details see :ref:`eliashberg`. + Parameters ---------- U_d : np.ndarray, @@ -497,11 +501,11 @@ def construct_gamma_triplet_rpa(U_d, U_m, phi_d_wk, phi_m_wk): The local static interaction in the magnetic channel. phi_d_wk : Gf, The reducible ladder vertex in the density channel - `:math:\Phi^{\mathrm{d}}(i\omega_n, \mathbf{q})`. The mesh attribute of the Gf + :math:`\Phi^{\mathrm{d}}(i\omega_n, \mathbf{q})`. The mesh attribute of the Gf must be a MeshProduct with the components (MeshImFreq, MeshBrillouinZone). phi_m_wk : Gf, The reducible ladder vertex in the magnetic channel - `:math:\Phi^{\mathrm{m}}(i\omega_n, \mathbf{q})`. The mesh attribute of the Gf + :math:`\Phi^{\mathrm{m}}(i\omega_n, \mathbf{q})`. The mesh attribute of the Gf must be a MeshProduct with the components (MeshImFreq, MeshBrillouinZone). Returns @@ -509,7 +513,7 @@ def construct_gamma_triplet_rpa(U_d, U_m, phi_d_wk, phi_m_wk): gamma_triplet : Gf, The irreducible triplet vertex in the RPA limit for a symmetrized calculation of the Eliashberg equation - :math:`\Gamma^{\mathrm{t}}(i\omega_n,\mathbf{q}). + :math:`\Gamma^{\mathrm{t}}(i\omega_n,\mathbf{q})`. """ gamma_triplet = 0.0 * phi_d_wk.copy() From 84eee31dca3d240a45a2f7db175e10948d969c85 Mon Sep 17 00:00:00 2001 From: Stefan Date: Thu, 21 Jan 2021 16:25:01 +0100 Subject: [PATCH 114/121] [eli] update user-guide to new vertex construction --- ...the random phase approximation limit.ipynb | 93 +++++++++++++------ 1 file changed, 67 insertions(+), 26 deletions(-) diff --git a/doc/user_guide/Solving the linearized Eliashberg equation in the random phase approximation limit.ipynb b/doc/user_guide/Solving the linearized Eliashberg equation in the random phase approximation limit.ipynb index 1744a550d..d39a60a49 100644 --- a/doc/user_guide/Solving the linearized Eliashberg equation in the random phase approximation limit.ipynb +++ b/doc/user_guide/Solving the linearized Eliashberg equation in the random phase approximation limit.ipynb @@ -11,7 +11,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "Starting run with 1 MPI rank(s) at : 2020-08-19 16:58:28.975762\n" + "Starting run with 1 MPI rank(s) at : 2021-01-21 16:24:22.474799\n" ] } ], @@ -52,7 +52,7 @@ " fig.suptitle(r\"$\\lambda = %.3f$\" % lamb, fontsize=20)\n", " \n", "\n", - "def plot_chi(chi_s_wk, chi_c_wk):\n", + "def plot_chi(chi_m_wk, chi_d_wk):\n", " path = [(r'$\\Gamma$', 2*np.pi*np.array([0.0, 0.0, 0.0])), \n", " ('X', 2*np.pi*np.array([0.5, 0.0, 0.0])),\n", " ('M', 2*np.pi*np.array([0.5, 0.5, 0.0])), \n", @@ -62,12 +62,12 @@ "\n", " ax_bs = plt.subplot(111)\n", "\n", - " ax_bs.bsplot(chi_s_wk[(Idx(0), slice(None))], path)\n", - " ax_bs.bsplot(chi_c_wk[(Idx(0), slice(None))], path)\n", + " ax_bs.bsplot(chi_m_wk[(Idx(0), slice(None))], path)\n", + " ax_bs.bsplot(chi_d_wk[(Idx(0), slice(None))], path)\n", "\n", " ax_bs.set_ylabel(r'$\\chi(i\\nu_n=0, \\mathbf{k})$', rotation=0, ha='right')\n", - " ax_bs.text(0.62, 0.6, \"$\\chi^{s}$\", transform = ax_bs.transAxes, size=22, color='C0')\n", - " ax_bs.text(0.55, 0.18, \"$\\chi^{c}$\", transform = ax_bs.transAxes, size=22, color='C1')" + " ax_bs.text(0.62, 0.6, \"$\\chi^{m}$\", transform = ax_bs.transAxes, size=22, color='C0')\n", + " ax_bs.text(0.55, 0.18, \"$\\chi^{d}$\", transform = ax_bs.transAxes, size=22, color='C1')" ] }, { @@ -90,7 +90,7 @@ "In this notebook we will walk you through the steps of solving the linearized Eliashberg equation in the random phase approximation (RPA) limit. Make sure, that you have read the [theory](https://triqs.github.io/tprf/latest/theory/eliashberg.html) before reading further.\n", "\n", "The steps are\n", - " 1. Construct the charge- and spin-susceptibilties in RPA\n", + " 1. Construct the density- and magnetic-susceptibilties in RPA\n", " 2. Construct the particle-particle vertex in RPA\n", " 3. Construct the symmetrizing functions\n", " 4. Solve the linearized Eliashberg equation\n", @@ -101,7 +101,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## 1. Construct the charge- and spin-susceptibilties in RPA\n", + "## 1. Construct the density- and magnetic-susceptibilties in RPA\n", "\n", "First we need a model and in this example we use the 1-band square lattice." ] @@ -159,7 +159,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Next we solve for the charge- and spin-susceptibilties in RPA by first constructing the bare bubble $\\chi_0$ `imtime_bubble_chi0_wk`" + "Next we solve for the density- and magnetic-susceptibilties in RPA by first constructing the bare bubble $\\chi_0$ `imtime_bubble_chi0_wk`" ] }, { @@ -216,8 +216,8 @@ "\n", "U = 1.0 * np.ones(shape=(1, 1, 1, 1), dtype=np.complex)\n", "\n", - "chi_c_wk = solve_rpa_PH(chi0_wk, -U) # Minus here for correct charge RPA equation\n", - "chi_s_wk = solve_rpa_PH(chi0_wk, U)" + "chi_d_wk = solve_rpa_PH(chi0_wk, -U) # Minus here for correct density RPA equation\n", + "chi_m_wk = solve_rpa_PH(chi0_wk, U)" ] }, { @@ -234,7 +234,7 @@ "outputs": [ { "data": { - "image/png": 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lhJfK/o80SvLWdXbYje/puc9LOt+0aXgqK4lv2QpA8G0rKb3qqgG/W0Yv1byIiMigDWWkEXRpNupHn5ck/2GHuZ+fOZPK7313wO+V0U3hRUREBi1jgroBLMqY+kzaUOn+NhtFnn+ejmefBaD4A+/DU1Y24PfK6KbwIiIig2YPcmmAJG/aJHV2fT1OLNbr/fHGJhqvvBoSs/FGX83datQycim8iIjIoMWHMEwawAgEOkOP42DX1/d4r2PbNH3sY8R37KDgtNMAiL64bsDvlNFP4UVERAYtY4K6yoFNUJf63MT+ddo98N3v0fHY4/gXL6L6Zz/FqCgn9sZG7ORQbRk3FF5ERGTQ7MahddiF/k1UF374EQ58/wcYFRVU3fxTjGCQwMIjIB4n+tLLg3qvjF7DPlTasqwngGOBBaZpvtHN9XuBs4FPm6b5neEu31hmWZbT5dQppmk+2s/PeoBXgKnAHNM0+zemUUTGtKH2eYG+J6qLbdtG4//7OABVP/g+vmnTAPAvOoKOJ54g/MADFCxfNqh3y+g0rOHFsqy3AycAt3YXXBIWJbbjpiHTsqw64DrgHGAK0AL8F7jJNM1/5bNsSaZp2pZlfR24BbgB+Fh+SyQiI8FQRxtB7xPVOR0dNF5xJU5zM6Wf+DjB005NXSs48QRaf/wTWn/yUyIvvEDw9NM038s4MWzNRomf3L8GOMBXe7inGGgDXgPWDlfZ8smyrEXAS8DHgdlAB1CDG2Qesizrc3ksXle3ApuBKyzLmpXvwohI/mWl5iWjz0tmeGm+wSS67kUKTjyR0ms/lXEtePLJlF3/BbwzZxBZvYb4zt2Der+MPsPZ5+VM4HDgCdM0X+3uBtM020zTPNQ0zQXjoVnCsqxC4G9ANfA8sNA0zXKgEvguYABftyzrrT0/ZfiYphkDfgP4Uc2LyLjnxOPYTUPvsJs5UV1mAKn81jeYsmMbNbf9EcNz8FdW6dVXUffkE0zZsomKL904qPfL6DOc4eWyxPZPw/jOke5KYAbQCpxrmubLAKZp7jdN81rgrsR9X89T+brzx8T2A5Zl+fNaEhHJK7ulBRy3K51RXo7hH9w/CRmjjfo5UZ2MbwPq82JZ1q3AO4E3cX8C/5ppmk6Xe6pw+6tMAX5smuZHLcuqBs7FbTK6vZfn3wWcB1xnmuY30s4/DywBvmqa5vVdPnMC8ASwG5hhmmZkIP9Nefa+xPYPpmnu6Ob6t4FVwFLLshaYprk+l4WxLOty4GddTmd0nDZNc4NlWWuBxbhNW3fmskwiMnKlLw0w2CYj6N9oI5F0A615mYLbZDAP+ArwkW7u+VnivvXAtYlzpyQ+97ppmvt6eX6ys27X/i7JL/YpXT9gmuaTuE0udcCIaF7pD8uySoGjEocP9HDbf3A77wKc2sM92SrPu4Gfdjn9mR5GfD2Z2I6a328Ryb6MdY2GEl7Sm43q63Fse0jlkrFvQOHFNM0VuP0zHkycWpV+3bKsD+HWzESA95qmmZw56ITEdk1Pz7YsqwyYmTjsGl52JrYHhZeEpxLbE3su/YhzKG6fFoBuJykwTdPG7bwMcFiuCmJZ1lnA78j8+/AZ0zS/3cNHVie2b8lVmURk5MuYoG6QI40AjGAQo7zcPYjFMjoBi3RnwEOlTdNstizra7g/dS9Onrcsaw7w/cThDaZpPp/2saMT296GPy/C/TKvN01zZ5drPda8JGxLbLM2AsayrBsBc7AfN03zxj7umZS23/W/l26uTerlnkGzLOsk4A7cmrGkz/YSXKAzXB5mWVapaZoHclE2ERnZstVsBG7tS6zFrWiO796Dt6amj0/IeDbYeV6ew+2/UmtZ1iRgH/B7oAR4FOja1JD84u150YrOINTdEOm+al4KEttszlvTCgx2xFNrP+4pTtvvbW7rUGJbMsiy9GYZ7pwthWnnPmea5rf6+Fzyz9EAJgIKLyLjUMYw6UHOrpvknTiR2Ouvu8/duxd3cKpI9wb1ZW+a5gHLsjYBc3BrTE7AnTW3Gbg40dyRLhmhm+hZb+ElWfNSbllWsWmabV2uH5fYZq1Da6KvRy5n+DX6viXnvklmU9HnTNP8Zj8+l/7nWAP0NOGgiIxh8fQJ6qoGN0w69fmMierG/EwZMkRDGSqdDBlXAp9P7F9lmua2bu5N1oz0NhKoPzUv0KX2xbKsGcDpicO7e3n+SJNeO1PY411Q1M392ZL+5/9MP4MLQDhtv7eyi8gYZjelh5ch1rzUpQ2X3qXJ5qR32Qgv7wC8wO9M07yth3uTf8MruruYmH13YeKwu34x6cOIuzYd/R9uDdLjpmn+t69CjyDpgWxyL/clr+3KYVkAjklM/98f6T9iNfR4l4iMaRmjjYbabDSl85/B+M7eugGKDK2PSHoNyRZ6n3G1Hncoc0/1inNxaxiiuIv/dff5CBAgLbxYlnUl7lwjYeCj6R+wLOsfQBXu5HhfBVbg9i35sWmaVi9lTX7+WjqHeg/Ud/qxqOR63H5DBm7j7mtdb0iEukMSh939vgzV3bjz6iR9zrKsPaZp3tTH59L/HHvrxyQiY1jGaKMhNht5p0xN7ce3bR/Ss2TsG0rNS/rf1EtN09zfy73JL+aeRgMlm4zWdzfJXGIivGTNwxQAy7KOA36QOHeFaZovdfnYItxOsQ/ifvF/GngduNGyrP7MmVKC2xl1ML/67FybGKGTHHJ8Rg+3HQMkxg+SiwUabwJ+2OXc9yzLem8fn5uZ2LbgTg4oIuNQxmijIda8+KZ1hpfYdoUX6d2gal4sy5oO/G/aqb4G5T+JO/9LT2uW99bfJWkH7lT6ky3LOhR36vwA7nwkv+tSvirc5pYi4CjTNDclzt+F+2W7DHi4twInhjrf2Ns9WfAHYDnwPsuyvmSaZtemoWTNzxrTNA+qmcmSa4BpdM7ZYwC3WJbVaJrm/T18Znli+2Q3nbNFZJzIxqKMSd6paTUvO3bg2Ha3axmJwCBqXhJNGb8ls//K4h5uT3oisT3SsixvN9f7E16SjaDH4QaPCbjzqXQ3H0lypt6vJoNLQkdiO1KWELgZ2AqUAvdalnUYuLPvWpb1LeD8xH2f7/pBy7JWWJblJH6tGGwBEuHjvcAzaaf9wB2WZR3Tw8eS4eXfg32viIxudiiEE0703S8owCgu7v0DffCUlGBUJL5WIhHsfb1Nxi7j3WBi7WeAk3FHvyRn2u0rvKwGNuE246zo5np/a17A/eKsA77cy0RwyfByV5fzCxLbXNViDEhiBuLzcDu9LgVetiyrBXfI+adx+8RcZ5rmgz0/JWvlOBfYmHa6GLjPsqwF6fdalhXEXe6h13WqRGRsy6h1qazEMIY++4Nv2rTUfkz9XqQXAwovlmUtBb6UOPw4nUOTew0viT4rv0ocXtTlmZW4zRbQ+wy8yfDiANeapvnFXu49AmgyTbPr/CNLEtveQtKwMk1zLe5Iqx/gBrwC3DBzH3BG+gKVXSQn/guRhc68iTWn3kZmB9xq4EHLsqamnTsHt6boUdM008OOiIwj2RxplHrO1M7BpPEdCi/Ss373ebEsqwi4lUSTgmmav7YsK7mWUF81LwC/xp1u/3zLsj5mmmYHgGmaTfRjwrZE81BvU9anW0T3AWUx3S8/kFemae4GPpH41V8nJ7Y/MU2zX8uwmqbZ6++zaZqvA7V9POY9ie3P+/NOERmb7Ibs9XdJyuj3opoX6cVAal6+i9vssgN3YjrorCmptSxrWrefSkgEhptxhy9fOsBy9ptlWcmhxy90c3kxI6jWZYhOxh363d9AN2SWZc3FbeZ6BehpTh8RGQcylwbITnhJbzaKa8SR9KJf4cWyrHOAq3CbbD5ommYjQGJ49JbEbTcm+kP05su4fWU+a1lWNtchSjcHt79GRnhJhJojGAPhxbKsWtwgebNpmsM5j/Z1uBMSfkGjjETGt3gWF2VMSm82im3rbrJ2EVef4cWyrInALxOH3zVNs+t8I8l+Lx8C9luW9euenpVo3rgY+A0wtaf7huiIxLZrzcsc3PlXeutXMyqYprnPNE3DNM1PDtc7E6PMNgKfNk2za0doERlnsjlMOsk3c2ZqP7ZxU883yrjXn9qPX+EOS14LfKGb65/D7bNyPu4ooF7r+kzTvBO4c2DF7L/E8w/q25HovDsSFkMclRI1LV/LdzlEZGTIWXjxeMC2iW/fjt3ejqdQy6fJwfoML6Zpnt3H9TAD72wqIiKjWHp4ydZoI6OgAO+MGcQ3bwbHIbZxI4GFC/v+oIw7mr5QREQGLBejjQD88+am9mOvv56158rYovAiIiIDlovRRgC+efNS+7HXu07VJeJSeBERkQGLZ3FRxnS+uZ01L9E3NA+mdE/hRUREBsSJxXBaWlLHnoqKXu4emIxmozfUbCTdU3gREZEBsZubwXEAMCoqMHzZm7YrveYltmkzTmSkrKMrI4nCi4iIDEjGukZZ7KwL4CktxTtjunsQjRJ96eWsPl/GBoUXEREZkMzOutnr75IUOGpZaj+yenXWny+jn8KLiIgMSOYw6cqsPz+w7KjUfsfqNVl/vox+Ci8iIjIgua55KVi+PLUfWf0sTqJ/jUiSwouIiAxILhZlTOc7ZD5GSQkA9p69xLVIo3Sh8CIiIgNi7+lczN5bU5P15xteL4GjlqaOw/c/kPV3yOim8CIiIgMS27krte+dPDkn7yg855zUftsf/qimI8mg8CIiIgNi70oPL5Ny8o7C896OUVwMuGscadSRpFN4ERGRAYnt3Jnaz1XNi6e4mMJV56WO2/92T07eI6OTwouIiPSb3d6O09zsHvj9eGprc/auwretTO1H1mjItHRSeBERkX6L70irdamrw/Dk7mskcOSRqf3oy6/gtLfn7F0yuii8iIhIv8XT+7tMqsvpuzwVFZ1rHcViRF58Mafvk9FD4UVERPotPgz9XdKlD5mOrHku5++T0UHhRURE+i2+ZUtq3zt1as7fF1iaFl6eU3gRl8KLiIj0W2zT5tS+b86cnL8vPbxEX1ib8/fJ6KDwIiIi/RbbtCm175s9O+fv882bC4EA4DZZ2S0tOX+njHwKLyIi0i+ObWeEF/+c3IcXw+/HP29e6ji6fn3O3ykjn8KLiIj0S3zXbpxwGABPZSWeysphea/v0ENT+9FXXx2Wd8rIpvAiIiL9Etu4MbU/HE1GSf5DF6T2o6+o5kUUXkREpJ8y+rsMQ5NRkv8w1bxIJoUXERHpl+HurJvkT2s2iq1fj2Pbw/ZuGZkUXkREpF8ya15yP0w6yVtbi6emBgAnFMooh4xPCi8iItIvmTUvs4b13YElS1L7WqRRFF5ERKRPTkcH8W3b3QPDwDdz5rC+P7DsqNR+ZLXCy3in8CIiIn2Kbd0Kib4m3qlTMYLBYX1/RnhRzcu4p/AiIiJ9yhgmPYwjjZL8S5aA1+uW5bUNmml3nFN4ERGRPmWsaTSMI42SPIWF+A8/LHWsFabHN4UXERHpU75rXgACy49O7YcffTQvZZCRQeFFRET6lO+aF4Dg6ael9sMPPoTjOHkph+SfwouIiPQpXxPUpSs49hiM0lIA4tu2EdMijeOWwouIiPTKbm7GbmhwD4IFeCdPzks5jECA4IqTU8ftDzyYl3JI/im8iIhIrzKajGbNwvDk76sjeOZbU/uhW/+AE43mrSySPwovIiLSq8zVpIdvWYDuFK5cmVoqIL5zJ+133Z3X8kh+KLyIiEiv8rksQFdGYSElH7o0dbz/m98itm1bHksk+aDwIiIivYpu7Awv/mFckLEnxR+8GKOsDID4rl3Uv/si7NbWPJdKhpPCi4iI9GokjDRK56mooOonP4KCAgDiW9+k7de35LdQMqwUXkREpEeObRPfnD7HS36bjZKCK1ZQ8SUrdXzgpzdjHziQxxLJcFJ4ERGRHsV37cIJhwHwVFXhqazMc4k6Fb37QrwzpgPgNDcTuv2OPJdIhovCi4iI9CiW1t/FNwL6u6Qz/H5KLr88dRx+9LE8lkaGk8KLiIj0KLYpfZj0yGgyShc8ZUVqP/Kf/2jel3FC4UVERHqUMUHdCKt5AfDOmIF32jQAnLY2Ii+8kOcSyXBQeBERkR5lTlA38mpeDMOg4MQTUscd/34ij6WR4aLwIiIiPcro8700uWEAACAASURBVDIChkl3p+AtJ6b2ww8/kseSyHBReBERkW7ZBw4QT85e6/Phmzkzr+XpSfCkk8DnAyD6/PPEtm/Pc4kk1xReRESkW9H161P7vnlzMRKTwo00nsrKjNqX9nvvy2NpZDgovIiISLeiL7+c2vcfdngeS9K3wnPPSe2333NPHksiw0HhRUREuhV9+ZXUvv+wQ/NYkr4Vnnkm+P0ARF9YS2TdujyXSHJJ4UVERLoVXfdiat9/+MiuefFUVFB4ztmp49Yf/SSPpZFcU3gREZGDxBubOpuNPB4Ci47Ib4H6ofTqq1P77X//e0bNkYwtCi8iInKQyJNPguMA4F+yBE95eZ5L1Df/4YdRkJxx17ZpuPIq4rt357VMkhsKLyIicpDwv/+d2g+e9JY8lmRgym80MYqKAIhv3syek1Zw4Kc348TjeS6ZZJPCi4iIZHAch47HO8NL+jDkkc4/dy4V3/h66thpa2P/l79C4xVX4th2Hksm2aTwIiIiGeJbtqQmpzOKiggsXZrnEg1M0TvPp/o3t+CbPz91Lnz/A0SefTaPpZJsUngREZEM4bRal8Bxx2EEAnkszeAETz+NCQ/eT+C441Ln2u+8K48lkmxSeBERkQwdo7S/S1eG30/Zpz+VOg7dcy9OJJLHEkm2KLyIiEiKE4vR8eRTqeOCURxeAALLl+OdPBkAp7mZ8MMP57lEkg0KLyIikhJduw5n/34APHUT8c2bl+cSDY3h8VB4/jtSx62/+GUeSyPZovAiIiIp4ccfT+0H3/IWDMPIY2myo/jii1OrTkee/g+RF17Ic4lkqBReREQkJb2/S8FJJ+WxJNnjmzKZwre/PXW8/5vfwklMwCejk8KLiIgAYLe2ElnzXOp4NM3v0pfSq68Cj/uV1/H4vzXyaJRTeBEREQA6nv4PxGIA+A49FG9tbZ5LlD3+ww6l+NJLUsfNn/ks7X//B04shpP4b5bRQ+FFREQA6HjssdT+aB4i3ZOyz3wa79SpADjt7TRefgU7Z8xi14LDCN19d55LJwOh8CIiIgCEH3k0tV9wyin5K0iOeEpKqPnjH/BOmpRx3mlvp+WLN+KEw3kqmQyUwouIiBDbvJn4li2AuyRAwdHL81ugHPHNnkXt3+6m6D0XYZSUpM7b9fWE1A9m1FB4ERERwo92NhkVnHA8RkFBHkuTW97Jk6j8zreZtP4Vyq77XOp8609vVv+XUULhRUREMpuMVqzIWzmGk2EYFF/8gVQNTOyNNwj94Y95LpX0hy/fBRARkfxywmEiTz6ZOg6esmJ43+84/O25Hdy1ehub9rVS4PNy2JRyPn/e4UwoC+b03Z6yMkquvooD3/4OAPu/9W2CZ5+Ft7o6p++VoVHNi4jIONf+wIOpzqq+2bPxzZgxrO//yl0v8b1/vMqxc2v45kVH8ulzDsXrMSgKeIfl/aVXXpEahWQ3NdF41UdwotFhebcMjmpeRETGufT1fgpXnTes7/7rs9t48MVd/OTSo1k4rSJ1/oyFk3r5VHYZhYVUfP1rNFz8QXAcIk89Rf173kfpxz6C09GBd8pUAgsPH7bySN9U8yIiMo5F1jxH9LnErLqBAMUXf2DY3u04Drc8vom3L52aEVzyIXjqKZR+6n9Sx5Gnn6bhfR+g8UOXse9tZ9H+4EN5LJ10pfAiIjKOtf7iF6n9olXnDeusupv3tbF3f5gVh00ctnf2pvSaT7gBputilLZN87WfJl5fn5+CyUHUbCQiMk7Fduyk/b6/p45LLrtsSM971w/+Tf2BDmbVlnDlqXM5Zm5NxvW9LWE+ePPTNIcifPOiIwn63T4tNSUjY1i2YRiU/c8nKTjxBEJ/+CMdTzxJfNcuAOyGBpo//RmqfvXLMbHS9minmhcRkXGq7Te/gXgcgMDxx+M//LBBPytuOyycWsGEsiCv7Gjhuj+/QKijc86UWNzmC7evpaktwvtPmMVJCyZQU+qGlk37Wof2H5JlBUcfTeVN/0vd6v9S/cdbU+fDDz6kodQjhMKLiMg4ZIdCtN3a+cVccvmHh/Q8r8fAPP8Ibv3I8cyZWEKoI86rO1tS12+6/zVe3NbMkTMrueq0eQDMqCnmkEll3HT/ev62ZjtrNjdyz3PbufEv64ZUlmwKnnQSxR+6NHXc/Pkv0P7AA3kskYCajURExqX2O/6C0+yGC+/MGQRPOy0rz/V5PZwwr5aNe1p5bdcBjppVzUMv7uKO/75JTWkBX7lgMV6P2+zi9Rh86z1L+NFDG7j54ddpDceoqyjknCOnZKUs2VL2+evoePJJYq9tgFiMxg9fTtEF7ySwbBl2ayvB00/HP3dOvos5rii8iIiMM45tZwyPLvnQhzC82ZtTZcHkMgBe27WfzXtb+drfXsbrMfjKuxZTXZrZv2VieSFfumBx1t6dC57CQmpu/T37LngX8S1bwXEI3X4HodvvAODAd75L5Y9+SOGZZ+a5pOOHmo1ERMaZjkcfI7ZxIwBGaSlF774wq89fMLkcgJe3N/O5216gPRLnI6fPY8mMyqy+Zzh5J02i9i93UNBNDZXT3k7jZVeoOWkYKbyIiIwz6cOji99zEZ601ZWzYXJlIeVFfrY3trO1vo2TD53A+06YldV35IO3ro7q3/yamtv+RMlVV7pBJlljZds0feRjdDz5VH4LOU4ovIiIjCPR116j47HH3QOPh+JLL8nJe+ZNLAVgalURN6xamJN35INhGBSceALlN1xPzW9voe651XhnusspOOEw9e99H/tv+j72/v15LunYpvAiIjKO7P/Od1P7wZVn4ps+PevveHl7M2vfbALgHcumUhL0Z/0dI4W3pobq3/4Wz4QJ7olYjAPf/g67DlvIjjlz2Xn4ETR/7jpiO3bkt6BjjMKLiMg40X7vfYT//o/UcckVV2T9HS2hCF/481qicQeAjXtG1hwuueCfM5vae+/Bf8QRnScdB8IdOM3NtP3u9+x729lEX34lf4UcYxReRETGgXhjI81fuD51XPTe91CwfFlW32HbDl+8Yx27W8KcMN9dZmD9rvHRfOKbMpnae/9Gxbe+iX/hQvBkfr3aDQ3sO/+dtN32ZxzbzlMpxw4NlRYRGQdavmhiJ9bm8dTVUX7D9X18YuB+8egbPLOxgUMnl/G1Cxdz7ncfZWt9G+FInGAge0OxRyrD56P4fe+l+H3vxW5vh1iMjv88Q9PHP4Gzfz9OayvN//MpWv/vRxS85USMggKMsjL8CxcSPO1UDI/qE/pL4UVEZIxrf/BB2u+8K3Vc8Y2v4ykry+o7nnp9H79+fBNlhX6+euESCvxe5k8qY/WmRjbs3s+i6aN3mPRgeAoLASg843R8d9xOwxVXEt+yBYDYpk3ENm3KuL/g1FOp+sFNeCrH1+/TYCnmiYiMYXZLC82fuy51XHj++RSecXpW37GzqZ0b//IiADeefwSTK90v7gWT3ID02Pq9WX3faOM//DAmPHg/JR+5GqOHYekdDz/MnpNW0PqznxNvbBzmEo4+huM4+S6DyJhlWdajwMkzZszgkksuyXNpZDxq+tS1hP50GwCe2lomPvKvrP50H4nZXPHLZ1i/cz+XnjSbKxPrFgE880Y9n/jdGgCOnFnJifNrx8R8L0Nht7YS+e+zRF97DYDo2rW033PvQfd5KitxIhGcWIyCY46m/EsW/nnzDrpvjOtx+W41G4mIjFHhxx5LBReAiq99NevNEt/7+6us37mfZbOruPyUuRnXls+u5oyFdTy2fi8vbG1iRnVxVt89GnlKSgieegrBU09JnWs//3xarr+BeNpwarupKbXf8fi/2XvGmRRdeCHF73sP/iOOSPWPcRwHw+jxO37MUs2LSA6p5kXyJbZ9O/vOW4W9ew8AheecQ9XNPxm29z+3pZEfPvAar+7sHG1UXRLg+lULOW5e7bCVY7Sw29tpv+MvhG6/g8iLL0Ik0uO9RnExnppqnP0HsNtDBE89jdKrriRw1NJhLPGw6DGVKbyI5JDCi+RDvL6efavOJ755M+A2QUx45F94a3MfGrbWt/GjhzbweC/9XFYumsQVp85L9Y2RTE4kgt3SglFQQGzrVlq+aBL577N9fs6/eBHBU0/FN28uRmEhdlMznuJiAscfj7dqVHYEVrORyGgT27ETb3UVRjCY76LIKGIfOEDD+y9OBRcCAapu/mnOg4ttO9z88Ov8/sktxO3OH4oLfB7OPnIKj766h8ZWtzbh/nW7+NfLuznvqGmsWjaVuYmlBMRlBAKpP6/AEUdQ89e/EHnqadr+fDsdjzyC3dDQ7eeia9cRXbvu4AseD4GlSwmeegqB5csTswE72M0teCor8U2fhuHP/izIjm0T27AB/4IFWX+2al5EcmgoNS/1730fkTXPETzjdArPPovgihUYhfpJVXrmhMPUv/9iIk8/7Z7weKj62U8pfNvbcvpe23b4xj0v87fnMqfAf9viyVx56lzqKgppaovwrXtf4ZFX9hz0+QWTy7j69HkcM6cmp+UcCxzHwW5owDlwACMYxG5sovXnPyd0190QjQ7qmUZREQXHH49/yWJ8U6diFBXhtLdjtx7A8PrwzZmD/4iFeEozQ6bjOOA4B81PE9u6lfZ776Pt97cS37uHSWtW46moGFTReryg8CKSO4MNL/HGJnYvORLi8dQ5o6iI4GmnUnj22fiXLsUI+MHrdf/h8Hjc1W09HoxAAMM79icEk0xOLEbjlVcRvv+B1LmK73yb4vdclNP3xm2Hr939Eve9sDN17sgZlXxi5SEsmFx+0P3Pb2nkRw9t4KXtLRnnPQb8v7cewkXHzRiXHVCHKt7YRMfjjxFd9yKxbdtwwh14SoqJbd9B9Pnn3eUKhshTV4enqAgKAjjNLcQbGsC28c2ejae6GqJRYtvexN6T2WRYbt1IyWUfHswr1WwkMprEt2/DO21aalIrACcUov2ee7sdVpnBMDDKy/BUVuGprMRbXYXvkEMIHLWUwNKleGv00+1Y49g2zZ/9XEZwKfv8dTkPLrG4zZfveokH1u1KnTtr8WS+sGohXk/33ztHzqzi55cdw383NnDP8zt4fP1eIjEb24HvP/Aam/e18qmzDqXArwA+EN6qSopWrYJVqw66Fm9spOOxx+h47HGiGzdhJ+aR8ZSXEd+zJ9Wpuy/27t10t7BBbMOGHj9jVJTjpP0Qli2qeRHJoaE0GzmOQ+yVV2m/7z7a772P2MaNWSmTd8Z0AkuXUnDssRSefZZm9Bzl7JYWmj5xDeGH/pk6V3LVlZRd/4Wc1mDE4jY3/vVF/vnS7tS5c4+cwufefniPwaU79Qc6uO62F3hxW3Pq3KzaYq49+zCOmlWV1TLLwRzHIbZpM5HVq4mtX098716cSATD78dTXo4daif26qvuvDSxWL+eaQSDBI4/nsJzz6Ho3HOG0tytZiORfMjWaCPHcYht2ED7fX8n/OBDxPftg2jU/YnGtt1f8TiOY0O4o/8PDgQoPPOtFL37QgpOOknNTaNM9NVXabjsiowauqIL30XF976b0+ASjsT5wu1reXLDvtS5dyybyqfPPgzPAIJLUkc0ztf+9nJGDQ7AwqnlnHZ4HcvnVKtTb5454TDx+nqccNhtkiorxVNTA7ZNbPNm7OYWjIAfT00tvhnTMXxZadhReBHJh3wMlXZiMeyWFuzGRuymJuK7dhN94QUizz3vzh/R0X248dRNpOiCCyh617vwz50zLGWVwQvddRfN134Gp709da7kyiso+/x12fri6FZLKMK1f3g+o6bkgqOn86mzFgwpMDmOw52rt/PDB1+jPXJwM8NbDqnlmpULmFJVNOh3yKij8CKSDyNtnhcnEiH68st0/PdZ2u+6i+i6F7u9r+CEEyj+8KUETz9dtTEjjBON0vKVr9L2i1+mzhlFRVR+77sUnntOTt+9tyXMNb9fw6a9ralzF584i6tPn5e1mp7dze388tGN/GPdTmLxzO+nooCXj54xn/OOmorPq6X5xgGFF5F8GGnhpavoq68Suv0OQn/5K3Z9/UHXvdOnU3zJBym+6N14yg8eOSLDq2P1Glqu+zzRV15JnfPNnk3VL3+Of/78nL57y75WrvndGna3hFPnrll5CBcdNzMn72tqi/DIK3v4zxv1B014N726iHcsm8YJ82uZUlU0oD42MqoovIjkw0gPL0lONEr4kUcJ/fnPhB98KGOINrg/2Rdd+C6KL71UTUp5YDc10fL1bxC69Q8Z54NvW0nl/37voPk3su3l7c38z63P0RJy5xHxegy++I6FnLlock7fm/7+L935Elvr2w665vMaHDq5nNMPr2PVsqkapTS2KLyI5MNoCS/pYjt20Pab39J26x9wmpsPul5wygpKPvQhClacfNDkVJJdjuMQuv0O9n/5K6nhreCO5ij99LWUXHlFzudEeeK1vdxwx7pUP5TCgJevv3sJx84d3iH34WicPz29ld89sZm2ju5HvUyrLuKKU+ZyymET1aw0Nii8iOTDaAwvSXZ7O+1/vZPWX/2K2PrXDrrumz2bonddQOE7VuGbNi0PJRy7nHic8P0PcOAnP3UnGEsTPON0yr/8pZz/nkdiNj/+5wb+9PTW1LnyIj/fe99SDp86qNlSs6KtI8ZDL+7iiQ37eHl7C01tBy9gWFUS4Ph5tcyrK2VCWZDasgIOqSvD71OgGWUUXkTyYTSHlyTHcYg8+RStv/ylO5dIN/9mBJYvp/Adqyg899zRugDciGAfOEDoT7fR+stfEd+2LeOad/Jkyr/yJQrPPDPn5dha38YNd6xlw64DqXN15UFu+sBRzKwtyfn7B6K5LcID63bx80ffoDXc8zwktWUFfPjkObxt8WQ1LY0eCi8i+TAWwku62NattP76FkJ/ug3nwIGDb/D5KHjLiRSeeSbBt56Bd+LE4S/kKOM4DpE1zxH68+203303Tmtr5g1+PyWXfZjST16Dp7g452W59/kdfPfv6wlHO/s9nTC/lutXLaSyOJDT9w9FSyjCbf/Zyt1rttPQenBtTFJZoZ8T59dy+NRyKosD+Lweyov8LJxaoY6/I4/Ci0g+jLXwkmSHQoTvf4DQnXfS8djjB3XwTfIvXUrhyjMJnnE6vnnZG047FsR37yb0l78S+vPtxN5446DrnspKij/wfoo/eDHeurqcl2fv/jA3/WM9D6ctnBjwefjYGfN51zHTR82fXdx2eHFbMy9vb2Z7Y4i9+zt4cVsz+9t7X7RwenUR7z52BqcvrKO8aOSGtHFG4UUkH8ZqeEkXr6+n/Z57Cf31TqLPPdfjfZ7qagLLjiKweDH+xYvwL1qEt2r8TP/uxOPEXttAx7PPEv7nP+l49DF3ZuQufHPnUnLZhym84J14hmEV8XAkzq1PbeZ3T2zJqG2ZWVvMly9YzLy60T+zbagjxl+f3cYdz77J7uZwr/d6DJhXV8bM2mJKgz6icYcJZQWcengds0ZYk9k4oPAikg/jIbyki23fTviBB2m//wEizzzTY41MknfaNPyLFhFIhJnAEQvxVOSvM2g22aEQ0eeep+PZZ4msXk1kzXPdN7UBRnGxuw7Muy8ksHz5sNRyOI7DP1/azf89tIE9LZlf6KuOmso1KxcQDIytviG27bB+137WbG5k895W2qNx2iNxXtzW3OMIpnTz60o5bl4Nh0wuo668kAKfh7jtMLWqiKICrXOcAwovIvkw3sJLOrupifC/Hqb9gQfpeOqpboddd8c7cyaBRUfgmzMH75QpqV++KZMxgsEcl3rw4jt3dQaV1auJvvxKn+EtcNxxFL/7QoJnn4WnaHimvXcch9WbG/n5I2+w7s3MP5N5daVcs3LBuFsQsTUc5R9rd/LAul28sqMFe4Bfix4D5kwsZeHUCo6YVs7CqRVMKAtS4PeMmua2EUrhRSQfxnN4SefYNrENG4isXUt07Toi69YRfeXVHtdZ6omnpgbv1Cl4p0zFN20q3mnT8E6Zgqe0BKOoCKOwMLX1FBZCMDjkLw/HcXBaWojv3p32aw/2nj3E9+4lvmcv8V07sXfv6fNZngkTCCxbRsHyZQRXnolv+vQhlW0gYnGbf728m1uf2pIxigigsjjAlafO5dylU8d9p9X97VFe332AXc3ttHXEcByHtW828+SGfURiBzfz9cZjQFGBj5Kgj/l1ZSyaVsH8SWXUlBZQVRzA7/PgNQwCPs+gFrQcBxReRPJB4aVnTiRCdMOGRJh5kei6tURfXQ/R3jtWDkhBAd6qKjzV1XiqqzBKSsGOQzSGE4tCLO5uozGceJdmA8dxF7jcvQcn3Hs/iW4ZBr5D5hNYtpyC5csILF+Gd/rwd3xt64hxz3Pb+dPTWzOm9gd3dtoLj5nBh06eTUnQP6zlGm1aw1H+u6mBdW82s7W+jYbWDiIxG8eBNxvauptBoN8KfB7mTyrjkEllTKkspLIkQEmBD9txw3NNaQGzJ5RQGBh3TVMKLyL5oPAyME5HB9H164m+9DKxbduI79hJfOcO4tt3EN+1q89mmHwygkH8Rx6ZCCrLCRy1NG/rQdm2w5otjdz3/A4efXVvRkdcgAK/h3OWTOG9x8/UKs1Z0BaO8crOFl7c1sxL25p5bdd+DoRjA66p6Y1hQF15IVUlASqKAng9BrG4jWEY1JUHmVZdxITyIOWFfkqCfgJeDz6vgc/rIej3UlboH421aj0WeNzFOJHR4mO/eRYDg+qSANWlBdSUFFBdWkB1SQE1pQUU+r0YBngM46Ctx2PgMcDv9YyqadKNggICixcTWLz4oGtOPE589x7iO7YT376D2JtvEt++nfiuXTihEE6oHafd/WWHQjihEER6nu9jQOUqKsJbV4enrg5vXR3eSXV4J07EO2ECnokT8NbW4p06FcOfv9oLx3F4Y08r/3xpF/ev23VQJ1yAiiI/7zpmOu9cPp2KETxny2hTHPSxfHY1y2dXZ5yPxW1CkTj1BzpY92YTL25rZkdTO42tHTS1RYjZDnHb6VfIcRzY1dzOrub2QZXR6zGoLA5QXOBzQ43Hg8dwQ1HQ76WyOEBZYYCAz72G4YZgx4FgwEtxgY+igJfCRCfuZK1Q+tZ2HBzHoT0SZ+/+MLtbwuxtCfP58w5nweTsBnmFF5ERyLYdnt/SRHygPQe7UeDzUFTgo7zIT2VxgMqigLstDjChLMjU6iKmVRVRU1owojsXGl4vvimT8U2ZDEf37zN2KITd0JD41Yjd2orh84Hfh+FNbH1+d+vxup0U0t9ZUoK3rg6jpGRE/t5EYjbr3mzimY0NPPbqHt5sCHV73+wJJVxw9HTOWjKZoGaXHTY+r4eyQg9lhX5mTyhh1bLul3RobO1g/a79vL7rAA2JYNPWEcPjMXAc2N4YYltD24A7EqeL2w71BzqoPzCwfmbZsL2xXeFFZDxoaY9mJbgAdMRsOmIRmtoibNl38Kq8SUG/l6lVhUytKmJadTHTqoqYUVvMzJriUTtpl6eoyB3FM0bWXrJthy31bfx3Yz3PbGzg+S1NBzUJJVUU+XnrEZM4a8kUDplUOiLDl7iqSgo4fl4tx8+r7fGejmic3S1hWkIRmkNRbMfB5zGIxh12NoXY1hCiqS3C/vYoB8JRonGHuG0TjTu0R2Lsb+97KHiu7GkZXG1RbxReJOcsy5oKfAlYCVQDu4C7AMs0zaZ+PuMC4GRgCbAYKAVuNU3z/T3cPxPY3MsjbzNN86Iun9kCzOijKF80TfPL/SnzUJQGffz2quOob+2gsTWS+ompodXdNrZ2EIm7nQXdqlr3J6v0aty446Q6FPZHOBrnjT2tvLGn9aBr5UV+ZtQUM6PGDTPTE/uTKwpHVbPUaBOOxHllZwvr3mxm3ZtNvLS9udcvocKAl7ccUsvpCydx3NwaLUQ4hhT4vcyoKQYGt0REJGbT1NZBeyRONO4Qi9upfzvaIjFaQlH2h6JE4zZx28F2nEQfGYNwNEaoI05bR4z2aLz7pmoDjMTW5/UwsSzIxHL317Tq7C9rofAiOWVZ1hzgKWACcDewHrfS/xPASsuyTjBNs6Efj7oeN7S0AtuBBf0swlrcoNTVS92cuwnoboY0A7gO8AP/6Od7h8TndUcfzB/icxzHoSNq09YRoykUobnNrYFpbIvQ2BphV3MoUSUd4kAvi9q1hKKJL9DMeUF8XoNpVUVMT4SaGYlgM7mikMrigH7a76dozGZbY4jN+1rZvLeVzfva2LKvlS31bX3WwE2tKuKYOdUcM7eGo+dUq1lIuhXweZhYnvsZm4eLwovk2o9xg8vHTdP8YfKkZVnfAz4JfBW4qh/P+SRuaHkDtwbmkX6+/wXTNG/sz42mad7U3XnLss7EDS7Pm6a5up/vHREMwyAY8BIMeKkuLejxPsdx2N8eZVtDiG2NIbY3hHizoY2t9W282RDqsWkiFnfYvK+NzfvaeKzLtQKfJ/GTVyF15UHqKtz96pIAlcUFVBb7qSgKjIsVfh3Hoa0jxt79HezdH2bf/jA7m9rdsLKvje2NoX43E1YWB1gyo5Jj5lRz9JxqJldqtJCMPwovkjOWZc0G3gpsAX7U5bIJXAF8wLKsT5mm2XNnDMA0zVRYsSwryyXt0xWJ7c3D/eLhYhgG5UUByosCLJyWWflk2w5794fZWt920K99vXT+64jZvNkQ6rETaVJRgZfKogAVxe4Q0Krizv3KYj+FAR9Bvye1DfrdEQ9Bv/sr4Bv+WUxjcZvWcIzWjhit4Sit4RgHwp37zaEo+w6EE0Glg337w4QigxvmPau2mEXTKzliWgWLplcwrapINVoy7im8SC6dmtg+aJpmxlhA0zQPWJb1JG64ORb4V47KMNmyrCtx+9o0AE+bprmuvx+2LGsicC5uc9UfclPEkc3jMairKKSuopBj5tZkXGsLx3izoY0tiTDzZn0bbza0sbslTGsvzVDpQh1xQh3t7GgaXKc+T2KoZzARaArT9gM+jztc3OPOd+H3Gvi9v76KwwAAB3tJREFUntQoDpe7kzy2HYeY7RBLdHgMReJuUEkEk9aOGO2DDCK9mVRRyKzaYmbVljBrQgkza4uZVVNCcVD/TIt0pf8rJJcOSWw39HD9ddzwMp/chZczEr9SEhPHfdA0zTf78fkP4TYZ3WKaZver6rnPvAS4pJtLS/pb0NGoOOjj0CnlHDrl4GGQreEou1vC7GkJs6u5nT0tYfa0tNPYGkn1v2kODX1Ule1AKBIfdM3GcCnwu50Ya8uCTEj8mllbzKxat6/QOJw9VWTQ9H+L5FLyG62lh+vJ87lYRjgEfBm3s+6mxLlFwI3AKcC/LMta0ltzlWVZBnBZ4vBnfbxvJm5fHEkoCfqZG/Qzd2Jpj/c4jsOBcIzmRCfi5rROxc2hCC2hKO3ROOFI3N2m7XckVgSOxod/lnCPASVBHyVBv7st8FEa9FMc9FEadPdry4LUlhWkgkpp0KfmHpEsUXiRfEr+S571bx/TNPcCX+xy+nHLst4KPAEcgxtMvt/LY04HZgPP9aOj7hY4qM8qwNzq6uopdXV1/Sr3eGMYBmWFfsoK/UyvGdxwyljcpiNq0x6N0x6JEY7ahBPBJha3icbduS6icTtx7GDbDhidfwGTocLAnXHU5/Xg9Rj4vAZFAR/FBW4oSQaWooBXQUQkjxReJJeSNSs9Ta1Y1uW+nDNNM2ZZ1i9ww8tJ9B5ekh11+6p1wTTNW4BberisBcRyyJdYAsHtG9LziCoRGTs0g5Hk0muJbU/TlcxLbHvqE5Mr+xLbHn/UtyxrAnAe47ijrojISKXwIrmUHN78VsuyMv6uWZZVCpwAtAP/GeZyHZvYburlnktxO+r+sbeOuiIiMvwUXiRnTNPcCDyI25n1o10uW7g1H79Ndpq1LMtvWdaCxKy8Q2JZ1jGWZR20II9lWafiTngH8PsePpveUXfMzu0iIjJaqc+L5NpHcJcH+IFlWacBr+L2NzkFt7noC2n3Tklc34obeFIsy1oFrEocJnu/HmdZ1i2J/XrTNK9N+8g3gcMTw6K3J84tonPumRtM03yqhzKfCszF7ai7pl//lSIiMmxU8yI5lah9WYbbmfUY4FPAHOAHwHH9XNcI3PlSPpj4dWbi3Oy0cxd0uf93wDPAcuBy3BA1D/gzcJJpml/p5V397qgrIiLDz3D6u+SsiAyW/icTERm4HucjUM2LiIiIjCoKLyIiIjKqqMOuyAh1//33s3v37nwXQ0RkSOrq6li5cmVWn6nwIpJ7g5pH/plnnllP5+KWIiKj0tatW19buXLlgmw+U+FFZOQqSWxbgBfyWZAxbgnuEhb6fc4d/R6PT8k/95K+bhwohReRkesN3LlvXjBNc0WeyzJmJeYCOhn9PueMfo/Hp7Q/9zey/Wx12BUREZFRReFFRERERhWFFxERERlVFF5ERERkVFGHXZGR6xbgUWBLXksx9t2Cfp9z7Rb0ezwe3UKO/ty1tpGIiIiMKmo2EhERkVFF4UVERERGFYUXERERGVXUYVdkhLEsqz8d0SpN02zOeWHGGMuyLgN+DtxvmubberjnPuAs4KOmaf54OMs32qX93XWAeaZpbuzhvkeAFYnDS03TvCX3pZPhMFz/fim8iIxcVi/XwsNWijHENM1fWJZ1LvB2y7I+aprmj9KvW5Z1NW5w+YeCy6DFcL9bPgx8vutFy7Lm4U4Zn7zv/7d3L68+hHEcx99uC1aSIk7s5A9g4Q9wWSASK5ecUFJipcT5+lqKhSxcTqEQSUpZWohSFiKXhdWpk3IpG0InwmJ+6ZeVdJzHPPN+1Wye+S0+/ZpmPj0z84zq9E/PXx440n8qIo6UzlCpncAy4Fhm3omIlwCZuQg4DrwHBgvma7u3wGtge2YORcS33/bvoPnS+m1g3USH08T41+cvn3mR1CkR8Y6mwMwALmfm1MycClzuje2KiDclM1ZgGJgLrO4fzMxpwDbgAfCiQC5VwvIiqXMi4hZwHlgCDPW2pcDFiLhZMlslrgKfaGZZ+q0F5tCUG+mvWV4kddU+YITmuYyDNKuA7i0ZqBYR8RG4BqzKzIG+XTuBD8D1IsFUDcuLpE7qXWCPAlN62+7emMbHMM3/OgiQmQuB5cCViPhcMpjaz/IiqZMyczpwoG9oY6ksNYqIh8AzYDAzJ9PcQpqMt4w0DiwvkrrqGLAYOAk8obnIrikbqTrDwEJgFbAdeBQRj8tGUg0sL5I6JzNXAHtoZgYOAFuAMWA4M2eXzFaZS8AX4CwwHzhXNo5qYXmR1CmZOQu4AHwFNkfEWEQ8Bw7TvAlzpmS+mvRWUb0BDNC8fXS1bCLVwvIiqWtOA/OAQxHxtG/8BHAf2JCZm4skq9MhYD2w0geiNV5cYVdSZ2TmFmATcI+mrPwSEd8zcxvwFDiVmXcj4lWBmFWJiFFgtHQO1cWZF0mdkJkLgFM064xsjYjvv/8mIkaA/cBM4HxmTprYlJL+xKQfP/7kA5CSJEn/B2deJElSq1heJElSq1heJElSq1heJElSq1heJElSq1heJElSq1heJElSq1heJElSq1heJElSq1heJElSq/wEIZYkHG5GuMYAAAAASUVORK5CYII=\n", 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\n", "text/plain": [ "
" ] @@ -246,7 +246,7 @@ } ], "source": [ - "plot_chi(chi_s_wk, chi_c_wk)" + "plot_chi(chi_m_wk, chi_d_wk)" ] }, { @@ -255,14 +255,36 @@ "source": [ "## 2. Construct the particle-particle vertex in RPA\n", "\n", - "Now we have all the ingredients to build the particle-particle vertex in the RPA limit. In this example we limit us to the singlet particle-particle vertex, which we construct by calling `gamma_PP_singlet`. For the 1-band case it is given by\n", + "Now we have all the ingredients to build the particle-particle vertex in the RPA limit. In this example we limit us to the singlet particle-particle vertex for a symmetry constraint calculation of the Eliashberg equation.\n", "\n", "\\begin{align}\n", "\\Gamma^{\\mathrm{singlet}}(i\\omega_n, \\mathbf{q})\n", "=\n", - "3 U^2\\chi^{\\mathrm{s}}(i\\omega_n, \\mathbf{q}) - U^2\\chi^{\\mathrm{c}}(i\\omega_n, \\mathbf{q})\n", - "+ U\\,.\n", - "\\end{align}\n" + "3\\Phi^{\\mathrm{m}}(i\\omega_n, \\mathbf{q}) - \n", + "3\\Phi^{\\mathrm{d}}(i\\omega_n, \\mathbf{q})\n", + "+\n", + "\\frac{1}{2}\n", + "U^{\\mathrm{d}}\n", + "+\n", + "\\frac{3}{2}\n", + "U^{\\mathrm{m}}\n", + "\\,\n", + "\\end{align}\n", + "\n", + "where\n", + "\n", + "\\begin{align}\n", + "\\Phi^{\\mathrm{d/m}}(i\\omega_n, \\mathbf{q})\n", + "=\n", + "U^{\\mathrm{d/m}}\n", + "\\chi^{\\mathrm{d/m}}(i\\omega_n, \\mathbf{q})\n", + "U^{\\mathrm{d/m}}\n", + "\\,.\n", + "\\end{align}\n", + "\n", + "\n", + "\n", + "For the 1-band case $U^{\\mathrm{d/m}}=U$ and we don't have to take correct orbital ording in the products into account, which simplifies everything. But for generality we will show the process which also works for multi-orbital systems, where we first construct the density/magentic reducible ladder vertex $\\Phi^{\\mathrm{d/m}}$ via `construct_phi_wk`." ] }, { @@ -271,9 +293,28 @@ "metadata": {}, "outputs": [], "source": [ - "from triqs_tprf.lattice import gamma_PP_singlet\n", + "from triqs_tprf.lattice import construct_phi_wk\n", + "\n", + "phi_d_wk = construct_phi_wk(chi_d_wk, U)\n", + "phi_m_wk = construct_phi_wk(chi_m_wk, U)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And then construct the singlet particle-particle vertex via `construct_gamma_singlet_rpa`." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "from triqs_tprf.eliashberg import construct_gamma_singlet_rpa\n", "\n", - "gamma_singlet = gamma_PP_singlet(chi_c_wk, chi_s_wk, U, U)" + "gamma_singlet = construct_gamma_singlet_rpa(U, U, phi_d_wk, phi_m_wk)" ] }, { @@ -308,7 +349,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 11, "metadata": {}, "outputs": [], "source": [ @@ -330,7 +371,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ @@ -356,7 +397,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ @@ -375,12 +416,12 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 14, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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bAiSZlNr33JN5F/+COef9F5m5c6PCQoFN53yDde99P2Fvb2Mr2ECF3l7WvuOdbPrGucNlwewe5px/HvN+ciHte+1V4mwRESmHAiSZtIIgYMZrX8P8P/yejiOPHC7vveIKVr/hjRQ2bmxg7RqjsH49a055E33X/GG4bNrRR7PDtX9ixmtOUleaiEiNKECSSS+7445s98uL6HrH24fLBm6/ndWnvnlKBUmFjRtZ/YY3MnDbbcNlM9/zbub9/Kdkd9ihgTUTEWk9CpCkKQTZLLO/YPR83g2XDf7976xZ8jbC/povZzfphL29rHnb2xm8667hsh77PD2fO1Nr24mI1IECJGkqM9/1TnrO+uLw84G/3sq6T/w/WnnC0zAMWffhjzJwy1+Hy2Z//T+Z+c53NLBWIiKtTQGSNJ2ZS5bQ/dnPDD/v/c1v2Pyd7zawRvW1+bvfpfeKK4afd5/5Wbre9MYG1khEZPIIguAPQRCE8c9/lDjuB4njfjDWdRUgSVOa+d7TmZEIEjZ+9WsM3HlnA2tUH/233MLGs74y/LxryVuZdfrpDayRiMikczCQix8fmHZAEASHA28DhtZAvS3tuCQFSNKUgiBg9pfPov3gg6OCXI617/sAhS1bGluxGips3cq6j34M4nmfOg45hB73uQbXSkRk8giCYA9gLnAr8BQpAVIQBBngAuBpRgIjBUjSuoL2duZ+6zyCmTMByK9cyaazz2lwrWpn41f/k/xDDwMQ9PQw9zvfJujoaHCtREQmlUPj7e3AHcD+cUCU9B7gEOCTwB7AIPCPsS6sAEmaWtuCBfR88QvDzzf/4IcM/vvfDaxRbQwsW8aWH/5w+HmP+xzZnXdqYI1ERCalZID0d2AGURAEQBAE2wFnAX8BbgC2A/4ZhuGY6c8KkKTpzXjdyXQceUT0JJ9n/WfPaOqstjAM2fDFL0H8GqYddywzXv+6BtdKRGRSGgqQbiNqQYLR3WxfBXqA9xO1Ig0dOyYFSNL0giBg9llfgmwWgIFb/krfH/7Y4FpVr+8PfxxJ6W9rY/YXv6gZskVEigTRf4zPBrYC/yZqQYI4QIoHZr8d+G4YhnegAEmmovZ99qFryVuHn2/6xrlN2YoU5vNs/HIia+3Np9G2+6IG1khEZNLam6h1aFkYhvkwDB8E1gMHJgZmrwHOiI9PtjaNSQGStIxZH3g/dE4DYPCf/6Tvj39qcI0q1/f7a8jdfz8AwcyZzPrIhxtbIRGRySst4FkGHAC8m6jF6NNhGK6N9x0M9AN3UQatUSAtIzt/Pl2nncaW70fzf20691w6X/iCpuqeSk542fW2JWTnzWtgbaTRzOwOYBGwGXigwdURaZQ9gZnACufcsxPlyQHaQ+4AjgW+DPwN+AFAEASLgHnArWEYDpZzUwVI0lJmve+9bPnZz6Cvn8E7/8Hg3++g45CDG12tsvT/7TYGbo//nXd0MPNtSxpaH5kUFhF1IfQAuzS4LiKNVjzeIC1A+jsQALOBD4QjYy0qGn8ECpCkxWR32IEZr3oVW3/5KwA2/+SnzG2SAGnz//zP8OMZrzmJ7A47NLA2MklsBnqmTZvG/Pnzyzqh0pF3vqF6YYkr+c4peMrznhNynhP6c4XU8t7B9PLNfekNAn39udTygd70DO9cX/pEs2Ehn1oOEGSyqeVtnV2p5R3Tp6WWd05L/3U8s7M9tXx6e/oImWlt6eVtmfSW9Kynhd1zOAC+RvmA9B2VNuIXH75q1Sr6o0XJN49cM8gAi4EtwD2Jw68CTgLWh2F4a6K8ovFHoABJWlDXW948HCD1Xn45efc5snPnNLhWpeWffpq+318z/Hzmu9/VwNrIJPIAsMv8+fN50xtHr7/nC198QYrv+LznhEHfhYCBvCew8ZRv8QQ263rTA5vHNqYHMMvXpAcwD65cl1q+wlP+1KOPppavX/lUavng1o2p5QDtM7pTy2cvXJhavsPuu6aWL5qf/n/UwQvTy3eblx6A7dKdHoDNmZ4eaHX5Aq2sP6rp8Oxr9wVhnnLfHYoPv+iii3jkkUdgdDfzM4m63W4Kw3D4CxaPN7o05bIVtyBpkLa0nI7Fi2k/8IDoSX8/W3/1q8ZWqAy9l14G+eiv1I7nHEb7Pvs0uEYiIpPaUMBze8mjRhwM9AJ3l3sDBUjSkrre8pbhx1t//esG1qQ8W399yfDjGSef3MCaiIhMfmEY/iQMwyAMww+Vefy8MAxnhGHo7y8toi42aUnTT3wl6884A/r6yf37XgYfeID2PfdsdLVSDd59D4P/+lf0pHMa01/5isZWSJpCud0TQzy9Xy0t4xn8km1LX9Owvaun4nv4zvHdw1enqcj3XZ0s75BakKQlZbq66Dz++OHnvZdf0cDalLb1f/93+PH0l7yETHf6mAYREZk4CpCkZU1/xcuHH/deeWUDa+IXhiG9v7t6+PmM17ymgbUREZEhCpCkZXW+8IXDM2vn7vk3gw8sb3CNtpVb/iD5lSsBCGbMYNrRz21shUREBFCAJC0s09VF5/OfP/y876qrGlibdH1/HFlUd9oxzyPo7GxgbUREZIgCJGlp0084Yfhx39IbG1iTdMkAqfNFL2xgTUREJElZbNLSph3zvOHHA7fdRmHrVjIzZjSwRiMK69czcOvfhp8nB5WLjBZCWDTZYpD+960vA8hbXsVMyt7soyA9Vc53vC+jy3e8b8LBDt/s0R3p5Z3eRIg9UkvzuQHP8f5sNd89fHXyvQbfa67Ve+pLqiuVbefb5/suVfqdnCzUgiQtLTt/Pm37xpMuDg4y8Ne/NrZCCX033DA8OWT74oPIlrmUhIiI1J8CJGl5044+evhx/41/bmBNRuu/+Zbhx8mxUiIi0ngKkKTldR5zzPDjyTQOaeDWkXUUpx1xRANrIiIixVp+DJKZHQWcARwBdBItdvdD4HznXFlTjpvZXsBrgJcAewE7AOuAW4BvOueuSzlnCfCjEpd9r3PuO+W/EqlWxxGHQ3s7DA6Su+ce8k8/TXb77Rtap/zadeTuuy960tZG+yEHN7Q+IiIyWku3IJnZq4ClwDHA/wEXAB3AucDFFVzqi8BXiQKjq4BzgJuAlwPXmtl/lDj3MsBSfspeUVjGJ9PVRUciAOn/yy0ljp4YA7eNDM5uP+AAMtOnN7A2IiJSrGVbkMysG/gekAeOc87dFpefCVwLnGxmpzjnygmUrga+5py7o+gexwJ/AL5uZr92zj2Rcu6lzrkLx/FSpAY6DjuMgVuiAdqDd94JJ76yofUZ+Guie+3w5zSwJtIUQrbNYit+PsST3Zb1lPuWaCu1ZJg388mTlxR4yrO+jKsKs9Wmd2TTy2dOSy2fm1oKuTnpf6gUQv9Cdr6MLl+2mq9Ovtfge82+98j3nvo+A+9nVs3n78s+9F3L9x3e5rvemIUEW7kF6WRge+DioeAIwDnXR9TlBvDeci7knLuwODiKy28AridqlTpqvBWW+ul49uLhxwPLljWsHkP6EwFShwIkEZFJp2VbkIChSWWuTtm3FNgKHGVm05xz/eO4z2C8zXn2LzazDxONf3oMuM459+g47idV6Fi8ePjx4J3/IMzlCNoa8/UvbN3K4D//Ofy849DDGlIPERHxa+UAKZ78hvuKdzjncma2Atgf2B24p5obmNkC4AVEwdZSz2EfKnqeN7PvAx+OW7N8114CLEnZtbjiigrZHXYgu9NO5J94grC3l9x999O+3zMbUpfBf/4TclE83bb33mTnzmlIPURExK+VA6SeeLvBs3+ofHY1FzezacDPgWnAJ51z64oOWQF8ELgGeDSuz9HAV4D3AN3Am0rcYiFwbDV1k3Ttz15M/olomNjAsmWNC5D+dffw447FBzWkDiIiUtqkDpDMbCWwoIJTfu6cO63MY4eGjVU8+svMssBPgecCvwTOLj4mHp90Q6JoK/BrM7sFuBN4o5l9zTl3p+c2K4vOH7KYkeBPKtCxeDF9V/0OiAKkrje9sSH1GPzXv4Yft++3X0PqICIipU3qAAlYDni7oVI8nng81ELkCya6i44rSxwc/Qx4HfAr4DTnXNlBlnPuETO7CjiVaPqB1AApzny7MOX+16OWpaqMGod0x7KG1SPZgtS+//4Nq4c0k5Cg4BvmWHSkJ1vNl93WlvH8GiixGJsvqSiXSd+R9VSp3ZPe1O65d2dbeqbX/O7O9Bt49Hqy1QZynqyqKlSaced7Db7X7HuPfO+p7zPwfjYlPn/fvjbfKb7vrieLLdimvDFZbJM6QHLOvWAcp98LHArsDdye3GFmbcAiooHVD5Z7wfi8XxAFR78A3lLuZJNFno63XVWcK1VqP/CAKD81DBm8914Kvb0TPv9QODjI4L33jtSpQd18IiJSWiun+V8bb09I2XcMMAO4udwMNjPrAC4hCo5+Ary5yuAI4PB4W3ZwJuOXmTWLtt13j57k8+QSgcpEyT3wAAxEK4Nnd92VzOzZE14HEREZWysHSJcAq4FTzOzQoUIz6wS+FD/9dvIEM+sxs33NbKei8mlEM3G/CvgB8DbnXMm2WDN7XkpZYGafBo6M65Y2BYHUUdu++w4/Hvz3vyf8/qO71zT+SERksprUXWzj4ZzbaGbvIgqUrjezi4G1wIlEUwBcQjTAOukkovXTfszoFPvvAC8jCmoeAz5nZsW3vN45d33i+VIzuw/4W3xOD9Gg7mcRDdg+1Tm3cXyvUirV/sx96bvySgAG72lEgJQYoK3xRyIik1bLBkgAzrlL4+VAPgu8lpHFaj8KnFfB4OpF8XY74HMljrs+8fhs4DlEE1bOBQrAw0TrwX3DOafutQZof+ZIC1KuIQGSWpBERJpBSwdIAM65m4haf8o59kJSMsecc8dVcd9PVHqO1F97A7vYwjBkQC1IUo2wALmBsg4NKsxiCz2/BbzZbUDek63U5sus8q2t5kmhmtGenrnV05lep93mzkgtn9+dvu6ZL1stX6hdtlS2wvXkfNlqvtfse49876k388y7pltqcXROhdlqge+7W/ZabLXLLqxEK49BEtlGdrfdCDqjdNrCmjXk166dsHsX1q4lXL8egKCri+yuu07YvUVEpDIKkGRKCTIZ2vbYY/h5bvnyCbt37sGRXtW23XcnKLVctoiINJQCJJly2vZMBEgPTGSAtGKkDosWTth9RUSkcgqQZMpp23PP4ccT2oK0IhkgLSpxpIiINJoCJJlyRnWxPfDAhN13VAvS0ISVIiIyKSlAkimnPdGCNDiBXWx5tSCJiDSNlk/zFymWXbhg+HH+kUcIczmCtvr+UwjDcHQX2+4KkKR8QRgS5MpaFcmbzu8t96VQZ/3/Jqa1pS+s6kvGzhV8af7p5b7Udp+ZngVgBz1p+wVfeQ3XRPWt9ZqpcCqESqc88L2nlZZPK5HnH+Q8a8jnPWn++cH048tM8w98qyPXmVqQZMrJdHWRmT8/epLLkX/88brfs/Dkk4S9vQAEs2eTmTOn7vcUEZHqKUCSKaltwUgrUm7lQ3W/X27FypF7q3tNRGTSU4AkU1I2ESDlH5qAAKloDiQREZncFCDJlNSWGIeUm4gAaYXmQBIRaSYKkGRKGt3FtrLu9xs9QFstSCIik52y2GRKSgZI+Ucerfv9cg8/MnLvROuVSFkKeYKBreUd68tWy3jK855fA9mOEvVJzz6a3pG+aGwYpt/bnzWWXqfpngVdB/Lp9RnMp98g78mKKtQwWyrjWUoo6ylv92aZpb93vuyzGe3px0/3LJI73XOdUt83b0ZlPn1R2sCziK3ve7RNdlsh761LPakFSaak7K67DD/OPVr/ACn/xEimXHbnnet+PxERGR8FSDIlZbbfHjqiv5DD9espbNlSt3sVtm4lXL8hetLRQWbevLrdS0REakMBkkxJQSYzqiUnX8dWpOQ8S9mddiTwdXWIiMikof+pZcpq23XX4cf5Rx+r231GBUjqXhMRaQoKkGTKmqhxSKNbkBQgiYg0A2WxyZSVTbYgPVbPFqQnRu658051u4+0sDBPpn9TecdWuBZbmEn/NRBm2/33aE9fi823ttaMaTM9F0qvk28dswFPVtqgZ603T3IbIY1biy3Ak93m+dh8a7T5sth82Woz2jzZav2b08sH/OMyg8H0tdh8a655s9jKXIuNUFlsIhMqu8tIC1J9A6RkC5ICJBGRZqAASaas7I47Dj/OP/lk3e6jMUgiIs1HAZJMWcnurvwTT5Q4cnxGd7EpQBIRaQbjHoNkZl3ADsB2wHRgDbDaOVe/P8lFamB0C9JThGFI4JnltlphGKoFSUSkCVUcIJlZFngF8GLgecB+sO2oMzPbANwE3Aj82jm3ovgYkUbKzJxJMHMm4ebN0N9PYd16snPn1PQe4caNhPEklEFnJ5k5s2t6fRERqY+yAyQzWwB8AHgzsD0pQVGR2cDLgZcBXzaz64DvOed+VV1VRWovu+OO5B54AIDCk0/WPEAqbj2qdQuVTBG5QQobVpd1aJBJX68MT3nQlp6tFnRM894j9KzFFXqykjy5St7stsCTcdeWSU8zy3nSz3xZbAVPFlsNl2LD9089U2EWW1ulWWy+tdU82Wq+7Migz581GeTSs9gY8HwvcunZbb411sLict/5dTZmgGRm2wNnAu8GhlYvvJOodei2+PFqYB3QB8yJfxYCh8U/zwdeABxvZmcAn3XOXV7LFyJSjWSAlH/ySdr3e2ZNr6/xRyIizamcFqQHgS5gBfBj4CLn3P0ljn86/rkPuAbAzKYRdcu9CTgRuNTMPuGc+8Y46i4ybpk6Z7KNbkFSir+ISLMoJ0B6FPgK8HPnXFWzNTnn+oHfAL8xsz2BTzHSGiXSMNkddxh+XJcAKZEdpzmQRESaRzkB0n7OuZr1zDrnHgDeaWYajCENl8xkK6xaVfPr559+evhxZocdShwpIiKTyZjzIDnnQjPrrvWNaxl0iVQru/32w4+TwUytFFaPDKxN3ktERCa3crPYnjSzS4GfAL9XcCOtIjM/ESCtqn2AlH96JEDKbDev5teXqSEc6CP/5MPlHZytURZbZ5f3FplZs9PP8Rzvy0rzrQ83vWNG+n091897Mr0GPdltYZh+fKGGaWwZTxqbL7vNt+aaJymNab5stYGtnvL0tdW82Wqb16aXA/lN61PLw770e1SaxUZ+dHk44Mmaq7NyZ9LuBN4AXAk8amZfM7P961ctkYmRbNUp1KMFac2a4ceZedvV/PoiIlIf5bYgfZBo/qPnADsBHwc+bmZ3ABcCFzvnypukQ2QSycyfP/w4//Sqms+mPbqLTQGSiEizKCtAcs5dAFxgZnsDbwVOBXYDDgaeDZxjZlcRdcFd7pzL1am+IjWV6eoimDGDcOtW6Osn3LSJoLs2Q+4KW7dG1wXo6CCYNasm1xURkfqraKkR59x9wGeBz5rZcUTB0muAWUTzG50IrDWzi4CfOOduq2ltq2BmRwFnAEcQdRU+APwQOL/caQvMbCHRPFA+v3TOneI5963A+4mWZMkDdwBnO+euKPc1SH1l5m9PfuVDQDQOKVOrACnZejRvnmbRFhFpIlUvVuucux643szeB5wEvIVotux5RAHB+83s30RdcD93zj3uuVTdmNmriOZf6gN+CawFXgmcCzwXeF2Fl7wTuDSl/C7P/c8GPkY0l9T3iOZ+OgW43Mw+6Jz7VoX3lzrIbjcSIBWeXgV77lGT6xZWJ8YfqXtNRKSpVB0gDXHO9QK/AH5hZjsSjVU6DTgAeCbwVaK12P7knDthvPcrVzw1wfeIWm2OG2rNMrMzgWuBk83sFOfcxRVcdplz7vNl3v8oouBoOXCYc25dXP514HbgbDO7wjm3soL7Sx3UK5MtvzoxB9J2CpCkeoW+fnofXlnWsYFnUa9se/p/95nOzvTymbPLut+oe3SmZ58Fg5513bKe+YIz6a9hWlt6XXOe5DNfo60vWc2T9FaVWmWxtXmO962HFnjWyQsGfcenl/sy1QDya9In1S1sTj+n0Oe5x2D6aJywaBG9Ql8H5eeU1U5N7+ice9I593Xn3EFE45O+DYRAFnhRLe9VhpOJFtW9ONnV55zrI+pyA3hvHe9/erw9ayg4iu+/ErgAmAa8rY73lzKNymRbXbtcg2QLUlYBkohIUxl3C1IaMzuCqMvt9finxqi34+Pt1Sn7lgJbgaPMbFq8FEo5djaz9xB1I64B/uKc+0cV9/8d0QLAxwOuzHtLnWTmjcxPlEzLH69ksKUWJBGR5lKzACkeyPzm+GdoEEcADBLNn/TjWt2rTPvE2/uKdzjncma2Atgf2B24p8xrvoiiljAzux54q3Pu4URZF7ALsNk59wTbGlrsd2/fjcxsCbAkZdfiMusqZcrMmzv8OL/GPzlapfLJAGmeJokUEWkm4wqQ4nE+rydqLXpuXDzUYnQ7UVB0kXOudn+Wl68n3m7w7B8qn13GtbYCXyQaoP1gXHYg8Hng+cCfzGyxc25oGtFa3HshcGwZdZNxysxNtCCtrU8LkpYZERFpLhUHSGaWAV5KFBS9kmgszVBQ9ATwM+DHzrm7x1s5M1sJLKjglJ87504r89ihOo85LM85twr4XFHxUjN7MfBn4HDgncB/lVvRMu69ErghpXwxIwGY1EC2bl1siSw2LTMiItJUyg6QzOxgoqDoFKLBzxAFGX3AZUStRdc45wrpV6jK8vj65UpOJTDUSuMLJrqLjqtY3FX3faIA6RhGAqSx7j1WCxPOuQuJpkgYJe7SU8tSDSW72Aq17GJbk2hB2k4tSFK9wa29rClzLTZftlp2enrG2PS56f9NzdjFf49Ml2fS0wFPBlV7+lpcYX4g/Tr59PXhyKRnPbVlPL/KPJlhvmy1Gi7F5p33zFMlb7YaBc+8y3lfefp7GuQ966F5PjPfumrgz1bb+tiq1PLetem/6vK96XUtzm4b7N4N2v1rA9ZLWQGSmd1FlLIPIy0vNxMFRb90zm2sQ91wzr1gHKffCxxKNM7n9uQOM2sDFgE5RrrMqjWUyz386TnntpjZY8AuZrZTyjikveLtNuOjZOLVbZC2FqoVEWla5bYg7RdvHwJ+StSFtrw+VaqZa4mWRDkBuKho3zHADGBpBRlsPkfE2+JA61qiAesnAD8q2vfSxDHSYJnZs4cfF9avJ8znCXwropcpzOcprB1pjcrMnVviaBERmWzKnQfpJ8DxzrlFzrnPNUFwBHAJsBo4xcwOHSo0s07gS/HTbydPMLMeM9vXzHYqKj/czLZpnzaz44GPxE9/VrT7O/H2s2Y2J3HOQqKZxvvZNnCSBgja2wlmx90MYUhh3brSJ5ShsG7dcHt9Zs4cgnZPl4GIiExK5S5Wu6TO9ag559xGM3sXUaB0vZldTLTUyIlEUwBcQrT8SNJJREHLjxmdYv81YP94/M+jcdmBjMx1dKZz7uai+99sZt8APgr8w8wuIVpq5A3AXOCDmkV78sjOnUdufdRPXlizZtwTOxae1izaIiLNbNzzIJnZDsBxwDOAGc65L4z3mrXinLvUzI4lWmD3tYwsVvtR4DznXLlD8n5KFDwdRtQ91g48BfwK+JZz7kbP/T9mZv8APgC8GygAfwe+rsVqJ5fMvHnwYNRLWouB2vlRGWwKkEREmk3VAVLcVXUu8Pai63whccxsorE53cAi59wj1d6vWs65m4CXlXnshaRkjjnnfgD8oMr7/5iJnyRTKjQqk23t+AMkjT+SWhrY1M+Tf390VFkm61m7qzO9O3fGdtMrumfnvG7vvjDnyUrzlAeeTCxfOb6MqyB9VEjo+U3my27Lpx9O6FsorQq+K3k+Nm+2WpCrLCut0ve60s8S/Gur+bLVNq54KrV86+re1PJc3+h7Dz57R5gz8VlsVa3FFmeBXUXUKjJANNh4m8HOzrn1wP/E93lt1bUUqbNMz0iqc2FD1TM/jFxj/fqRaycGgYuISHOodrHadxB1q90LPMs59yL8c/r8Kt6+osp7idTdqEy2GgRIYeIamTmz/QeKiMikVG2A9GaiWaA/6Jx7aIxj7yRq0dy/ynuJ1N2oFqRE60+1RrUg9WjicxGRZlNtgLQ/UdBz/VgHOufywHqizC2RSSkYNRdSDbrYki1I6mITEWk61QZInUBfHPyUo4vKlgwRmVCZ2WpBEhGREdVmsT0BLDCz7Zxzq0sdaGbPYSS9XmRSSrbyhLUYpK0WJKmhvq05Hrxn9DI4HZ5FvXpmpa+55mvE79qxvPWwktoLnr+NfeWhZ4nOgqfcd3yNyrO+bLj0q3jXbgP/2mrefLg6v7aK39NKP0v83w3f2mq+bLU196dnDG/YNPo6ffsMwpzUQ+uq2hak6+Pt20sdZGYZ4MtE37s/VHkvkborXm5kvJLXCNSCJCLSdKoNkM4hCnrOMLMT0w4ws2cSTQVwPNFUAP+VdpzIZFDzNP9160eurSw2EZGmU1WA5Jz7F/BhYCbwf2a2nLgBzMwuMbO7gbuAFxEFUqc75x6uSY1F6qDWLUij0vzVgjQlmFntZhmUpjCzawYzZqT/TI9/1tfg/xPxC4JgdhAE64MgWBMEwayU/ZkgCC4JgiAMguD7lVy76pm0nXPfMrNHiFqGFiV2vSbx+GGiqQAur/Y+IhMh6O6GIIAwJNy0iTCXI2ir7p9H2N9P2Bv3ube1EXRN/Ayw0hB3mdmnnXO/bXRFZGJ95jOf2aZsKFru7Oyc2MpMMWEYrg+C4DzgTKJlvb5SdMh5RBNVXwG8p5Jrj2stNufcZWZ2OdGkkUcBOxG1Sj0F/AX4k3POP9JPZJIIMhmCnm7CoQVrN24kW+USIYWi1qOghssXyKT2GHCpmd0M/L94mSOZAs4444xtyvSvfkKdC3wI+FgQBOeHYbgZIAiCzwLvB24B3hCGYbmZ90ANFqt1zhWIlhq5drzXEmmkTE8P+ThACtdvgGoDJC0zMiU5515sZi8EvgYsNbMrgE875+4e77W35AvctXH0ak497ekjJPbwXKOnL31tLV9GUpj3ZD0B5NN/z4SezKegzplbvuuHvut4sth8QY0vU22s81JV+BrqnfXm+8x8nzH4vxu+71Lx2mpDirPVhizfMro8V+q7CIRhuC4IgvOJFqZ/P/C1IAjeBnyJaMWPV4RhuLXkRVJUO0hbpOXUahxSsgVJGWxTi3Puj865Q4DTiCbUvdPMfmhmz2hw1URa3TeAzcDHgyB4PdE6sE8AJ4RhuKbkmR7jbkGKF67dk2iQdvoy0jHn3NLx3k+kXkZnsq2v+jqjMtjUgjQlOecuMrNLgPcS/VV7ipldAHzZObeusbUTaT1hGK4NguBbwKeAXwIbgZeGYbiy2mtWHSCZ2R7AWcCJwLQyTgnHcz+ReqtVC9KoDLbZakGaqpxzg8B5ZvZb4KfAR4F3mtnXgG8657S6gEhtXUEUIAGcGobhneO5WFUBi5ntDywFZhN1v/YBq4nWZxNpSrWaC0ljkKYuM9sRODj+eXa83Y3o/8kC8CRgwPvM7APKeBOpjSAIdgZ+nijajyhgqlq1LTpfI+pSuxd4F3CTc67EZOwik9+oBWsT3WSV0jpsU5OZPQHMZ2TM7grgr8C3gL8BtzvntpjZAqIVBv4vDpK+3ZAKi7SIIAhmA1cDC4DPAf+PaCzSBWEYbqn2utUGSM8j6jJ7bS0yNEQmg1FdbONpQdI6bC3JzA5yzpVqsv8bcGu8/ZtzLnWhKefcQ8CpZrYR+DQwZoCUC0M25kpn8gwZ8CwcVsjrb9hhNcpuq+oeU5Dvu+f7rm4YHP3edYaQ9Vw7CIJO4DLgAOALYRh+MQiCbuDjRGMAz66u1tUHSAVgk4IjaSXJ8ULheLLY1ILUqi41s0NKBD6pyy6VsJQKJ64TkRFBEGSBXwDHAP8ThqGLd/0n8D7gE0EQ/Hc1Kf5QfZr/XcAMM5te5fkik049WpACtSC1kgXAJWbm+2N2G2Ok918NvG7ctRKZui4ATgIuJQqIAAjD8Gngv4m6vE+v9uLVBkjnEbU+vaPaG4tMNqMGaY+nBWlUmr9akFrIZcCxRP//jcnMnkvU3ZbKObfOOfebGtVNZEoJgsCIWmBvBN6YMkv214GtwCeDIKiqMafaxWp/TdSEdY6ZfdbMZlRzHZHJZHSaf/UtSKHGILWqNwP3Aaeb2TtLHWhmbwP+CGw/ERUTmUqCIDidaDD2XcCJYRhuM2VGGIariMb37UCVXdnjWaz2U2a2gWgq7zPMbCXRrJU+oXPuBdXeT6TeMj2zhx+Pa6JIjUFqSc65zWb2aqKB2N8ys3855/6SPMbMAuAconWhAqLFvKVF9W6tamiLjFMYht8BvlPGcR8nGqxdlWrnQQqAbxKteRIQTRS5T/zjoxQKmdSCObOHH1fbghSG4TaL1UrrcM7da2ZvAf4X+I2ZHeqcexzAzLqBXwEvAgaB9zrnftS42orIeFTbgvQh4IPx42uJmpJXoYkipYkFnZ3Q0QEDA9DfT6G3l8z0yrquw82bhxd5DKZPJ5hWziTz0kycc5eZ2ZeAM4ky255HNID7MqI/Ep8CXlPcujQebUFAd9voERG+xWo7PCurZrJaX36YJ53fp9Rf99531XePKZj+7/vu+b6rxd/tXIO+utUGSO8m+s6c6Zz7cg3rI9IwQRCQ6emh8PTTAIQbN0KFAVJh46aR6/V017R+MnHM7CPAMmBZ2tppzjlnZocALyWarfcQopUFbgde7Zx7bOJqKyL1UG2AtJCotegbtauKSOMFM2dCHCAVNm0mu8MOFZ0fbh4JkDKzFCA1sXOIGw7M7BHgDqKA6Q6ioOlh4E1EWWrHEzUkXAS8Q2usibSGagOk1cAs/UcgrSbTPWu4nzjctLHi8wubNg8/DmbOrFGtpAGuAg4CdiFaS203ooW5ATCz9UQB04PAXsDPgLc753ITXVERqY9qA6SrgHeZ2f7OuX/VskIijZSZOWv4cTLYKdfoFiQFSM3KOfcKADObS7To7EHA4vhnX6K1KJ/PyPCUU4HXm9m/gTsTP/9wzj09kXUXkdqoNkD6PNFfU98xs5c55zaNcbxIUwgSQU24qfKvdTiqBWlWiSOlGcTLivwp/gHAzDqAZzE6aDoQ6Im3BwKnxYeHjGM6FRFpnGr/4e4NfAY4F1hhZt8B/knpeZBwzi2t8n4iEyIzK9GCtLnyAKmweSRAUgtSa3LODQB/j3+GmdkiRgdNzwZKLTVStq5shj27R2dEejOAZnWklrd1tqeWZ9vTfw0E2RKZXtn01VaCjGcVFl9GV43Kw0qv4+HLVvOsqQqA52OoOLvN9xqCOr933s/M8xmD/7vh+y75vnu+7+oeRc8fzmbo9damfqoNkK5n5LsUEK1IPRb9JSWTXpAIkMJqutgSrU5qQZpanHMrgBVE60IBYGaaCEukSVUbsDyMJn6UFjSqBamKLja1IEmSc676NWtEpKGqCpCccwtrXA+RSWF0C1I1Y5ASLUgKkEREmlbLd3mZ2VHAGcARQCfwAPBD4HznXFkzf5vZhcBbxzjs2uRac2a2BCi1zMB7nXNjriUjE6umLUjqYhMRaVotHSCZ2auA3wB9wC+BtcAriQaXPxd4XZmXuhRY6dn3ZmB34Hee/ZcRzZdS7LYy7y0TaPxZbGpBEhFpBWMGSGa2u3PuwVre1MwywK7xbLR1ES8c+T2iGb+Pc87dFpefSbR+3Mlmdopz7uKxruWcu5TEwMvEPWYDnwQGgAs9p1/qnPPtk0kmOfu1WpBksuic0cbuz5w3qsy3vpUvY2jGdunL5mSnp2cS+TKS4ptXVu7LrMrUN0PLV573jKCtZmCt71q+LLZsnV9bxe9ppZ8l/u+G77vk++7B3NTSnr7BUc9XzWhvSBZbOTmQ/zazH5vZPuO9mZm1m9m7gfuBJeO93hhOBrYHLh4KjgDi2b/PiJ++d5z3eDMwHfhf59zqcV5LJoHRLUjVZLEl5kFSC5KISNMqp4vtVqJA4FQzuxG4GLjEObemnBuYWQAcB5wCvIYoZNxCNMtsPR0fb69O2bcU2AocZWbTnHP9Vd7jXfH2f0ocs9jMPkw0/ukx4Drn3KNV3k/qbPxjkBIzaasFSUSkaY0ZIDnnjjazE4EvA8cCxwAXmNn9RCtX/4NobbZ1RF1Ns4mm4V8EHEo0WVoXUYvjIHAB8MUJmH5/qMXrvuIdzrmcma0A9icaP3RPpRc3syOBA4D7nHPXlTj0Q0XP82b2feDDpdayiwd5L0nZtbiymkolxp/FphYkEZFWUNYgbefcb83scuAE4J3AK4gCkH2AN5Y4dagb9kGizLEfOedKzrZdQ0MTtPnmIRkqn13l9d8db7/n2b8C+CBwDfBoXJ+jga8A7wG6iVYD91lIFJDKBMokFphNjicq1+gxSAqQRESaVdlZbM65kChT63fxAo7PJ8oEew6wE7AdMI0oU2w1cC9wE/Dn5BigSpjZSmBBBaf83Dl32tiHASPBW8Xj8uLZcV9PicHZzrkbgBsSRVuBX5vZLUTdi280s68553xdjSuLzh+ymJHgT2osSAQ14ebNhIUCgW/QY5EwDItm0laAJCLSrKqdKHItUfr8b2pbnW0sJ0rRL9fjicdDLUS+YKK76LhKnAbMIBoAXtHgbOfcI2Z2FdHq38fgGYsVZ75dWFxuZtejlqW6CbJZgq4uwi1bIAwJt2wZ1e1WStjbC4VCdJ3OToL29GwikUp1zJrGjgfvWtaxlWYYTZ+b/l9kprPTe4+gLf277SsPM+l18pZnPddpS38NeK6T8/z561tbLQxrt0BEEKTnsfnu0OZ7L3y/pcNCenm+sve60s8S/N8N33fJp2vHgdTy/GBu1PP2mZ7Pvc4m9TxIyYkXq3Av0RiovYnGSg0zszaiMVI5ou6/Sg0Nzv5ulXUbGn/VVeX5UkfBrFlRgAQUNm4aNXC7lNFzIGmAtohIM6tsqePmcm28PSFl3zFELUA3V5rBZmaHE63YfZ9z7voq63Z4vK3p/FJSG8mAKNxc/kDtQnKAtrrXRESaWisHSJcQjYU6xcwOHSo0s07gS/HTbydPMLMeM9vXzHYqcd2hwdmlUvsxs+ellAVm9mngyLhuaVMQSIMlW38KG8sPkJLBlBaqFRFpbpO6i208nHMbzexdRIHS9WZ2MdEA8hOJsu8uIVp+JOkkovXTfkxKin08O/cbiAZn/3iMKiw1s/uAvxHNf9RDNKj9WUQDtk91zm2s6sVJXSWDm6pbkLoUIImINLNWbkEaWiLkWKKJIV9LlHY/CHwUOCXOzKvEqUTjhsqZOfts4EmiCSs/BLwFaCeaB+oA59w1Fd5bJsjo5UbKT/VXC5KISOto2RakIc65m4CXlXnshfjXVMM5922KuuVKHPuJco6TyafaBWtHj0HSIG2pnfYZ05n3jEVlHRtk0//u9WW3+TKSMjNn++/R6ckv6ZiWWuzLSiPryU7Ken41VZitNuhJV/MlqxVqmMWW8SzG5klu857gy27zvkee99T3GQSez8z7GeP/bszYJf34znndqeXF2WpDwvzoDL32NR1R08YEa+kWJJFqJAdYV7LcSJicJFItSCIiTU0BkkiRTPfIXzuVtCApzV9EpHVMWIAUD3AWmfRGLTdSwRgkLTMiItI66joGycwC4CXAW4myxzQxokx6QXdywdryEw1HtyApQBIRaWZ1CZDMbH+ioOhUYEeidc9qN/pNpI4yiQHWlSxYO7oFSV1sIiLNrGYBkpnNI1qd/q3As+Ni33h9kUlrdAtSBWn+ySw2tSBJDWU6pzF9t53LOzib9Vwkvdy7FlepLKZZs1PLw7b0jLiw3VPe5sl681ynP5/+d7anuKmy2Hy3znuOn+Z5j4bWg9yG7zPIpS8m4fuMS8l0pf9hGObSU9DaC/n0C+VHl2e2rIHBiU9jG1eAFK9p9kqioOil8fWGPs57gYuA3wJ/H899RCbSqBakCrrYCsl5kNSCJCLS1KoKkOKlO94KnALMZSQoehS4GLjIOXdHfKzGHUlTGdWCVMlSI2pBEhFpGWUHSGa2M3AaUWC0b1wcAGuIlu24yDm3tOY1FJlgma6RmL6wpZIxSGpBEhFpFWUFSGZ2NfAComkBAmALcBnwC+Aa51z6dJgiTSg5h1G4eUvZ56kFSUSkdZTbgvRioiy0W4Fzgcudc711q5VIAwUzZgw/DrdsIcznCXwDXxM0D5KISOuodAzSocB7gFlm9hvn3PraV0mksYJMhmDmzOGlQ8ItWwi6S89zGvb3w8BA9KStDTzrW4lUI+joJLvjbuUd68lWqzSLzbeuGpTIVuv0ZDF1pA9FDTtmpJb3etLSBjzlOU+2Wt6T0FXwzDpTwyQ2giD9YhlPcncuk358mycdzvPSmO55TwnTzwg95aVS0LOdnnsMpGfE+bLY8GSxhUXlwfItNGIxtnIDpJOIxh69HHg+cBxwQdz1djFwmVqUpJUEM7tGAqTNW2CMACnZehTMnEngXZFSRESaQVkBknPuMuAyM5tLNPnjW4GDiWbHfiWw1cwuIwqWrtaYJGl2mZmzKPAUEA2+zrJTyeOTs2hntA6biEjTq6iLzTm3FjgfON/M9gOWEAVMOxFNEvlGYL2ZDWW1XV/T2opMkOQg63IGahe3IImISHOrerFa59zdzrlPAs8AXgb8CugH5gDvBP5kZo8C/1mLiopMpExXYsHazWPPhTS6BUkBkohIsxv3UiPOuQJwNXC1mXUTTR75FuAoYGfg9PHeQ2SiVdyClEzx1xxIIiJNr6aL1TrnNgL/A/yPme1B1AV3GrCglvcRqbcg2YK0qYwWpGSKv1qQpNba2sn0bFfesYGnY8BTHmbSfw2EWU92GyXWVvNlq01L/zexNZeeudWbS8+s8mWx+dZc82WxhZ4sNs9lquJdi82TH5b1fGztngvlCunlYZh+oRmez8CXDRf4vkdAMJie4Ri0p2eaBQXPsGRfBl1xuS/Tss5qGiAlOeeWA2cCZ5rZ84lalUSaQjLICbeU04I0EkSpBUlEpPnVLUBKcs5dB1w3EfcSqYUgsdxIqBYkEZEpp+pB2iKtLJmqn8xQ8xndgqQASUSk2SlAEkkRzEy0IJURII1uQVIXm4hIs1OAJJIiM7PSFiQtVCsi0komZAySSLMZneZfTgtSYh4kDdKWWguyFKaV+b3yZR9lKstiI9vhvUXYlp7F5FtbzZettmUwPYtpq6fcl8U24ElXG/Qcn/csulao4WJsGc9yQ1lPeXs2vbzDk97W4Tnen4lXWXab93sE3u9GmB9Iv5Qvi63gSzMsKg/GXiy8HtSCJJJi1ESRm8oIkNSCJCLSUhQgiaQY1YK0pYwuNrUgiYi0FAVIIikCtSCJiExpCpBEUlQ8UWQyi01p/iIiTU8BkkiK5FxGZU0UmZwHSWn+IiJNT1lsIimCGTMgCCAMCXt7CXM5gjbPmlW5HGFvb3xiEJ0rUkuZrDdDbBuVrsXmW3Mt6//1ELalr8XW68ka862t5stW29CfnvW0oS+9fOtgPrXct0ZbwVc+AWuxZTw7fGuuzWhPz+Dq6fR9Punl3rXhPN+L6aW+b56MSPKe71I+fY0231ps25RnlMUmMmkEQTC6FalEN1tyGoBg5kwC338eIiLSNPQ/uYhHcixRqckiNf5IRKT1KEAS8UiOJSo1WaTGH4mItB4FSCIeQdfIemylUv0LRV1sIiLS/Fp2kLaZtQPvAxYDzwb2A9qBdznnvl/lNY8CzgCOADqBB4AfAuc751JHCZrZW4H3x/fPA3cAZzvnrqimDjJxMmVOFpmcAymjOZBERFpCK7cgdQHfBJYAOwJPjudiZvYqYClwDPB/wAVAB3AucLHnnLOBC4GdgO8BPwMOAC43sw+Mpz5Sf6NT/cttQVIXm4hIK2jZFiRgK/AyYJlz7gkz+zzgqrmQmXUTBTh54Djn3G1x+ZnAtcDJZnaKc+7ixDlHAR8DlgOHOefWxeVfB24HzjazK5xzK6t8fVJnowdp++dCSo5PUguS1EMYBN4FYrdRaZp/m2dRWt8itkC/d9HY2pT70vlXbUlfDNV3fF8uPf1/wDPtQL6Gef5ZT159R1v659DZVmk6f7rpnuv43uu2THp5qdaTaZ5pHsh4FqX1fSfLTPMPPQv81lvLtiA55wacc79zzj1Rg8udDGwPXDwUHMX36CPqcgN4b9E5p8fbs4aCo/iclUStT9OAt9WgblIno1qQNvvT/AvJQdoagyQi0hJaNkCqsePj7dUp+5YStVYdZWbJP/FKnfO7omNkEhrVglRiNu3RLUjqYhMRaQWt3MVWS/vE2/uKdzjncma2Atgf2B24x8y6gF2AzZ4WrPvj7d6+G5rZEqLxU8UWl11rGZdyJ4pUC5KISOtRgFSenni7wbN/qHx2lcenWQgcO3bVpF6CUS1I5c2DpBYkEZHWMKkDJDNbCSyo4JSfO+dOq1N1ShkaQVbpCL9Sx68EbkgpX8xIACZ1lOlOTBS5aaP3uMJGtSCJiLSaSR0gEWWA9VVw/ON1qsdQi48vMOkuOm6s48dqYcI5dyHRFAGjmNn1qGVpQmRmdQ8/LjkGKdmC1NPtPU6kakEGfNlmRcIKs9h82Wq5En++eRKiyHmywHyLxg7kfYvYpmef+bLVHl67NbV81cb0Xx+9A5Vlt1XDl602vSM9y2x+d3pm2G5z0xeNnem5ju89HSykZ4L5PrO8b3Vb/N+NNs93KfRFGp4stqC43PfdrbNJHSA5517Q6DrE7gUOJRozdHtyh5m1AYuAHPAggHNui5k9BuxiZjuljEPaK95uM6ZJJo8gEeyEG0q1II3EuZluNe6JiLQCZbGV59p4e0LKvmOAGcDNzrn+Ms95adExMgklxxOVakEa1cXWrTFIIiKtQAFSgpn1mNm+ZrZT0a5LgNXAKWZ2aOL4TuBL8dNvF53znXj7WTObkzhnIdHSI/3Aj2pYfamxZGtQspWoWLhxpHUp060uNhGRVjCpu9jGy8w+BewbP10cb99mZkfHj/9ctC7bSURBy49JpNg75zaa2buIAqXrzexiYC1wItEUAJcAv0ze2zl3s5l9A/go8A8zu4RoaZI3AHOBD2oW7ckt2Rrk62ILw3BU65Ky2EREWkOrtyCdALw1/jkoLjsqUXa057xtOOcuJRocvRR4LfBBYJAoADrFObfNsDXn3MeIAq0ngXcDbwH+BbzSOfetal6QTJygqwsy0T+RsLeXcHBw24P6+mAgXv6gowM6PVPwi4hIU2npFiTn3HEVHn8hKZljif03Ea3vVsk1f0zUIiVNJggCgu5ZhOuj7rXCpk1k584ddUxx61HQoDWDpNUFhCXWRht9aGVZbL6MJF/mWal9ngQqb/mgJx3Od33f2mq+bLUVT6XPX9a7uT+1PDeQXtFC6H8vMp5/820dniy2mWWuqReb351+vO898r2nFX82JT5/739znsw3X3abL4st3KZca7GJTDrJcUjJsUZDComyQOOPRERahgIkkRJGZbKlBEhhIoMtoww2EZGWoQBJpIRkq1AhZaC25kASEWlNCpBESkjOjB2mzIU0eg4kdbGJiLQKBUgiJYzuYtt2LqTRcyCpi01EpFW0dBabyHgFowZpp7QgJbPY1IIk9RKwbRZahetT+dZP8yUrlUjc8u4reNbfDj3lec+FCr612zxrpfnWVvNlq619aktqeV/KOEOAfG4gtRwg61kjr9Pz/8Hc1FLonTM9tdz3mn3vke899X0G3s8s9GeOeT9/T3n6pwPZcjMuG5QdrBYkkRKSXWyFDdu2IBXWrx9+HGiSSBGRlqEASaSEzJzhVWIorF27zf7CunUjx871/W0oIiLNRgGSSAmZeSNBT35NSoC0Zs3w4+y8eRNSJxERqT8FSCIlZOaOBD2FtWu22V9IBE3JYEpERJqbAiSREpKtQoUxWpAyakESEWkZymITKSHZKpQMhobk1ypAkokQlJ215ks+85b7MslKpLH59lWa3eS7jjcbqsLsNt/aar5stY1PLE8tH9yybYLGkPYu3wSxe6TXqcJsNd9rrtV76v/MSn3+lV0r9GSh+e4wWVa0VAuSSAnJgdeFdesICyP/iYWDg8ML2RIEZGbPnuDaiYhIvShAEikhaG8fmSG7UBiV1j8qg232bIJsdoJrJyIi9aIASWQMo1qREt1sGn8kItK6FCCJjGH0QO1kgKQMNhGRVqVB2iJjGD1QeyQoyqsFSepvT4BVq1bxi4suGteF/IO0fcf7B+lWvNSE54Sc54R+36DrwfTy3fsGU8t3zuRSywd3Sj8+N88zmDg/M7UcIMimn9PW8URqeXtmdWp556r0X8e5je2p5Q+3p7dvPNWWXt6WSa9n1jOA2nM44F/5I/AMr/YfX55Vq1YNPdyzzFNqQgGSyBgy228//Dg/8g+VwtNPDz/WJJFSJzMB+vv7eeSRRxpdl0nLF77M9P0GTk8kg+m+E9KDlNL6Kiv3LffmKe/1HO4rbxH+SLUOFCCJjKFt112HH+ceeij1cXa33Sa0TjJlrAAWAZuBBxpcF5FG2ZMoOFoxkTdVgCQyhuyCBcOP88kAaeXI47bEMSK14px7dqPrIDJVaZC2yBjaFo4EP8lWo2SwlFWAJCLSUtSCJDKGtkT3Wf6hh6OZh8OQXGJMSNsCdbGJiLQSBUgiY8jMmUPQ00O4YQNhXx+FVasIc3kYiEZPZubOJTNrVoNrKSIitaQASaQMbQt2Y/Af/wQgt3Il5EfSjdW9JtLczOwK4OXAx51z5zS6PjI5aAySSBnaFi0afpx7cAW55ctT94lIU1ocb5c1sA4yyagFSaQMbXvtNfw4d//9URdbrH2vCZ27TERqyMzmAbvET5c1sCoyyShAEilD2x57DD8evP8ByI/M0Nu2pwIkkSY2NJXCI865NSWPlClFAZJIGZKtRLnlD0CiBalNLUgizeygeHtHQ2shk44CJJEytC1aBJkMFArkH3o4saONtoULG1YvERm3xfF2WfEOM5sF/AR4NfAw8GrnnAKpKUKDtEXKEHR2kn3GrtuUt+22G0F7Nes0icgksTjejgp8zGwf4Fai4GgpcKiCo6lFAZJImTLzttu2bDstUivSrMxsGrBv/HRZovxVRMHRvsB3gRc6557e5gLS0tTFJlKmTE/3tmXdPQ2oiYjUyLOIfg+ud86tNLMA+DxwJpADTnfOfbeB9ZMGUoAkUqZM97YBUpBSJiJNY2iA9jIz6wF+TjRh5Crgtc65PzesZtJwCpBEypQWIKW1KolI01gcb/uBvwF7AX8nGoz9iO8kmRoUIImUKejZtjstLWgSkaaxON6+JN5eC7zCOdfbmOrIZNKyAZKZtQPvI/oH8GxgP6AdeJdz7vsVXmsv4DVE/4j2AnYA1gG3AN90zl2Xcs4S4EclLvte59x3KqmHNJa62ERazoHx9ufAqcAhwG7AvQ2rkUwaLRsgAV3AN+PHTwFPAs+o8lpfBN4A3A1cBawF9gFOBE40sw85587znHsZ6dPX31ZlXaRBMrNmbVumAEmkKZnZ7kAPMAi8nSir+43Ab83scOfc+pRzdgKWA5c6596UKH8OcD3wv8650+pfe5kIrRwgbQVeBixzzj1hZp8HXJXXuhr4WvEcGGZ2LPAH4Otm9mvn3BMp517qnLuwyvvKJBKkZrEpQBJpUkMDtP/tnBsws3cAexO1Iv3KzF7qnMsnT4h/l3wH+JCZfd45d5+ZLQB+S/RH79sn8gVIfbXsPEjOuQHn3O88QUul17owbYIw59wNRH81dABHjfc+Mrmpi02kpSyOt3cCxOOOXk3U4/Ai4BzPeV8D+oDPmFk3cAWwETjJOTdQx/rKBGvlFqSJMhhvc579i83sw0An8BhwnXPu0bEuGo9hWpJ2vYprKDWRNueRsthEmtbieHvnUIFz7lEzew1wHVEr0T+dcz9InuSce8rMvg18CNgT2Ak4Qgvdtp6WbUGaCHHT6guIuvOWeg77EHAu8BWiNX1Wmtl3zKxzjMsvBI5N+dHMhA2iLjaRlrI43t6ZLHTO3Qy8N37632Z2dMq55xD9/nwO0ZQAD9SrktI4CpCqFE9R/3NgGvB559y6okNWAB8kGszdBewMvB5YCbwH+OEYt1gJ3JDys6EmL0AqltrFlpL6LyKTm5nNJspWA/hH8X7n3A+B84iGT/xv/Mdw0meJfn9miTKapQUFYRg2ug5eZrYSKP5ilvJzXwZBYpB2xWn+KdfKAhcBrwN+CbzROVfWG2lmzyD6i2UOsNg5d+cYpxSffz1w7IIFC1iyZEklp8o4hX19PL7HXqPKdl75oBarbZyg0RWQqSceMnEu8BGi3yl/dM69rqGVkrqY7C1Iy4nmoyj35/F6VygOjn5GFBz9Cjit3OAIIJ6d9ar46TG1r6HUS9DZCZnEP5nOaQqORKYQM3slUffaV5xz3wT+C3itmR1U8kRpSpN6kLZz7gWNrkOSmbUBvyAKjn4BvKU4DbRMQ6tCd9WqbjIxZrz+dWy9+JfR49ee3ODaiMhEMbODiXoOfkPUxQZRgPRRwIgy4KSFTPYWpEnDzDqAS4iCo58Ab64yOAI4PN4+WIu6ycSZffbX2f73VzP/mt8z+2tfaXR1RGQCmNmuwOXAXUR/GIcA8djTbwGvMrNDGlhFqYNJ3YI00eLVnHcCNiTnT4oHZP8v0cSTPwDe7ZwrjHGt5znnbiwqC4BPAUcCq4kmoJQmEgQBHc/av9HVEJEJFE/Nsotn32eAz0xsjWQitHSAZGafAvaNny6Ot29LpG3+uWjA9klE66f9mNFzEH2HKDhaTTSX0efMrPh21zvnrk88X2pm9xGtEP0YUXr+c4FnEU0LcKpzbmO1r01ERETqp6UDJOAEormDko5i9KzX5WS0LYq32wGfK3Hc9YnHZxPNkXE8MBcoAA8DFwDfcM6pe01ERGSSmtRp/rItpfmLDFOav4jUjQZpi4iIiBRRgCQiIiJSRAGSiIiISBEFSCIiIiJFFCCJiIiIFGn1NP9WtCfAk08+yYUXXtjgqog0zkMPPXQ9sMw59+EGV0VEWpACpOYzE6C/v5+HHnqo0XURaaTiOc5ERGpGAVLzWUE0ceVm4AHPMYuJZu7eACybkFpNLYvR+1tviynvPS61T0SkapoosgUNTSYJ3OCcO66xtWk9en/rT++xiDSaBmmLiIiIFFGAJCIiIlJEAZKIiIhIEQVIIiIiIkWUxdaaLgSuB1Y2tBat60L0/tbbheg9FpEGUhabiIiISBF1sYmIiIgUUYAkIiIiUkQBkoiIiEgRDdJuImbWDryPaBmGZwP7Ae3Au5xz3x/j3LcC74/PyQN3AGc7567wHD8d+BRwCrAA2Eg0aNY55+6pwctpOma2K/AF4ARgHvAEcClgzrl1DazapGNmJxPNhL0YOAiYBfzcOXdaiXOOAs4AjgA6iZbS+SFwvnMu7zmnou+1iEi51ILUXLqAbwJLgB2BJ8s5yczOJsoK2gn4HvAz4ADgcjP7QMrx04A/AJ8jCoz+C/gjcBJwm5kdPr6X0XzMbA/gduBtwK3AucCDwIeAv5jZvAZWbzI6A/gAUYD02FgHm9mrgKXAMcD/ARcAHUTv88Wecyr6XouIVEIBUnPZCrwM2Nk5tyPRX9clxX+VfwxYDhzonPuIc+79wCHAWuBsM1tYdNpHgecClwCHO+f+n3PuTcDJwAzgh2Y21b47/w3MB/7DOfdq59ynnHPHE/0C3wc4q6G1m3w+AuwNdAPvLXWgmXUTBTh54Djn3Ducc58gCq7+ApxsZqcUnVPN91pEpGxT7ZdcU3PODTjnfuece6KC006Pt2clu4GccyuJ/kqfRtQqAoCZBYlzPumcKyTOuQy4kag749iqXkQTMrPdgRcTzclzQdFuB2wB3mxmXRNctUnLOXedc+5+51w584icDGwPXOycuy1xjT6ilijYNsiq6HstIlIpBUit7/h4e3XKvt8VHQOwB7AbcJ9zbkWZ57S6odd6TTJgBHDObQJuImpZO2KiK9YiSn1HlxK1nB4Vd/2Wc85U/I6KSI0pQGphcYvGLsBmT6vT/fF270TZPvH2Ps9l085pdXpP6sv7/jrncsAKooSS3aHq77WISEUUILW2nni7wbN/qHz2OM9pdXpP6qvS91efh4jUndL8J5iZrSRKmy9XydToGqlkvZmginNand6T+qr2/dXnISJVU4A08ZYDfRUc//g47jX0l3SPZ3/aX+JjndOdck6r03tSX5W+v9V8r0VEKqIAaYI5514wgffaYmaPAbuY2U4p4zX2irfJsR/3xlvf+I20c1qd3pP6uhc4lOj9vT25w8zagEVAjmjeqWq/1yIiFdEYpNZ3bbw9IWXfS4uOgaiF62FgbzNbVOY5re66ePvi4vmfzGwW0ZxRvcAtE12xFlHqO3oMUYbgzc65/jLPmYrfURGpMQVIre878fazZjZnqDCeRO/9QD/wo6HyeN6aoXP+MxkQxLMdPw+4G7ihvtWePJxzy4FrgIVE71mSEc1w/hPn3JYJrlqruARYDZxiZocOFZpZJ/Cl+Om3i86p6HstIlKpIAw1jrGZmNmngH3jp4uJ1rm6mZHU5j8Xr8tmZucQzY79KNEvow7gDUTriX3QOfetouOnEf31fRRwG/AnormRXgcMAMc75/5a69c2mcVLjdxMNJv2ZcA9wOHA84m6co5yzq1pXA0nFzN7NfDq+OmOwEuIushujMtWO+c+XnT8JUTj8y4mmg37RKIpAC4BXl886WSl32sRkUqoBan5nAC8Nf45KC47KlF2dPEJzrmPEa3f9iTwbuAtwL+AV6b9Eom7Ml5ItDDrbKJlI15EtDDrYVMtOILhVqRDidb+OpxomYs9gPOAIxUcbWMxI9/Jl8RluyfKTk4e7Jy7lGh29qXAa4EPAoNEAdApaTNyV/q9FhGphFqQRERERIqoBUlERESkiAIkERERkSIKkERERESKKEASERERKaIASURERKSIAiQRERGRIgqQRERERIooQBIREREpogBJREREpEhboysgMlmY2RXAy4FPOOfObnR9RESkcdSCJDLiwHj7j4bWQkREGk4BkghgZl3AFuBe4M4GV0dERBpMi9WKiIiIFFELkoiIiEgRDdIWAczsUuBVwKedc1+Ny+4AFgNnOefOKDr+ucCfgSeBBc65gQmtsIiI1JVakEQiQwO0k+OPHou3uxQf7Jy7CbgD2BF4cX2rJiIiE00Bkkx5ZtYNLIyfJgOkx+PtNgFS7OZ4e3QdqiUiIg2kAEkkaj0KgNXOuccT5d4WpNgj8XZRvSomIiKNoQBJBA6Kt8Xp/WO1IE2LtxrLJyLSYhQgifgDpKEWpJ54nqRiR8bbf9elViIi0jAKkETGbkGColYkM1sAvDB+elmd6iUiIg2iAEmmNDPLAM+KnxYvMfJY4nFxN9u3iLrWljrnbq1T9UREpEE0dkKmuj2BGcAgcHfRvtXAANBBIkAys/cArwD6gPcXX9DMfgfMBd4JnAUcB/QC/+2cs5q/AhERqTm1IMlUN9S99u/iyR6dcyHwRPx0FwAzOxI4Ly57t3PurpRrHgh0AdcQBV2fAO4HPm9mx9e2+iIiUg9qQZKpzjf+aMhjwAJgZzN7JnApUYvSJ51zPy0+2MzmAjsTtUod4px7MC6/lGjW7UOBa2tYfxERqQO1IMlUN1aANDRQ+0iiwGY+YM65r3uOH5qR+6yh4CjWH2+1JImISBNQC5JMdeW0IAEcFm+/6Jz7fInrDQVIlxaV7xtv762kciIi0hgKkGTKMrM5wDPip8UZbEOGAqQQ+IRz7pwxLnsAsM4590BR+eJ46wvERERkElGAJFOWc24d0RIjpY75OuDrTktzIOlB0EFsu5SJiIhMUhqDJFIjZhYA+wPLUnYfhFqPRESahgIkkdrZgyi9f1myMA6cDkABkohI01CAJFI7B8TbZUXlewAz8Y9zEhGRSSYIw7DRdRARERGZVNSCJCIiIlJEAZKIiIhIEQVIIiIiIkUUIImIiIgUUYAkIiIiUkQBkoiIiEgRBUgiIiIiRRQgiYiIiBT5/xYQNP4O5wj/AAAAAElFTkSuQmCC\n", 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" ] @@ -397,12 +438,12 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 15, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] From dc7a07bba72d58df84c95d38844de90fa6b55062 Mon Sep 17 00:00:00 2001 From: Stefan Date: Thu, 21 Jan 2021 17:02:21 +0100 Subject: [PATCH 115/121] [eli] update tests to new singlet/triplet version --- python/triqs_tprf/utilities.py | 22 +++-- .../eliashberg_benchmark_one_band.tar.gz | Bin 22006 -> 21999 bytes .../eliashberg_benchmark_two_band.tar.gz | Bin 79013 -> 80625 bytes test/python/eliashberg/gamma_creation.py | 89 ++++++++++-------- .../preprocess_gamma_for_fft_benchmark.tar.gz | Bin 176260 -> 144374 bytes test/python/eliashberg/preprocessing_gamma.py | 12 +-- 6 files changed, 69 insertions(+), 54 deletions(-) diff --git a/python/triqs_tprf/utilities.py b/python/triqs_tprf/utilities.py index 21aacfb71..adde4f977 100644 --- a/python/triqs_tprf/utilities.py +++ b/python/triqs_tprf/utilities.py @@ -34,11 +34,12 @@ from triqs.gf.tools import fit_legendre from triqs.gf.gf_fnt import enforce_discontinuity -from triqs_tprf.lattice import lattice_dyson_g0_wk, solve_rpa_PH, gamma_PP_singlet +from triqs_tprf.lattice import lattice_dyson_g0_wk, solve_rpa_PH, construct_phi_wk from triqs_tprf.tight_binding import create_model_for_tests from triqs_tprf.ParameterCollection import ParameterCollection from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors +from triqs_tprf.eliashberg import construct_gamma_singlet_rpa # ---------------------------------------------------------------------- def show_version_info(info): @@ -182,22 +183,25 @@ def create_eliashberg_ingredients(p): chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw) - U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors( + U_d, U_m = kanamori_charge_and_spin_quartic_interaction_tensors( p.norb, p.U, p.Up, p.J, p.Jp ) - chi_s = solve_rpa_PH(chi0_wk, U_s) - chi_c = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation + chi_d = solve_rpa_PH(chi0_wk, U_d) + chi_m = solve_rpa_PH(chi0_wk, -U_m) # Minus for correct charge rpa equation - gamma = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) + phi_d_wk = construct_phi_wk(chi_d, U_d) + phi_m_wk = construct_phi_wk(chi_m, U_m) + + gamma = construct_gamma_singlet_rpa(U_d, U_m, phi_d_wk, phi_m_wk) eliashberg_ingredients = ParameterCollection( g0_wk = g0_wk, gamma = gamma, - U_s = U_s, - U_c = U_c, - chi_s = chi_s, - chi_c = chi_c, + U_m = U_m, + U_d = U_d, + chi_m = chi_m, + chi_d = chi_d, ) return eliashberg_ingredients diff --git a/test/python/eliashberg/eliashberg_benchmark_one_band.tar.gz b/test/python/eliashberg/eliashberg_benchmark_one_band.tar.gz index 011d2f6d0a8d9d8f77b35afb1cdff2e45e9f94f4..22d940a674241869b86294bb879cc95064ae1aca 100644 GIT binary patch literal 21999 zcmb5#Q*bgQYj3L1}&Ma8ZFtPZ!DN;5iN-%Ycog!noqd01cZu+1fS@9{-U}FAE>AgCM_7) zqAxS3YJh=gXv6Km1&Ue`bj&XRj<0*~2EHqF|z+U|?Zk zqZ}P!V`3g-V^fU`?Gq#agIw>QoklUYgX4hE!OhUYTh9b1)g;L;2u@+0hdUg$qq+wu zBdY8J-1J4{|NdP3*Q2sTx{-6%H~f9{UG#p#{ZHU|UkB*;wKUYN)yYrkJF&B_Xu==2 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dGjnFn%$YeeXXebDne#t8{{oy9Hl_fm0sskDt-1gJ diff --git a/test/python/eliashberg/gamma_creation.py b/test/python/eliashberg/gamma_creation.py index 04fa7b88f..8e2377c01 100644 --- a/test/python/eliashberg/gamma_creation.py +++ b/test/python/eliashberg/gamma_creation.py @@ -5,53 +5,65 @@ from triqs_tprf.utilities import create_eliashberg_ingredients from triqs.gf import MeshProduct, MeshImFreq, MeshBrillouinZone -from triqs_tprf.lattice import gamma_PP_spin_charge, gamma_PP_singlet, gamma_PP_triplet +# from triqs_tprf.lattice import gamma_PP_spin_charge, gamma_PP_singlet, gamma_PP_triplet +from triqs_tprf.lattice import construct_phi_wk +from triqs_tprf.eliashberg import ( + construct_gamma_singlet_rpa, + construct_gamma_triplet_rpa, +) -def test_gamma_PP_spin_charge_mesh_types(chi_c, chi_s, U_c, U_s): - gamma = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, 0.0, 0.0) - assert type(gamma.mesh) == MeshProduct - assert type(gamma.mesh[0]) == MeshImFreq - assert type(gamma.mesh[1]) == MeshBrillouinZone +def test_phi_wk_mesh_type(chi_d, U_d): + phi_d_wk = construct_phi_wk(chi_d, U_d) + assert type(phi_d_wk.mesh) == MeshProduct + assert type(phi_d_wk.mesh[0]) == MeshImFreq + assert type(phi_d_wk.mesh[1]) == MeshBrillouinZone -def test_gamma_PP_spin_charge_zero_input(chi_c, chi_s, U_c, U_s): - gamma = gamma_PP_spin_charge( - 0.0 * chi_c, 0.0 * chi_s, 0.0 * U_c, 0.0 * U_s, 0.0, 0.0 - ) - np.testing.assert_equal(gamma.data, 0) +def test_phi_wk_one_zero(chi_d, U_d): + phi_d_wk = construct_phi_wk(chi_d, 0 * U_d) + np.testing.assert_equal(phi_d_wk.data, 0.0) + + phi_d_wk = construct_phi_wk(0 * chi_d, U_d) + np.testing.assert_equal(phi_d_wk.data, 0.0) -def test_gamma_PP_spin_charge_only_constant(chi_c, chi_s, U_c, U_s): - gamma = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, 0.0, 0.0) - np.testing.assert_equal(gamma.data[0, 0], 0.5 * (U_c + U_s)) +def test_gamma_singlet_mesh_type(chi_d, chi_m, U_d, U_m): + phi_d_wk = construct_phi_wk(chi_d, U_d) + phi_m_wk = construct_phi_wk(chi_m, U_m) + gamma_singlet = construct_gamma_singlet_rpa(U_d, U_m, phi_d_wk, phi_m_wk) -def test_gamma_PP_singlet_mesh_type(chi_c, chi_s, U_c, U_s): - gamma_singlet = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) assert type(gamma_singlet.mesh) == MeshProduct assert type(gamma_singlet.mesh[0]) == MeshImFreq assert type(gamma_singlet.mesh[1]) == MeshBrillouinZone +def test_gamma_singlet_constant_only(chi_d, chi_m, U_d, U_m): + phi_d_wk = construct_phi_wk(chi_d, U_d) + phi_m_wk = construct_phi_wk(chi_m, U_m) + + gamma_singlet = construct_gamma_singlet_rpa(U_d, U_m, 0*phi_d_wk, 0*phi_m_wk) + benchmark_value = 0.5 * U_d + 1.5 * U_m + np.testing.assert_equal(gamma_singlet.data[0, 0], benchmark_value) -def test_gamma_PP_singlet_value(chi_c, chi_s, U_c, U_s): - gamma = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, -1, 3) - gamma_singlet = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) - np.testing.assert_equal(gamma.data, gamma_singlet.data) +def test_gamma_triplet_mesh_type(chi_d, chi_m, U_d, U_m): + phi_d_wk = construct_phi_wk(chi_d, U_d) + phi_m_wk = construct_phi_wk(chi_m, U_m) + + gamma_triplet = construct_gamma_triplet_rpa(U_d, U_m, phi_d_wk, phi_m_wk) -def test_gamma_PP_triplet_mesh_type(chi_c, chi_s, U_c, U_s): - gamma_triplet = gamma_PP_triplet(chi_c, chi_s, U_c, U_s) assert type(gamma_triplet.mesh) == MeshProduct assert type(gamma_triplet.mesh[0]) == MeshImFreq assert type(gamma_triplet.mesh[1]) == MeshBrillouinZone +def test_gamma_triplet_constant_only(chi_d, chi_m, U_d, U_m): + phi_d_wk = construct_phi_wk(chi_d, U_d) + phi_m_wk = construct_phi_wk(chi_m, U_m) -def test_gamma_PP_triplet_value(chi_c, chi_s, U_c, U_s): - gamma = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, -1, -1) - gamma_triplet = gamma_PP_triplet(chi_c, chi_s, U_c, U_s) - np.testing.assert_equal(gamma.data, gamma_triplet.data) - + gamma_triplet = construct_gamma_triplet_rpa(U_d, U_m, 0*phi_d_wk, 0*phi_m_wk) + benchmark_value = -0.5 * U_d + 0.5 * U_m + np.testing.assert_equal(gamma_triplet.data[0, 0], benchmark_value) if __name__ == "__main__": p = ParameterCollection( @@ -72,15 +84,14 @@ def test_gamma_PP_triplet_value(chi_c, chi_s, U_c, U_s): ) eliashberg_ingredients = create_eliashberg_ingredients(p) - chi_c = eliashberg_ingredients.chi_c - chi_s = eliashberg_ingredients.chi_s - U_c = eliashberg_ingredients.U_c - U_s = eliashberg_ingredients.U_s - - test_gamma_PP_spin_charge_mesh_types(chi_c, chi_s, U_c, U_s) - test_gamma_PP_spin_charge_zero_input(chi_c, chi_s, U_c, U_s) - test_gamma_PP_spin_charge_only_constant(chi_c, chi_s, U_c, U_s) - test_gamma_PP_singlet_mesh_type(chi_c, chi_s, U_c, U_s) - test_gamma_PP_singlet_value(chi_c, chi_s, U_c, U_s) - test_gamma_PP_triplet_mesh_type(chi_c, chi_s, U_c, U_s) - test_gamma_PP_triplet_value(chi_c, chi_s, U_c, U_s) + chi_d = eliashberg_ingredients.chi_d + chi_m = eliashberg_ingredients.chi_m + U_d = eliashberg_ingredients.U_d + U_m = eliashberg_ingredients.U_m + + test_phi_wk_mesh_type(chi_d, U_d) + test_phi_wk_one_zero(chi_d, U_d) + test_gamma_singlet_mesh_type(chi_d, chi_m, U_d, U_m) + test_gamma_singlet_constant_only(chi_d, chi_m, U_d, U_m) + test_gamma_triplet_mesh_type(chi_d, chi_m, U_d, U_m) + test_gamma_triplet_constant_only(chi_d, chi_m, U_d, U_m) diff --git a/test/python/eliashberg/preprocess_gamma_for_fft_benchmark.tar.gz b/test/python/eliashberg/preprocess_gamma_for_fft_benchmark.tar.gz index b23be174e654acb2f6dff7a7988492b9b88da7c2..d6f1757ce89569c190767fb25ae885f3cf415bdd 100644 GIT binary patch literal 144374 zcma&N1yCJ9u&5nEkf6araCZ&vgb>_IJo-(&YySRefQq_ z>-|-KRaZ^zZq4@W>~#0nJ-Z}Ph=|_`J{x?5+B=%sJK7nWIyvc^8v+1^`et^H`etU% z`bMU<#uflWM{9jsQ#WR3L&pziJ_tI>Qje}5_~|>!G`=`9X^4Ch!wzR|(M>tpUHwh2 z`zsvt%g-@Y^`ThZ@_J(l5s`lvY00VRk;oe6{F zh0GwV9C?>|C%4u@zIlOiAW%=miv~SR^};pRRt24gL-~YXuRs}(fP|^-K_XgHRUxUQ4shptfwAQBwn{g9LX@PJ{iUZv1`_ER#?5H4B2Vn z4OJJ_TH}hnrIrn0Wr=^~KX)tcXSHL{BN+rdYVx1*YphKB5p_f*ekzxiyUJ6kMfNUu521QIW9hmS%pO8?CLfe_nmSr0XbRljPeHs2q} 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z|6@8@e8l?Ur*#D3{PpjxABHX$tsnlAA-sP0X&;};vahcnT6+*&@PuQB@J9)P!!O6K z)-JYR!n)7vD}OZ(9KQecYvq4nU8-`$m!%g7w2s`$%VfHC`Y2|6Bg^`$oqE>3>_v>L(SEeiA_h5kwF{gnyuZ`s>fB5f}Td=hSEzj;#4>I_SUcxjj;Y zn|nU@hr?hwZls>$P(HW6wW! zJ@UuimqBzAy)WbIybAwY^6KB$ACaQ|7||awf6M;({QM57q33r@`q%9I@b_iN5BvSC jLpp0n&iv)ymmT)|b4Bt%1QA5|TjBo!NV;ht0C)ue0*|h3 diff --git a/test/python/eliashberg/preprocessing_gamma.py b/test/python/eliashberg/preprocessing_gamma.py index 76f66bdfc..a498a82af 100644 --- a/test/python/eliashberg/preprocessing_gamma.py +++ b/test/python/eliashberg/preprocessing_gamma.py @@ -20,10 +20,10 @@ def test_split_into_dynamic_wk_and_constant_k_mesh_types(gamma): assert type(gamma_const.mesh) == MeshBrillouinZone -def test_split_into_dynamic_wk_and_constant_k_mesh_values(gamma, U_c, U_s): +def test_split_into_dynamic_wk_and_constant_k_mesh_values(gamma, U_d, U_m): gamma_dyn, gamma_const = split_into_dynamic_wk_and_constant_k(gamma) - analytical_constant_expression = 0.5*(U_s + U_c) + analytical_constant_expression = 0.5*U_d + 1.5*U_m np.testing.assert_allclose(gamma_const.data[0], analytical_constant_expression) gamma_without_constant_part = gamma.data - analytical_constant_expression @@ -91,13 +91,13 @@ def test_preprocess_gamma_for_fft_benchmark(gamma, p): ) eliashberg_ingredients = create_eliashberg_ingredients(p) gamma = eliashberg_ingredients.gamma - U_c = eliashberg_ingredients.U_c - U_s = eliashberg_ingredients.U_s + U_d = eliashberg_ingredients.U_d + U_m = eliashberg_ingredients.U_m test_split_into_dynamic_wk_and_constant_k_mesh_types(gamma) - test_split_into_dynamic_wk_and_constant_k_mesh_values(gamma, U_c, U_s) + test_split_into_dynamic_wk_and_constant_k_mesh_values(gamma, U_d, U_m) test_dynamic_and_constant_to_tr_mesh_types(gamma) test_preprocess_gamma_for_fft_types(gamma) - #save_new_preprocess_gamma_for_fft_benchmark("preprocess_gamma_for_fft_benchmark.tar.gz", p) + #save_new_preprocess_gamma_for_fft_benchmark(p.filename, p) test_preprocess_gamma_for_fft_benchmark(gamma, p) From 7ddac510a08d9dd77b22d439087ae9ffbbc58375 Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 22 Jan 2021 10:51:01 +0100 Subject: [PATCH 116/121] [eli] remove old singlet/triplet vertex functions --- c++/triqs_tprf/lattice/eliashberg.cpp | 56 ---------------- c++/triqs_tprf/lattice/eliashberg.hpp | 66 +------------------ doc/reference/cpp_reference.rst | 2 - python/triqs_tprf/lattice_desc.py | 95 +++++++-------------------- 4 files changed, 23 insertions(+), 196 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index 1caa24009..58e99bab3 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -214,62 +214,6 @@ g_wk_t eliashberg_product_fft_constant(chi_r_vt Gamma_pp_const_r, return delta_wk_out; } -chi_wk_t gamma_PP_spin_charge(chi_wk_vt chi_c, chi_wk_vt chi_s, \ - array_view, 4> U_c, array_view, 4> U_s, \ - double charge_factor, double spin_factor) { - - using scalar_t = chi_wk_t::scalar_t; - - size_t nb = chi_c.target_shape()[0]; - - auto Gamma_pp_wk = make_gf(chi_c); - Gamma_pp_wk *= 0; - - // PH grouping of the vertex, from cc+cc+, permuting the last two indices. - auto U_c_matrix = make_matrix_view(group_indices_view(U_c, {0, 1}, {3, 2})); - auto U_s_matrix = make_matrix_view(group_indices_view(U_s, {0, 1}, {3, 2})); - - auto meshes_mpi = mpi_view(Gamma_pp_wk.mesh()); - -#pragma omp parallel for - for (unsigned int idx = 0; idx < meshes_mpi.size(); idx++){ - auto &[w, k] = meshes_mpi(idx); - - array Gamma_pp_arr{nb, nb, nb, nb, memory_layout_t<4>{0, 1, 2, 3}}; - array chi_c_arr{chi_c[w, k], memory_layout_t<4>{0, 1, 2, 3}}; - array chi_s_arr{chi_s[w, k], memory_layout_t<4>{0, 1, 2, 3}}; - - // PH grouping of the vertex, from cc+cc+, permuting the last two indices. - auto Gamma_pp_matrix = make_matrix_view(group_indices_view(Gamma_pp_arr, {0, 1}, {3, 2})); - // PH grouping of the susceptibilites, from c+cc+c, permuting the last two indices. - auto chi_c_matrix = make_matrix_view(group_indices_view(chi_c_arr, {0, 1}, {3, 2})); - auto chi_s_matrix = make_matrix_view(group_indices_view(chi_s_arr, {0, 1}, {3, 2})); - - Gamma_pp_matrix = charge_factor * U_c_matrix * chi_c_matrix * U_c_matrix \ - + spin_factor * U_s_matrix * chi_s_matrix * U_s_matrix \ - + 0.5 * (U_s_matrix + U_c_matrix); - - Gamma_pp_wk[w, k] = Gamma_pp_arr; - } - Gamma_pp_wk = mpi::all_reduce(Gamma_pp_wk); - - return Gamma_pp_wk; -} - -chi_wk_t gamma_PP_singlet(chi_wk_vt chi_c, chi_wk_vt chi_s, \ - array_view, 4> U_c, array_view, 4> U_s) { - - auto Gamma_pp_wk = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, -1, 3); - return Gamma_pp_wk; -} - -chi_wk_t gamma_PP_triplet(chi_wk_vt chi_c, chi_wk_vt chi_s, \ - array_view, 4> U_c, array_view, 4> U_s) { - - auto Gamma_pp_wk = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, -1, -1); - return Gamma_pp_wk; -} - chi_wk_t construct_phi_wk(chi_wk_vt chi, array_view, 4> U) { using scalar_t = chi_wk_t::scalar_t; diff --git a/c++/triqs_tprf/lattice/eliashberg.hpp b/c++/triqs_tprf/lattice/eliashberg.hpp index 2df4eccda..ba8a1d7e5 100644 --- a/c++/triqs_tprf/lattice/eliashberg.hpp +++ b/c++/triqs_tprf/lattice/eliashberg.hpp @@ -165,70 +165,6 @@ namespace triqs_tprf { std::tuple dynamic_and_constant_to_tr(chi_wk_vt Gamma_pp_dyn_wk, chi_k_vt Gamma_pp_const_k); e_r_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, g_tr_t F_tr); - /** The particle-particle vertex in the singlet channel - - Computes the singlet channel particle-particle vertex in the - random phase approximation given by - - .. math:: - \Gamma^{\mathrm{singlet}}(i\omega_n,\mathbf{q}) = - 3 \mathbf{U}^{\mathrm{s}} - \mathbf{\chi}^{\mathrm{s}}(i\omega_n,\mathbf{q}) - \mathbf{U}^{\mathrm{s}} - -\mathbf{U}^{\mathrm{c}} - \mathbf{\chi}^{\mathrm{c}}(i\omega_n,\mathbf{q}) - \mathbf{U}^{\mathrm{c}} - + \frac{1}{2}\big(\mathbf{U}^{\mathrm{s}}+ - \mathbf{U}^{\mathrm{c}}\big)\,, - - where all products are particle-hole products. - Note, that this is a special case, where the particle-particle vertex only - depends on one bosonic frequency and momentum. It can therefore only be used - in the linearized Eliashberg equation, if symmetries are enforced, - as desribed in the theory here: :ref:`eliashberg_rpa`. - - @param chi_c charge susceptibility :math:`\chi^{\mathrm{c}}_{\bar{a}b\bar{c}d}(i\omega_n,\mathbf{q})` - @param chi_s spin susceptibility :math:`\chi^{\mathrm{s}}_{\bar{a}b\bar{c}d}(i\omega_n,\mathbf{q})` - @param U_c charge interaction :math:`U^{\mathrm{c}}_{a\bar{b}c\bar{d}}` - @param U_s spin interaction :math:`U^{\mathrm{s}}_{a\bar{b}c\bar{d}}` - @return The singlet channel particle-particle vertex :math:`\Gamma^{\mathrm{singlet}}(i\omega_n,\mathbf{q})` - - */ - - chi_wk_t gamma_PP_singlet(chi_wk_vt chi_c, chi_wk_vt chi_s, array_view, 4> U_c, array_view, 4> U_s); - - /** The particle-particle vertex in the triplet channel - - Computes the triplet channel particle-particle vertex in the - random phase approximation given by - - .. math:: - \Gamma^{\mathrm{triplet}}(i\omega_n,\mathbf{q}) = - -\mathbf{U}^{\mathrm{s}} - \mathbf{\chi}^{\mathrm{s}}(i\omega_n,\mathbf{q}) - \mathbf{U}^{\mathrm{s}} - -\mathbf{U}^{\mathrm{c}} - \mathbf{\chi}^{\mathrm{c}}(i\omega_n,\mathbf{q}) - \mathbf{U}^{\mathrm{c}} - + \frac{1}{2}\big(\mathbf{U}^{\mathrm{s}}+ - \mathbf{U}^{\mathrm{c}}\big)\,, - - where all products are particle-hole products. - Note, that this is a special case, where the particle-particle vertex only - depends on one bosonic frequency and momentum. It can therefore only be used - in the linearized Eliashberg equation, if symmetries are enforced, - as desribed in the theory here: :ref:`eliashberg_rpa`. - - @param chi_c charge susceptibility :math:`\chi^{\mathrm{c}}_{\bar{a}b\bar{c}d}(i\omega_n,\mathbf{q})` - @param chi_s spin susceptibility :math:`\chi^{\mathrm{s}}_{\bar{a}b\bar{c}d}(i\omega_n,\mathbf{q})` - @param U_c charge interaction :math:`U^{\mathrm{c}}_{a\bar{b}c\bar{d}}` - @param U_s spin interaction :math:`U^{\mathrm{s}}_{a\bar{b}c\bar{d}}` - @return The triplet channel particle-particle vertex :math:`\Gamma^{\mathrm{triplet}}(i\omega_n,\mathbf{q})` - - */ - - chi_wk_t gamma_PP_triplet(chi_wk_vt chi_c, chi_wk_vt chi_s, array_view, 4> U_c, array_view, 4> U_s); - chi_wk_t gamma_PP_spin_charge(chi_wk_vt chi_c, chi_wk_vt chi_s, array_view, 4> U_c, array_view, 4> U_s, double charge_factor, double spin_factor); /** Computes reducible ladder vertex for the approximation of a local and static vertex. @@ -249,7 +185,7 @@ namespace triqs_tprf { where all products are particle-hole products. The reducible ladder vertex in then only dependent on one bosonic frequency and momentum. It can then be used in :meth:`triqs_tprf.eliashberg.construct_gamma_singlet_rpa` - or :meth:`triqs_tprf.eliashberg.construct_gamma_triplet_rpa` to construct the + or :meth:`triqs_tprf.eliashberg.construct_gamma__rpa` to construct the irreducible singlet/triplet vertex. @param chi density/magnetic susceptibility :math:`\chi^{\mathrm{d/m}}_{\bar{a}b\bar{c}d}(i\omega_n,\mathbf{q})` diff --git a/doc/reference/cpp_reference.rst b/doc/reference/cpp_reference.rst index 81b7f8825..f328b093b 100644 --- a/doc/reference/cpp_reference.rst +++ b/doc/reference/cpp_reference.rst @@ -107,8 +107,6 @@ Linearized Eliashberg equation /cpp2rst_generated/triqs_tprf/eliashberg_product_fft /cpp2rst_generated/triqs_tprf/split_into_dynamic_wk_and_constant_k /cpp2rst_generated/triqs_tprf/dynamic_and_constant_to_tr - /cpp2rst_generated/triqs_tprf/gamma_PP_singlet - /cpp2rst_generated/triqs_tprf/gamma_PP_triplet /cpp2rst_generated/triqs_tprf/construct_phi_wk Hubbard atom analytic response functions diff --git a/python/triqs_tprf/lattice_desc.py b/python/triqs_tprf/lattice_desc.py index 9e18c1dfe..702c97e42 100644 --- a/python/triqs_tprf/lattice_desc.py +++ b/python/triqs_tprf/lattice_desc.py @@ -597,91 +597,40 @@ module.add_function ("triqs_tprf::e_r_t triqs_tprf::eliashberg_constant_gamma_f_product (triqs_tprf::chi_r_vt Gamma_pp_const_r, triqs_tprf::g_tr_t F_tr)", doc = r"""""") -module.add_function ("triqs_tprf::chi_wk_t triqs_tprf::gamma_PP_singlet (triqs_tprf::chi_wk_vt chi_c, triqs_tprf::chi_wk_vt chi_s, array_view, 4> U_c, array_view, 4> U_s)", doc = r"""The particle-particle vertex in the singlet channel +module.add_function ("triqs_tprf::chi_wk_t triqs_tprf::construct_phi_wk (triqs_tprf::chi_wk_vt chi, array_view, 4> U)", doc = r"""Computes reducible ladder vertex for the approximation of a local and static vertex. - Computes the singlet channel particle-particle vertex in the - random phase approximation given by + In this approximation the reducible ladder vertex in density/magnetic channel are given by - .. math:: - \Gamma^{\mathrm{singlet}}(i\omega_n,\mathbf{q}) = - 3 \mathbf{U}^{\mathrm{s}} - \mathbf{\chi}^{\mathrm{s}}(i\omega_n,\mathbf{q}) - \mathbf{U}^{\mathrm{s}} - -\mathbf{U}^{\mathrm{c}} - \mathbf{\chi}^{\mathrm{c}}(i\omega_n,\mathbf{q}) - \mathbf{U}^{\mathrm{c}} - + \frac{1}{2}\big(\mathbf{U}^{\mathrm{s}}+ - \mathbf{U}^{\mathrm{c}}\big)\,, - - where all products are particle-hole products. - Note, that this is a special case, where the particle-particle vertex only - depends on one bosonic frequency and momentum. It can therefore only be used - in the linearized Eliashberg equation, if symmetries are enforced, - as desribed in the theory here: :ref:`eliashberg_rpa`. - -Parameters ----------- -chi_c - charge susceptibility :math:`\chi^{\mathrm{c}}_{\bar{a}b\bar{c}d}(i\omega_n,\mathbf{q})` - -chi_s - spin susceptibility :math:`\chi^{\mathrm{s}}_{\bar{a}b\bar{c}d}(i\omega_n,\mathbf{q})` - -U_c - charge interaction :math:`U^{\mathrm{c}}_{a\bar{b}c\bar{d}}` - -U_s - spin interaction :math:`U^{\mathrm{s}}_{a\bar{b}c\bar{d}}` - -Returns -------- -out - The singlet channel particle-particle vertex :math:`\Gamma^{\mathrm{singlet}}(i\omega_n,\mathbf{q})`""") - -module.add_function ("triqs_tprf::chi_wk_t triqs_tprf::gamma_PP_triplet (triqs_tprf::chi_wk_vt chi_c, triqs_tprf::chi_wk_vt chi_s, array_view, 4> U_c, array_view, 4> U_s)", doc = r"""The particle-particle vertex in the triplet channel + .. math:: + \Phi^{\text{d/m}}_{a\overline{b}c\overline{d}}(Q) + &\approx + \frac{1}{(N_\mathbf{k}\beta)^2} + \sum_{K'', K'''} + \overline{U}^{\text{d/m}}\chi^{\text{d/m}}(Q, K'', K''') \overline{U}^{\text{d/m}} + \\ + &\approx + \overline{U}^{\mathrm{d/m}} + \chi^{\text{d/m}}(Q) \overline{U}^{\mathrm{d/m}}\,, - Computes the triplet channel particle-particle vertex in the - random phase approximation given by - .. math:: - \Gamma^{\mathrm{triplet}}(i\omega_n,\mathbf{q}) = - -\mathbf{U}^{\mathrm{s}} - \mathbf{\chi}^{\mathrm{s}}(i\omega_n,\mathbf{q}) - \mathbf{U}^{\mathrm{s}} - -\mathbf{U}^{\mathrm{c}} - \mathbf{\chi}^{\mathrm{c}}(i\omega_n,\mathbf{q}) - \mathbf{U}^{\mathrm{c}} - + \frac{1}{2}\big(\mathbf{U}^{\mathrm{s}}+ - \mathbf{U}^{\mathrm{c}}\big)\,, - - where all products are particle-hole products. - Note, that this is a special case, where the particle-particle vertex only - depends on one bosonic frequency and momentum. It can therefore only be used - in the linearized Eliashberg equation, if symmetries are enforced, - as desribed in the theory here: :ref:`eliashberg_rpa`. + where all products are particle-hole products. + The reducible ladder vertex in then only dependent on one bosonic frequency and momentum. + It can then be used in :meth:`triqs_tprf.eliashberg.construct_gamma_singlet_rpa` + or :meth:`triqs_tprf.eliashberg.construct_gamma__rpa` to construct the + irreducible singlet/triplet vertex. Parameters ---------- -chi_c - charge susceptibility :math:`\chi^{\mathrm{c}}_{\bar{a}b\bar{c}d}(i\omega_n,\mathbf{q})` +chi + density/magnetic susceptibility :math:`\chi^{\mathrm{d/m}}_{\bar{a}b\bar{c}d}(i\omega_n,\mathbf{q})` -chi_s - spin susceptibility :math:`\chi^{\mathrm{s}}_{\bar{a}b\bar{c}d}(i\omega_n,\mathbf{q})` - -U_c - charge interaction :math:`U^{\mathrm{c}}_{a\bar{b}c\bar{d}}` - -U_s - spin interaction :math:`U^{\mathrm{s}}_{a\bar{b}c\bar{d}}` +U + density/magnetic local and static vertex :math:`U^{\mathrm{d/m}}_{a\bar{b}c\bar{d}}` Returns ------- out - The triplet channel particle-particle vertex :math:`\Gamma^{\mathrm{triplet}}(i\omega_n,\mathbf{q})`""") - -module.add_function ("triqs_tprf::chi_wk_t triqs_tprf::gamma_PP_spin_charge (triqs_tprf::chi_wk_vt chi_c, triqs_tprf::chi_wk_vt chi_s, array_view, 4> U_c, array_view, 4> U_s, double charge_factor, double spin_factor)", doc = r"""""") - -module.add_function ("triqs_tprf::chi_wk_t triqs_tprf::construct_phi_wk (triqs_tprf::chi_wk_vt chi, array_view, 4> U)", doc = r"""""") + The reducible ladder vertex in the density/magnetic channel :math:`\Phi^{\mathrm{d/m}}(i\omega_n,\mathbf{q})`""") module.add_function ("array, 6> triqs_tprf::cluster_mesh_fourier_interpolation (array k_vecs, triqs_tprf::chi_wr_cvt chi)", doc = r"""""") From 520aae101a08b340562a8b0d6f8665b760386ba7 Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 22 Jan 2021 12:08:22 +0100 Subject: [PATCH 117/121] [eli] make documentation consistent --- c++/triqs_tprf/lattice/eliashberg.hpp | 6 +++--- doc/theory/eliashberg.rst | 6 +++--- 2 files changed, 6 insertions(+), 6 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.hpp b/c++/triqs_tprf/lattice/eliashberg.hpp index ba8a1d7e5..98136bd10 100644 --- a/c++/triqs_tprf/lattice/eliashberg.hpp +++ b/c++/triqs_tprf/lattice/eliashberg.hpp @@ -175,11 +175,11 @@ namespace triqs_tprf { &\approx \frac{1}{(N_\mathbf{k}\beta)^2} \sum_{K'', K'''} - \overline{U}^{\text{d/m}}\chi^{\text{d/m}}(Q, K'', K''') \overline{U}^{\text{d/m}} + U^{\text{d/m}}\chi^{\text{d/m}}(Q, K'', K''') U^{\text{d/m}} \\ &\approx - \overline{U}^{\mathrm{d/m}} - \chi^{\text{d/m}}(Q) \overline{U}^{\mathrm{d/m}}\,, + U^{\mathrm{d/m}} + \chi^{\text{d/m}}(Q) U^{\mathrm{d/m}}\,, where all products are particle-hole products. diff --git a/doc/theory/eliashberg.rst b/doc/theory/eliashberg.rst index aa1afb7ae..e9e54a45e 100644 --- a/doc/theory/eliashberg.rst +++ b/doc/theory/eliashberg.rst @@ -327,11 +327,11 @@ momentum pair :math:`Q` &\approx \frac{1}{(N_\mathbf{k}\beta)^2} \sum_{K'', K'''} - \overline{U}^{\text{d/m}}\chi^{\text{d/m}}(Q, K'', K''') \overline{U}^{\text{d/m}} + U^{\text{d/m}}\chi^{\text{d/m}}(Q, K'', K''') U^{\text{d/m}} \\ &\approx - \overline{U}^{\mathrm{d/m}} - \chi^{\text{d/m}}(Q) \overline{U}^{\mathrm{d/m}} + U^{\mathrm{d/m}} + \chi^{\text{d/m}}(Q) U^{\mathrm{d/m}} \,, and the fully irreducible vertices become From c94c695be192b0e06e0279c1da209bf2e01b0e5f Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 22 Jan 2021 12:10:28 +0100 Subject: [PATCH 118/121] fix wrong PH ordering in comment --- c++/triqs_tprf/channel_grouping.hpp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/c++/triqs_tprf/channel_grouping.hpp b/c++/triqs_tprf/channel_grouping.hpp index 88fc24223..6eac1d2c4 100644 --- a/c++/triqs_tprf/channel_grouping.hpp +++ b/c++/triqs_tprf/channel_grouping.hpp @@ -55,7 +55,7 @@ template class channel_grouping { // Channel_t::PH // in the particle-hole channel (Channel_t::PH) the indices are grouped as -// {nu_1, a, b}, {nu_2, c, d} <=> {0, 2, 3}, {1, 4, 5} +// {nu_1, a, b}, {nu_2, d, c} <=> {0, 2, 3}, {1, 5, 4} template <> inline memory_layout_t<6> From 138f692ad1b21feef98d5ead8b9a5b72af6711aa Mon Sep 17 00:00:00 2001 From: Nils Wentzell Date: Fri, 22 Jan 2021 14:56:45 -0500 Subject: [PATCH 119/121] [gh-actions] Be sure to apt-get update before apt-get install --- .github/workflows/build.yml | 1 + 1 file changed, 1 insertion(+) diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml index a301b0077..74395174b 100644 --- a/.github/workflows/build.yml +++ b/.github/workflows/build.yml @@ -25,6 +25,7 @@ jobs: - name: Install ubuntu dependencies if: matrix.os == 'ubuntu-20.04' run: > + sudo apt-get update && sudo apt-get install clang-10 g++-10 From 02ea3e71e4683543df5bcca2db6ac6263512e9b1 Mon Sep 17 00:00:00 2001 From: Nils Wentzell Date: Fri, 22 Jan 2021 15:23:53 -0500 Subject: [PATCH 120/121] [eli] Consistently use 'auto const &' in range-based for-loops -clang-format edited lines --- c++/triqs_tprf/lattice/eliashberg.cpp | 18 ++++++++---------- 1 file changed, 8 insertions(+), 10 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index 58e99bab3..3639852f5 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -80,9 +80,9 @@ g_wk_t eliashberg_product(chi_wk_vt Gamma_pp, g_wk_vt g_wk, auto delta_wk_out = make_gf(delta_wk); delta_wk_out *= 0.; - - for (const auto [w, k] : delta_wk.mesh()) - for (const auto [n, q] : delta_wk.mesh()) + + for (auto const &[w, k] : delta_wk.mesh()) + for (auto const &[n, q] : delta_wk.mesh()) for (auto [c, a, d, b] : Gamma_pp.target_indices()) delta_wk_out[w, k](a, b) += -0.5 * Gamma_pp(w-n, k - q)(c, a, d, b) * F_wk[n, q](d, c); @@ -103,12 +103,12 @@ std::tuple split_into_dynamic_wk_and_constant_k(chi_wk_vt Gam auto Gamma_pp_const_k = make_gf(kmesh, Gamma_pp.target()); - for (const auto k : kmesh) { + for (auto const &k : kmesh) { auto Gamma_w = Gamma_pp[_, k]; auto tail = std::get<0>(fit_tail(Gamma_w)); for (auto [a, b, c, d] : Gamma_pp.target_indices()) Gamma_pp_const_k[k](a, b, c, d) = tail(0, a, b, c, d); - for( const auto w : wmesh ) Gamma_pp_dyn_wk[w, k] = Gamma_pp[w, k] - Gamma_pp_const_k[k]; + for (auto const &w : wmesh) Gamma_pp_dyn_wk[w, k] = Gamma_pp[w, k] - Gamma_pp_const_k[k]; } return {Gamma_pp_dyn_wk, Gamma_pp_const_k}; @@ -131,7 +131,7 @@ e_r_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, g_tr_t F_tr auto delta_r_out = make_gf(std::get<1>(F_tr.mesh()), F_tr.target()); delta_r_out *= 0.; - for (const auto r : std::get<1>(F_tr.mesh())) { + for (auto const &r : std::get<1>(F_tr.mesh())) { auto F_t = F_tr[_, r]; for (auto [c, a, d, b] : Gamma_pp_const_r.target_indices()) delta_r_out[r](a, b) += -0.5 * Gamma_pp_const_r[r](c, a, d, b) * F_t(0)(d, c); @@ -185,8 +185,7 @@ g_wk_t eliashberg_product_fft(chi_tr_vt Gamma_pp_dyn_tr, chi_r_vt Gamma_pp_const auto delta_wr_out = fourier_tr_to_wr(delta_tr_out); // Combine dynamic and constant part auto _ = all_t{}; - for (const auto w : std::get<0>(delta_wr_out.mesh())) - delta_wr_out[w, _] += delta_r_out; + for (auto const &w : std::get<0>(delta_wr_out.mesh())) delta_wr_out[w, _] += delta_r_out; auto delta_wk_out = fourier_wr_to_wk(delta_wr_out); @@ -208,8 +207,7 @@ g_wk_t eliashberg_product_fft_constant(chi_r_vt Gamma_pp_const_r, delta_wk_out *= 0.; auto _ = all_t{}; - for (const auto w : std::get<0>(delta_wk_out.mesh())) - delta_wk_out[w, _] += delta_k_out; + for (auto const &w : std::get<0>(delta_wk_out.mesh())) delta_wk_out[w, _] += delta_k_out; return delta_wk_out; } From 0e162ee30abb2f2af408c5f556ab6372c2ab3d52 Mon Sep 17 00:00:00 2001 From: "Hugo U. R. Strand" Date: Mon, 25 Jan 2021 13:46:45 +0100 Subject: [PATCH 121/121] [test] do not use triqs rw_h5(..) test function --- test/c++/bubble.cpp | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/test/c++/bubble.cpp b/test/c++/bubble.cpp index 477398d48..69e3b6cb6 100644 --- a/test/c++/bubble.cpp +++ b/test/c++/bubble.cpp @@ -62,8 +62,8 @@ TEST(Gf, Bubble) { EXPECT_ARRAY_NEAR(chi0q_from_r.data(), chi0q.data()); // hdf5 - rw_h5(chi0q); - rw_h5(chi0r); + //rw_h5(chi0q); + //rw_h5(chi0r); } // ------------------------------------------------------------ @@ -97,8 +97,8 @@ TEST(Gf, BubbleScalar) { } EXPECT_ARRAY_NEAR(chi0q_from_r.data(), chi0q.data()); - rw_h5(chi0q); - rw_h5(chi0r); + //rw_h5(chi0q); + //rw_h5(chi0r); } // ------------------------------------------------------------ @@ -134,8 +134,8 @@ TEST(Gf, BubbleTensor) { } EXPECT_ARRAY_NEAR(chi0q_from_r.data(), chi0q.data()); - rw_h5(chi0q); - rw_h5(chi0r); + //rw_h5(chi0q); + //rw_h5(chi0r); } // ------------------------------------------------------------

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b/test/python/eliashberg/fft_product_constant_vs_full.py index 904acfeec..0da3bcf98 100644 --- a/test/python/eliashberg/fft_product_constant_vs_full.py +++ b/test/python/eliashberg/fft_product_constant_vs_full.py @@ -21,7 +21,7 @@ from triqs_tprf.lattice import eliashberg_product_fft, eliashberg_product_fft_constant from triqs_tprf.eliashberg import semi_random_initial_delta, preprocess_gamma_for_fft -from triqs_tprf.tight_binding import create_square_lattice +from triqs_tprf.tight_binding import create_model_for_tests from triqs_tprf.ParameterCollection import ParameterCollection # ---------------------------------------------------------------------- @@ -29,6 +29,7 @@ if __name__ == '__main__': p = ParameterCollection( + dim = 2, norb = 1, t = 2.0, mu = 0.0, @@ -38,7 +39,7 @@ nw = 200, ) - H = create_square_lattice(**p) + H = create_model_for_tests(**p) e_k = H.on_mesh_brillouin_zone(n_k=(p.nk, p.nk, 1)) wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nw) diff --git a/test/python/eliashberg/previous_implementation.py b/test/python/eliashberg/previous_implementation.py index 0b0883854..e3a104e42 100644 --- a/test/python/eliashberg/previous_implementation.py +++ b/test/python/eliashberg/previous_implementation.py @@ -16,7 +16,9 @@ from pytriqs.gf import MeshImFreq from triqs_tprf.ParameterCollection import ParameterCollection -from triqs_tprf.tight_binding import TBLattice + +from triqs_tprf.tight_binding import create_model_for_tests + from triqs_tprf.lattice import lattice_dyson_g0_wk from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors @@ -35,7 +37,7 @@ p = ParameterCollection( filename = 'eliashberg_benchmark_new.tar.gz', dim = 2, - norbs = 1, + norb = 1, t = 1.0, mu = 0.0, beta = 1, @@ -47,18 +49,8 @@ # -- Setup model, RPA susceptibilities and spin/charge interaction -full_units = [(1, 0, 0), (0, 1, 0), (0, 0, 1)] -all_nn_hoppings = list(itertools.product([-1, 0, 1], repeat=p.dim)) -non_diagonal_hoppings = [ele for ele in all_nn_hoppings if sum(np.abs(ele)) == 1] - -t = -p.t * np.eye(p.norbs) - -H = TBLattice( - units = full_units[:p.dim], - hopping = {hop : t for hop in non_diagonal_hoppings}, - orbital_positions = [(0,0,0)]*p.norbs, - ) +H = create_model_for_tests(**p) e_k = H.on_mesh_brillouin_zone(n_k=[p.nk]*p.dim + [1]*(3-p.dim)) # A bigger w-mesh is needed to construct a Gamma with a twice as big w-mesh than GF @@ -73,7 +65,7 @@ chi0_wk = imtime_bubble_chi0_wk(g0_wk_big, nw=p.nw) chi0_wk_big = imtime_bubble_chi0_wk(g0_wk_big, nw=int(big_factor*p.nw)+1) -U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norbs, p.U, 0, 0, 0) +U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norb, p.U, 0, 0, 0) chi_s = solve_rpa_PH(chi0_wk, U_s) chi_c = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation @@ -104,7 +96,7 @@ # -- Check if the benchmark data was calculated for the same model, # -- otherwise a comparison does not make sense. -model_parameters = ['dim', 'norbs', 't', 'mu', 'beta', 'U'] +model_parameters = ['dim', 'norb', 't', 'mu', 'beta', 'U'] for model_parameter in model_parameters: run_time, benchmark = p[model_parameter], p_benchmark[model_parameter] diff --git a/test/python/eliashberg/previous_implementation_two_band.py b/test/python/eliashberg/previous_implementation_two_band.py index 5de5635dd..9820ab7ba 100644 --- a/test/python/eliashberg/previous_implementation_two_band.py +++ b/test/python/eliashberg/previous_implementation_two_band.py @@ -18,7 +18,9 @@ from pytriqs.gf import MeshImFreq from triqs_tprf.ParameterCollection import ParameterCollection -from triqs_tprf.tight_binding import TBLattice + +from triqs_tprf.tight_binding import create_model_for_tests + from triqs_tprf.lattice import lattice_dyson_g0_wk from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors @@ -38,7 +40,7 @@ p = ParameterCollection( filename = 'eliashberg_benchmark_two_band_new.tar.gz', dim = 2, - norbs = 2, + norb = 2, t1 = 1.0, t2 = 0.5, t12 = 0.1, @@ -52,20 +54,7 @@ ) # -- Setup model, RPA susceptibilities and spin/charge interaction - -full_units = [(1, 0, 0), (0, 1, 0), (0, 0, 1)] -all_nn_hoppings = list(itertools.product([-1, 0, 1], repeat=p.dim)) -non_diagonal_hoppings = [ele for ele in all_nn_hoppings if sum(np.abs(ele)) == 1] - -# -- Create hopping matrix for two-band model -t = -np.array([[p.t1, p.t12], [p.t21, p.t2]]) - -H = TBLattice( - units = full_units[:p.dim], - hopping = {hop : t for hop in non_diagonal_hoppings}, - orbital_positions = [(0,0,0)]*p.norbs, - ) - +H = create_model_for_tests(**p) e_k = H.on_mesh_brillouin_zone(n_k=[p.nk]*p.dim + [1]*(3-p.dim)) wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nw) @@ -74,7 +63,7 @@ chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw) -U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norbs, p.U, 0, 0, 0) +U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norb, p.U, 0, 0, 0) chi_s = solve_rpa_PH(chi0_wk, U_s) chi_c = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation @@ -103,7 +92,7 @@ # -- Check if the benchmark data was calculated for the same model, # -- otherwise a comparison does not make sense. -model_parameters = ['dim', 'norbs', 't1', 't2', 't12', 't21', 'mu', 'beta', 'U'] +model_parameters = ['dim', 'norb', 't1', 't2', 't12', 't21', 'mu', 'beta', 'U'] for model_parameter in model_parameters: try: diff --git a/test/python/eliashberg/product_summation_vs_fft.py b/test/python/eliashberg/product_summation_vs_fft.py index e5eb657e7..52e978c17 100644 --- a/test/python/eliashberg/product_summation_vs_fft.py +++ b/test/python/eliashberg/product_summation_vs_fft.py @@ -17,7 +17,7 @@ from triqs_tprf.ParameterCollection import ParameterCollection from pytriqs.gf import Gf, MeshImFreq, Idx -from triqs_tprf.tight_binding import TBLattice +from triqs_tprf.tight_binding import create_model_for_tests from triqs_tprf.lattice import lattice_dyson_g0_wk, solve_rpa_PH from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk @@ -73,19 +73,7 @@ def print_diff(diff): def compare_next_delta(p): # -- Setup model, RPA susceptibilities and spin/charge interaction - - full_units = [(1, 0, 0), (0, 1, 0), (0, 0, 1)] - all_nn_hoppings = list(itertools.product([-1, 0, 1], repeat=p.dim)) - non_diagonal_hoppings = [ele for ele in all_nn_hoppings if sum(np.abs(ele)) == 1] - - t = -p.t * np.eye(p.norbs) - - H = TBLattice( - units = full_units[:p.dim], - hopping = {hop : t for hop in non_diagonal_hoppings}, - orbital_positions = [(0,0,0)]*p.norbs, - ) - + H = create_model_for_tests(**p) e_k = H.on_mesh_brillouin_zone(n_k=[p.nk]*p.dim + [1]*(3-p.dim)) # A bigger w-mesh is needed to construct a Gamma with a twice as big w-mesh than GF @@ -99,7 +87,7 @@ def compare_next_delta(p): chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw) chi0_wk_big = imtime_bubble_chi0_wk(g0_wk_big, nw=int(p.big_factor*p.nw)+1) - U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norbs, p.U, p.Up, p.J,p.Jp) + U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norb, p.U, p.Up, p.J,p.Jp) chi_s = solve_rpa_PH(chi0_wk, U_s) chi_c = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation @@ -184,7 +172,7 @@ def compare_next_delta(p): p = ParameterCollection( dim = 1, - norbs = 1, + norb = 1, t = 2.0, mu = 0.0, beta = 5, @@ -201,8 +189,8 @@ def compare_next_delta(p): plot = False, ) - for norbs in [1, 2]: - p.norbs = norbs + for norb in [1, 2]: + p.norb = norb deltas = compare_next_delta(p) print('The summation and FFT implementation of the eliashberg product' diff --git a/test/python/eliashberg/symmetrize_delta.py b/test/python/eliashberg/symmetrize_delta.py index b51bd51b2..bfeb838fe 100644 --- a/test/python/eliashberg/symmetrize_delta.py +++ b/test/python/eliashberg/symmetrize_delta.py @@ -16,7 +16,9 @@ from pytriqs.gf import MeshImFreq, Idx from triqs_tprf.ParameterCollection import ParameterCollection -from triqs_tprf.tight_binding import TBLattice + +from triqs_tprf.tight_binding import create_model_for_tests + from triqs_tprf.lattice import lattice_dyson_g0_wk from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors @@ -36,7 +38,7 @@ p = ParameterCollection( dim = 2, - norbs = 2, + norb = 2, t1 = 1.0, t2 = 0.5, t12 = 0.1, @@ -53,19 +55,7 @@ ) # -- Setup model, RPA susceptibilities, spin/charge interaction and gamma -full_units = [(1, 0, 0), (0, 1, 0), (0, 0, 1)] -all_nn_hoppings = list(itertools.product([-1, 0, 1], repeat=p.dim)) -non_diagonal_hoppings = [ele for ele in all_nn_hoppings if sum(np.abs(ele)) == 1] - -# -- Create hopping matrix for two-band model -t = -np.array([[p.t1, p.t12], [p.t21, p.t2]]) - -H = TBLattice( - units = full_units[:p.dim], - hopping = {hop : t for hop in non_diagonal_hoppings}, - orbital_positions = [(0,0,0)]*p.norbs, - ) - +H = create_model_for_tests(**p) e_k = H.on_mesh_brillouin_zone(n_k=[p.nk]*p.dim + [1]*(3-p.dim)) wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nw) @@ -73,7 +63,7 @@ chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw) -U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norbs, p.U, p.Up, +U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norb, p.U, p.Up, p.J, p.Jp) chi_s = solve_rpa_PH(chi0_wk, U_s) @@ -110,8 +100,8 @@ vmax = np.max(np.abs(delta[Idx(0),:].data)) - for orb1, orb2 in itertools.product(range(p.norbs), repeat=2): - shape = (p.nk, p.nk, p.norbs, p.norbs) + for orb1, orb2 in itertools.product(range(p.norb), repeat=2): + shape = (p.nk, p.nk, p.norb, p.norb) data = delta[Idx(0), :].data.reshape(shape) plt.sca(axes[orb1,orb2]) plt.imshow(data[:,:,orb1,orb2].real, cmap="RdBu_r", @@ -119,7 +109,7 @@ plt.colorbar() plt.sca(axes[-1,-1]) - for orb1, orb2 in itertools.product(range(p.norbs), repeat=2): + for orb1, orb2 in itertools.product(range(p.norb), repeat=2): plt.plot(delta.data[:, 10, orb1, orb2].real) plt.plot(delta.data[:, 10, orb1, orb2].imag) From e7cd246687f2fe861a1693e9b094a79cca083ea4 Mon Sep 17 00:00:00 2001 From: Stefan Date: Tue, 11 Aug 2020 16:25:07 +0200 Subject: [PATCH 062/121] [eli] refactor g0_wk and gamma creation --- python/triqs_tprf/utilities.py | 68 ++++++++++++------- test/python/eliashberg/eigenvalue_solver.py | 44 +++--------- .../fft_product_constant_vs_full.py | 14 ++-- .../eliashberg/previous_implementation.py | 49 ++++--------- .../previous_implementation_two_band.py | 32 +++------ .../eliashberg/product_summation_vs_fft.py | 45 +++--------- test/python/eliashberg/symmetrize_delta.py | 31 ++------- 7 files changed, 102 insertions(+), 181 deletions(-) diff --git a/python/triqs_tprf/utilities.py b/python/triqs_tprf/utilities.py index bd479464a..1f41fa482 100644 --- a/python/triqs_tprf/utilities.py +++ b/python/triqs_tprf/utilities.py @@ -23,6 +23,24 @@ # ################################################################################ +import os +import tarfile +from tempfile import NamedTemporaryFile + +import numpy as np + +from pytriqs.archive import HDFArchive + +from pytriqs.gf import Gf, MeshImFreq, MeshProduct, BlockGf +from pytriqs.gf.tools import fit_legendre +from pytriqs.gf.gf_fnt import enforce_discontinuity + +from triqs_tprf.lattice import lattice_dyson_g0_wk, solve_rpa_PH, gamma_PP_singlet +from triqs_tprf.tight_binding import create_model_for_tests +from triqs_tprf.ParameterCollection import ParameterCollection +from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk +from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors + # ---------------------------------------------------------------------- def show_version_info(info): """ Return a string that formats the version information @@ -35,11 +53,6 @@ def show_version_info(info): # ---------------------------------------------------------------------- def write_TarGZ_HDFArchive(filename, **kwargs): - - import os - import tarfile - from pytriqs.archive import HDFArchive - filename = filename.split('.')[0] filename_h5 = filename + '.h5' filename_tar = filename + '.tar.gz' @@ -55,12 +68,6 @@ def write_TarGZ_HDFArchive(filename, **kwargs): # ---------------------------------------------------------------------- def read_TarGZ_HDFArchive(filename): - - import os - import tarfile - from tempfile import NamedTemporaryFile - from pytriqs.archive import HDFArchive - tar = tarfile.open(filename, "r:gz") f = tar.extractfile(tar.getmembers()[0]) @@ -77,9 +84,6 @@ def read_TarGZ_HDFArchive(filename): # ---------------------------------------------------------------------- def BlockGf_data(G): """ Returns a ndarray copy of all data in a BlockGf """ - - import numpy as np - shape = [G.n_blocks] + list(G[G.indices.next()].data.shape) data = np.zeros(shape, dtype=np.complex) for bidx, (b, g) in enumerate(G): @@ -110,12 +114,6 @@ def legendre_filter(G_tau, order=100, G_l_cut=1e-19): Fitted Green's function on a Legendre mesh """ - - import numpy as np - from pytriqs.gf import BlockGf - from pytriqs.gf.tools import fit_legendre - from pytriqs.gf.gf_fnt import enforce_discontinuity - l_g_l = [] for b, g in G_tau: @@ -141,7 +139,6 @@ def G2_loc_fixed_fermionic_window_python(g2, nwf): assert(n/2 >= nwf) - from pytriqs.gf import Gf, MeshImFreq, MeshProduct mesh_iw = MeshImFreq(beta=beta, S='Boson', n_max=nw) mesh_inu = MeshImFreq(beta=beta, S='Fermion', n_max=nwf) @@ -159,7 +156,6 @@ def G2_loc_fixed_fermionic_window_python(g2, nwf): def beta_to_temperature(beta): """Convert beta in 1/eV to Temperature in Kelvin """ - def eV_to_Kelvin(ev): return 11604.5250061657 * ev @@ -170,10 +166,36 @@ def eV_to_Kelvin(ev): def temperature_to_beta(T): """Convert Temperature in Kelvin to beta in 1/eV """ - def Kelvin_to_eV(K): return K / 11604.5250061657 T = Kelvin_to_eV(T) beta = 1./ T return beta + +# ---------------------------------------------------------------------- +def create_eliashberg_ingredients(p): + H = create_model_for_tests(**p) + e_k = H.on_mesh_brillouin_zone(n_k=[p.nk] * p.dim + [1] * (3 - p.dim)) + + wmesh = MeshImFreq(beta=p.beta, S="Fermion", n_max=p.nw) + g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh) + + chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw) + + U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors( + p.norb, p.U, p.Up, p.J, p.Jp + ) + + chi_s = solve_rpa_PH(chi0_wk, U_s) + chi_c = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation + + gamma = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) + + eliashberg_ingredients = ParameterCollection( + g0_wk = g0_wk, + gamma = gamma, + U_s = U_s, + U_c = U_c, + ) + return eliashberg_ingredients diff --git a/test/python/eliashberg/eigenvalue_solver.py b/test/python/eliashberg/eigenvalue_solver.py index 47fec8c69..b599d401d 100644 --- a/test/python/eliashberg/eigenvalue_solver.py +++ b/test/python/eliashberg/eigenvalue_solver.py @@ -17,45 +17,23 @@ from triqs_tprf.ParameterCollection import ParameterCollection from pytriqs.gf import Gf, MeshImFreq, Idx - -from triqs_tprf.tight_binding import create_model_for_tests - -from triqs_tprf.lattice import lattice_dyson_g0_wk, solve_rpa_PH -from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk -from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors -from triqs_tprf.lattice import gamma_PP_singlet +from triqs_tprf.utilities import create_eliashberg_ingredients from triqs_tprf.eliashberg import solve_eliashberg, semi_random_initial_delta from triqs_tprf.eliashberg import allclose_by_scalar_multiplication # ---------------------------------------------------------------------- def run_solve_eliashberg(p): - - # -- Setup model, RPA susceptibilities and spin/charge interaction - - H = create_model_for_tests(**p) - e_k = H.on_mesh_brillouin_zone(n_k=[p.nk]*p.dim + [1]*(3-p.dim)) - - # A bigger w-mesh is needed to construct a Gamma with a twice as big w-mesh than GF - - wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nw) - wmesh_big = MeshImFreq(beta=p.beta, S='Fermion', n_max=int(p.big_factor*p.nw)+1) - - g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh) - g0_wk_big = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh_big) - - chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw) - chi0_wk_big = imtime_bubble_chi0_wk(g0_wk_big, nw=int(p.big_factor*p.nw)+1) - - U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norb, p.U, p.Up, p.J,p.Jp) - - chi_s = solve_rpa_PH(chi0_wk, U_s) - chi_c = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation - chi_s_big = solve_rpa_PH(chi0_wk_big, U_s) - chi_c_big = solve_rpa_PH(chi0_wk_big, -U_c) # Minus for correct charge rpa equation - - gamma = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) - gamma_big = gamma_PP_singlet(chi_c_big, chi_s_big, U_c, U_s) + eliashberg_ingredients = create_eliashberg_ingredients(p) + g0_wk = eliashberg_ingredients.g0_wk + gamma = eliashberg_ingredients.gamma + U_c = eliashberg_ingredients.U_c + U_s = eliashberg_ingredients.U_s + + ## A bigger w-mesh is needed to construct a Gamma with a twice as big w-mesh than GF + big_nw = 2*p.nw + 1 + eliashberg_ingredients_big = create_eliashberg_ingredients(p.alter(nw=big_nw)) + gamma_big = eliashberg_ingredients_big.gamma if p.product == 'SUM': gamma = gamma_big diff --git a/test/python/eliashberg/fft_product_constant_vs_full.py b/test/python/eliashberg/fft_product_constant_vs_full.py index 0da3bcf98..b0f268f27 100644 --- a/test/python/eliashberg/fft_product_constant_vs_full.py +++ b/test/python/eliashberg/fft_product_constant_vs_full.py @@ -17,11 +17,9 @@ # ---------------------------------------------------------------------- from pytriqs.gf import Gf, MeshImFreq, MeshProduct -from triqs_tprf.lattice import lattice_dyson_g0_wk from triqs_tprf.lattice import eliashberg_product_fft, eliashberg_product_fft_constant from triqs_tprf.eliashberg import semi_random_initial_delta, preprocess_gamma_for_fft - -from triqs_tprf.tight_binding import create_model_for_tests +from triqs_tprf.utilities import create_eliashberg_ingredients from triqs_tprf.ParameterCollection import ParameterCollection # ---------------------------------------------------------------------- @@ -35,15 +33,15 @@ mu = 0.0, beta = 5, U = 1.0, + Up = 0.0, + J = 0.0, + Jp = 0.0, nk = 4, nw = 200, ) - H = create_model_for_tests(**p) - e_k = H.on_mesh_brillouin_zone(n_k=(p.nk, p.nk, 1)) - - wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nw) - g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh) + eliashberg_ingredients = create_eliashberg_ingredients(p) + g0_wk = eliashberg_ingredients.g0_wk wmesh_boson = MeshImFreq(beta=p.beta, S='Boson', n_max=p.nw) gamma_pp_wk = Gf(mesh=MeshProduct(wmesh_boson, g0_wk.mesh[1]), diff --git a/test/python/eliashberg/previous_implementation.py b/test/python/eliashberg/previous_implementation.py index e3a104e42..8834d1cc3 100644 --- a/test/python/eliashberg/previous_implementation.py +++ b/test/python/eliashberg/previous_implementation.py @@ -16,14 +16,7 @@ from pytriqs.gf import MeshImFreq from triqs_tprf.ParameterCollection import ParameterCollection - -from triqs_tprf.tight_binding import create_model_for_tests - -from triqs_tprf.lattice import lattice_dyson_g0_wk -from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk -from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors -from triqs_tprf.lattice import solve_rpa_PH -from triqs_tprf.lattice import gamma_PP_singlet +from triqs_tprf.utilities import create_eliashberg_ingredients from triqs_tprf.lattice import eliashberg_product from triqs_tprf.eliashberg import solve_eliashberg, allclose_by_scalar_multiplication @@ -42,40 +35,28 @@ mu = 0.0, beta = 1, U = 1.0, + Up = 0.0, + J = 0.0, + Jp = 0.0, nk = 2, nw = 100, version_info = version.info, ) -# -- Setup model, RPA susceptibilities and spin/charge interaction - - -H = create_model_for_tests(**p) -e_k = H.on_mesh_brillouin_zone(n_k=[p.nk]*p.dim + [1]*(3-p.dim)) - -# A bigger w-mesh is needed to construct a Gamma with a twice as big w-mesh than GF -big_factor = 2.0 +eliashberg_ingredients = create_eliashberg_ingredients(p) +g0_wk = eliashberg_ingredients.g0_wk +gamma = eliashberg_ingredients.gamma +U_c = eliashberg_ingredients.U_c +U_s = eliashberg_ingredients.U_s -wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nw) -wmesh_big = MeshImFreq(beta=p.beta, S='Fermion', n_max=int(big_factor*p.nw)) +## A bigger w-mesh is needed to construct a Gamma with a twice as big w-mesh than GF +big_nw = 2*p.nw + 1 +eliashberg_ingredients_big = create_eliashberg_ingredients(p.alter(nw=big_nw)) +gamma_big = eliashberg_ingredients_big.gamma -g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh) -g0_wk_big = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh_big) - -chi0_wk = imtime_bubble_chi0_wk(g0_wk_big, nw=p.nw) -chi0_wk_big = imtime_bubble_chi0_wk(g0_wk_big, nw=int(big_factor*p.nw)+1) - -U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norb, p.U, 0, 0, 0) - -chi_s = solve_rpa_PH(chi0_wk, U_s) -chi_c = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation -chi_s_big = solve_rpa_PH(chi0_wk_big, U_s) -chi_c_big = solve_rpa_PH(chi0_wk_big, -U_c) # Minus for correct charge rpa equation - -# -- The output of the following three functions shall be tested +# -- Setup model, RPA susceptibilities and spin/charge interaction -gamma = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) -gamma_big = gamma_PP_singlet(chi_c_big, chi_s_big, U_c, U_s) +# -- The output of the following functions shall be tested next_delta = eliashberg_product(gamma_big, g0_wk, g0_wk) E, eigen_modes = solve_eliashberg(gamma_big, g0_wk, product='SUM', solver='IRAM') diff --git a/test/python/eliashberg/previous_implementation_two_band.py b/test/python/eliashberg/previous_implementation_two_band.py index 9820ab7ba..1ed48a55f 100644 --- a/test/python/eliashberg/previous_implementation_two_band.py +++ b/test/python/eliashberg/previous_implementation_two_band.py @@ -21,12 +21,8 @@ from triqs_tprf.tight_binding import create_model_for_tests -from triqs_tprf.lattice import lattice_dyson_g0_wk -from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk -from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors -from triqs_tprf.lattice import solve_rpa_PH -from triqs_tprf.lattice import gamma_PP_singlet from triqs_tprf.lattice import eliashberg_product_fft +from triqs_tprf.utilities import create_eliashberg_ingredients from triqs_tprf.eliashberg import preprocess_gamma_for_fft, solve_eliashberg from triqs_tprf.eliashberg import allclose_by_scalar_multiplication @@ -48,30 +44,20 @@ mu = 0.0, beta = 1, U = 1.0, + Up = 0.0, + J = 0.0, + Jp = 0.0, nk = 2, nw = 100, version_info = version.info, ) -# -- Setup model, RPA susceptibilities and spin/charge interaction -H = create_model_for_tests(**p) -e_k = H.on_mesh_brillouin_zone(n_k=[p.nk]*p.dim + [1]*(3-p.dim)) +eliashberg_ingredients = create_eliashberg_ingredients(p) +g0_wk = eliashberg_ingredients.g0_wk +gamma = eliashberg_ingredients.gamma -wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nw) - -g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh) - -chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw) - -U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norb, p.U, 0, 0, 0) - -chi_s = solve_rpa_PH(chi0_wk, U_s) -chi_c = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation - -# -- The output of the following three functions shall be tested - -gamma = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) -Gamma_pp_dyn_tr, Gamma_pp_const_r = preprocess_gamma_for_fft(gamma) # This one is not tested +Gamma_pp_dyn_tr, Gamma_pp_const_r = preprocess_gamma_for_fft(gamma) +# -- The output of the following functions shall be tested next_delta = eliashberg_product_fft(Gamma_pp_dyn_tr, Gamma_pp_const_r, g0_wk, g0_wk) E, eigen_modes = solve_eliashberg(gamma, g0_wk, product='FFT', solver='IRAM') diff --git a/test/python/eliashberg/product_summation_vs_fft.py b/test/python/eliashberg/product_summation_vs_fft.py index 52e978c17..786fe6dde 100644 --- a/test/python/eliashberg/product_summation_vs_fft.py +++ b/test/python/eliashberg/product_summation_vs_fft.py @@ -16,13 +16,7 @@ from triqs_tprf.ParameterCollection import ParameterCollection from pytriqs.gf import Gf, MeshImFreq, Idx - -from triqs_tprf.tight_binding import create_model_for_tests - -from triqs_tprf.lattice import lattice_dyson_g0_wk, solve_rpa_PH -from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk -from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors -from triqs_tprf.lattice import gamma_PP_singlet +from triqs_tprf.utilities import create_eliashberg_ingredients from triqs_tprf.lattice import eliashberg_product, eliashberg_product_fft from triqs_tprf.eliashberg import semi_random_initial_delta, preprocess_gamma_for_fft @@ -71,47 +65,28 @@ def print_diff(diff): print(s) def compare_next_delta(p): + eliashberg_ingredients = create_eliashberg_ingredients(p) + g0_wk = eliashberg_ingredients.g0_wk + gamma = eliashberg_ingredients.gamma + U_c = eliashberg_ingredients.U_c + U_s = eliashberg_ingredients.U_s - # -- Setup model, RPA susceptibilities and spin/charge interaction - H = create_model_for_tests(**p) - e_k = H.on_mesh_brillouin_zone(n_k=[p.nk]*p.dim + [1]*(3-p.dim)) - - # A bigger w-mesh is needed to construct a Gamma with a twice as big w-mesh than GF - - wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nw) - wmesh_big = MeshImFreq(beta=p.beta, S='Fermion', n_max=int(p.big_factor*p.nw)+1) - - g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh) - g0_wk_big = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh_big) - - chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw) - chi0_wk_big = imtime_bubble_chi0_wk(g0_wk_big, nw=int(p.big_factor*p.nw)+1) - - U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norb, p.U, p.Up, p.J,p.Jp) - - chi_s = solve_rpa_PH(chi0_wk, U_s) - chi_c = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation - chi_s_big = solve_rpa_PH(chi0_wk_big, U_s) - chi_c_big = solve_rpa_PH(chi0_wk_big, -U_c) # Minus for correct charge rpa equation - - gamma = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) - gamma_big = gamma_PP_singlet(chi_c_big, chi_s_big, U_c, U_s) + ## A bigger w-mesh is needed to construct a Gamma with a twice as big w-mesh than GF + big_nw = 2*p.nw + 1 + eliashberg_ingredients_big = create_eliashberg_ingredients(p.alter(nw=big_nw)) + gamma_big = eliashberg_ingredients_big.gamma # -- Preprocess gamma for the FFT implementations - - if p.fit_const: gamma_dyn_tr, gamma_const_r = preprocess_gamma_for_fft(gamma, None) else: gamma_dyn_tr, gamma_const_r = preprocess_gamma_for_fft(gamma, 0.5*(U_s + U_c)) # -- Creating Semi-Random input Delta - v0 = semi_random_initial_delta(g0_wk, nr_factor=p.nr_factor, seed=1337) p.v0 = v0 # -- Test the Eliashberg product - print('Start the summation') next_delta = eliashberg_product(gamma_big, g0_wk, p.v0) print('Start the FFT') diff --git a/test/python/eliashberg/symmetrize_delta.py b/test/python/eliashberg/symmetrize_delta.py index bfeb838fe..675f33ef9 100644 --- a/test/python/eliashberg/symmetrize_delta.py +++ b/test/python/eliashberg/symmetrize_delta.py @@ -13,17 +13,10 @@ # ---------------------------------------------------------------------- -from pytriqs.gf import MeshImFreq, Idx +from pytriqs.gf import Idx from triqs_tprf.ParameterCollection import ParameterCollection - -from triqs_tprf.tight_binding import create_model_for_tests - -from triqs_tprf.lattice import lattice_dyson_g0_wk -from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk -from triqs_tprf.rpa_tensor import kanamori_charge_and_spin_quartic_interaction_tensors -from triqs_tprf.lattice import solve_rpa_PH -from triqs_tprf.lattice import gamma_PP_singlet +from triqs_tprf.utilities import create_eliashberg_ingredients from triqs_tprf.eliashberg import solve_eliashberg # ---------------------------------------------------------------------- @@ -54,22 +47,10 @@ plot=False ) -# -- Setup model, RPA susceptibilities, spin/charge interaction and gamma -H = create_model_for_tests(**p) -e_k = H.on_mesh_brillouin_zone(n_k=[p.nk]*p.dim + [1]*(3-p.dim)) - -wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nw) -g0_wk = lattice_dyson_g0_wk(mu=p.mu, e_k=e_k, mesh=wmesh) - -chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=p.nw) - -U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(p.norb, p.U, p.Up, - p.J, p.Jp) - -chi_s = solve_rpa_PH(chi0_wk, U_s) -chi_c = solve_rpa_PH(chi0_wk, -U_c) # Minus for correct charge rpa equation - -gamma = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) +# -- Setup non-interacing GF and particle-particle vertex +eliashberg_ingredients = create_eliashberg_ingredients(p) +g0_wk = eliashberg_ingredients.g0_wk +gamma = eliashberg_ingredients.gamma # -- Test symmetrizing function on eliashberg variables=["frequency", "momentum", "orbital"] From 415e9f407303348a1fd91c7f086b59f10e3492db Mon Sep 17 00:00:00 2001 From: Stefan Date: Tue, 11 Aug 2020 16:35:33 +0200 Subject: [PATCH 063/121] [eli] reduce to testing only eigenvalue solver --- test/python/eliashberg/eigenvalue_solver.py | 22 ++------------------- 1 file changed, 2 insertions(+), 20 deletions(-) diff --git a/test/python/eliashberg/eigenvalue_solver.py b/test/python/eliashberg/eigenvalue_solver.py index b599d401d..3d207c061 100644 --- a/test/python/eliashberg/eigenvalue_solver.py +++ b/test/python/eliashberg/eigenvalue_solver.py @@ -27,25 +27,10 @@ def run_solve_eliashberg(p): eliashberg_ingredients = create_eliashberg_ingredients(p) g0_wk = eliashberg_ingredients.g0_wk gamma = eliashberg_ingredients.gamma - U_c = eliashberg_ingredients.U_c - U_s = eliashberg_ingredients.U_s - - ## A bigger w-mesh is needed to construct a Gamma with a twice as big w-mesh than GF - big_nw = 2*p.nw + 1 - eliashberg_ingredients_big = create_eliashberg_ingredients(p.alter(nw=big_nw)) - gamma_big = eliashberg_ingredients_big.gamma - - if p.product == 'SUM': - gamma = gamma_big - - if p.fit_const: - gamma_const = None - else: - gamma_const = 0.5*(U_s + U_c) initial_delta = semi_random_initial_delta(g0_wk, seed=1337) - Es, eigen_modes = solve_eliashberg(gamma, g0_wk, Gamma_pp_const_k=gamma_const, - product=p.product, solver=p.solver, initial_delta=initial_delta) + Es, eigen_modes = solve_eliashberg(gamma, g0_wk, + product="FFT", solver=p.solver, initial_delta=initial_delta) return Es, eigen_modes @@ -65,9 +50,6 @@ def run_solve_eliashberg(p): Jp = 0.1, nk = 4, nw = 200, - fit_const = False, - big_factor = 2, - product = 'FFT', solver = 'PM', ) From 67a8509dc4aa3173eee6ceaf8c99a30022d9989a Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 12 Aug 2020 09:28:00 +0200 Subject: [PATCH 064/121] [eli] add test for preprocessing steps --- test/python/eliashberg/CMakeLists.txt | 1 + test/python/eliashberg/preprocessing_gamma.py | 58 +++++++++++++++++++ 2 files changed, 59 insertions(+) create mode 100644 test/python/eliashberg/preprocessing_gamma.py diff --git a/test/python/eliashberg/CMakeLists.txt b/test/python/eliashberg/CMakeLists.txt index 2f3066194..5980d197b 100644 --- a/test/python/eliashberg/CMakeLists.txt +++ b/test/python/eliashberg/CMakeLists.txt @@ -3,6 +3,7 @@ file(COPY ${CMAKE_CURRENT_SOURCE_DIR}/${all_tgz_files} DESTINATION ${CMAKE_CURRE set(PREFIX eliashberg-) +add_python_test(preprocessing_gamma ${PREFIX}) add_python_test(product_summation_vs_fft ${PREFIX}) add_python_test(eigenvalue_solver ${PREFIX}) add_python_test(previous_implementation ${PREFIX}) diff --git a/test/python/eliashberg/preprocessing_gamma.py b/test/python/eliashberg/preprocessing_gamma.py new file mode 100644 index 000000000..1a0450d6c --- /dev/null +++ b/test/python/eliashberg/preprocessing_gamma.py @@ -0,0 +1,58 @@ +import numpy as np + +from pytriqs.gf import MeshProduct, MeshImFreq, MeshBrillouinZone, MeshImTime, MeshCyclicLattice + +from triqs_tprf.ParameterCollection import ParameterCollection +from triqs_tprf.utilities import create_eliashberg_ingredients +from triqs_tprf.eliashberg import split_into_dynamic_wk_and_constant_k, dynamic_and_constant_to_tr + +def test_split_into_dynamic_wk_and_constant_k_mesh_types(gamma): + gamma_dyn, gamma_const = split_into_dynamic_wk_and_constant_k(gamma) + + assert type(gamma_dyn.mesh) == MeshProduct + assert type(gamma_dyn.mesh[0]) == MeshImFreq + assert type(gamma_dyn.mesh[1]) == MeshBrillouinZone + + assert type(gamma_const.mesh) == MeshBrillouinZone + +def test_split_into_dynamic_wk_and_constant_k_mesh_values(gamma, U_c, U_s): + gamma_dyn, gamma_const = split_into_dynamic_wk_and_constant_k(gamma) + + analytical_constant_expression = 0.5*(U_s + U_c) + np.testing.assert_allclose(gamma_const.data[0], analytical_constant_expression) + + gamma_without_constant_part = gamma.data - analytical_constant_expression + np.testing.assert_allclose(gamma_without_constant_part, gamma_dyn.data, atol=1e-12) + +def test_dynamic_and_constant_to_tr_mesh_types(gamma): + gamma_dyn, gamma_const = split_into_dynamic_wk_and_constant_k(gamma) + gamma_dyn_tr, gamma_const_r = dynamic_and_constant_to_tr(gamma_dyn, gamma_const) + + assert type(gamma_dyn_tr.mesh) == MeshProduct + assert type(gamma_dyn_tr.mesh[0]) == MeshImTime + assert type(gamma_dyn_tr.mesh[1]) == MeshCyclicLattice + + assert type(gamma_const_r.mesh) == MeshCyclicLattice + +if __name__ == '__main__': + p = ParameterCollection( + dim = 1, + norb = 2, + t = 2.0, + mu = 0.0, + beta = 5, + U = 1.0, + Up = 0.8, + J = 0.1, + Jp = 0.1, + nk = 3, + nw = 500, + ) + eliashberg_ingredients = create_eliashberg_ingredients(p) + gamma = eliashberg_ingredients.gamma + U_c = eliashberg_ingredients.U_c + U_s = eliashberg_ingredients.U_s + + test_split_into_dynamic_wk_and_constant_k_mesh_types(gamma) + test_split_into_dynamic_wk_and_constant_k_mesh_values(gamma, U_c, U_s) + test_dynamic_and_constant_to_tr_mesh_types(gamma) From 6776f780c2cc94eebcbcaff1abf0b8620ce35d8c Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 12 Aug 2020 09:28:43 +0200 Subject: [PATCH 065/121] [eli] add test for testing gamma creation --- c++/triqs_tprf/lattice/eliashberg.hpp | 1 + python/triqs_tprf/lattice_desc.py | 2 + test/python/eliashberg/CMakeLists.txt | 1 + test/python/eliashberg/gamma_creation.py | 75 ++++++++++++++++++++++++ 4 files changed, 79 insertions(+) create mode 100644 test/python/eliashberg/gamma_creation.py diff --git a/c++/triqs_tprf/lattice/eliashberg.hpp b/c++/triqs_tprf/lattice/eliashberg.hpp index de02554e6..c685ad040 100644 --- a/c++/triqs_tprf/lattice/eliashberg.hpp +++ b/c++/triqs_tprf/lattice/eliashberg.hpp @@ -144,4 +144,5 @@ namespace triqs_tprf { */ chi_wk_t gamma_PP_triplet(chi_wk_vt chi_c, chi_wk_vt chi_s, array_view, 4> U_c, array_view, 4> U_s); + chi_wk_t gamma_PP_spin_charge(chi_wk_vt chi_c, chi_wk_vt chi_s, array_view, 4> U_c, array_view, 4> U_s, double charge_factor, double spin_factor); } diff --git a/python/triqs_tprf/lattice_desc.py b/python/triqs_tprf/lattice_desc.py index be50f308a..110d4860d 100644 --- a/python/triqs_tprf/lattice_desc.py +++ b/python/triqs_tprf/lattice_desc.py @@ -571,6 +571,8 @@ out :math:`\Gamma^{(\mathrm{triplet})}_{a\bar{b}c\bar{d}}(\mathbf{k}, i\omega_n)`""") +module.add_function ("triqs_tprf::chi_wk_t triqs_tprf::gamma_PP_spin_charge (triqs_tprf::chi_wk_vt chi_c, triqs_tprf::chi_wk_vt chi_s, array_view,4> U_c, array_view,4> U_s, double charge_factor, double spin_factor)", doc = r"""""") + module.add_function ("array,6> triqs_tprf::cluster_mesh_fourier_interpolation (array k_vecs, triqs_tprf::chi_wr_cvt chi)", doc = r"""""") module.add_function ("triqs_tprf::chi_tr_t triqs_tprf::chi0_tr_from_grt_PH (triqs_tprf::g_tr_cvt g_tr)", doc = r"""Generalized susceptibility imaginary time bubble in the particle-hole channel :math:`\chi^{(0)}_{\bar{a}b\bar{c}d}(\tau, \mathbf{r})` diff --git a/test/python/eliashberg/CMakeLists.txt b/test/python/eliashberg/CMakeLists.txt index 5980d197b..23f56b532 100644 --- a/test/python/eliashberg/CMakeLists.txt +++ b/test/python/eliashberg/CMakeLists.txt @@ -4,6 +4,7 @@ file(COPY ${CMAKE_CURRENT_SOURCE_DIR}/${all_tgz_files} DESTINATION ${CMAKE_CURRE set(PREFIX eliashberg-) add_python_test(preprocessing_gamma ${PREFIX}) +add_python_test(gamma_creation ${PREFIX}) add_python_test(product_summation_vs_fft ${PREFIX}) add_python_test(eigenvalue_solver ${PREFIX}) add_python_test(previous_implementation ${PREFIX}) diff --git a/test/python/eliashberg/gamma_creation.py b/test/python/eliashberg/gamma_creation.py new file mode 100644 index 000000000..9701feb37 --- /dev/null +++ b/test/python/eliashberg/gamma_creation.py @@ -0,0 +1,75 @@ +import numpy as np + +from triqs_tprf.ParameterCollection import ParameterCollection +from triqs_tprf.utilities import create_eliashberg_ingredients +from pytriqs.gf import MeshProduct, MeshImFreq, MeshBrillouinZone + +from triqs_tprf.lattice import gamma_PP_spin_charge, gamma_PP_singlet, gamma_PP_triplet + +def test_gamma_PP_spin_charge_mesh_types(chi_c, chi_s, U_c, U_s): + gamma = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, 0.0, 0.0) + assert type(gamma.mesh) == MeshProduct + assert type(gamma.mesh[0]) == MeshImFreq + assert type(gamma.mesh[1]) == MeshBrillouinZone + +def test_gamma_PP_spin_charge_zero_input(chi_c, chi_s, U_c, U_s): + gamma = gamma_PP_spin_charge(0.0*chi_c, 0.0*chi_s, 0.0*U_c, 0.0*U_s, 0.0, 0.0) + np.testing.assert_equal(gamma.data, 0) + +def test_gamma_PP_spin_charge_only_constant(chi_c, chi_s, U_c, U_s): + gamma = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, 0.0, 0.0) + np.testing.assert_equal(gamma.data[0, 0], 0.5*(U_c + U_s)) + +def test_gamma_PP_singlet_mesh_type(chi_c, chi_s, U_c, U_s): + gamma_singlet = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) + assert type(gamma_singlet.mesh) == MeshProduct + assert type(gamma_singlet.mesh[0]) == MeshImFreq + assert type(gamma_singlet.mesh[1]) == MeshBrillouinZone + +def test_gamma_PP_singlet_value(chi_c, chi_s, U_c, U_s): + gamma = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, -0.5, 1.5) + gamma_singlet = gamma_PP_singlet(chi_c, chi_s, U_c, U_s) + np.testing.assert_equal(gamma.data, gamma_singlet.data) + +def test_gamma_PP_triplet_mesh_type(chi_c, chi_s, U_c, U_s): + gamma_triplet = gamma_PP_triplet(chi_c, chi_s, U_c, U_s) + assert type(gamma_triplet.mesh) == MeshProduct + assert type(gamma_triplet.mesh[0]) == MeshImFreq + assert type(gamma_triplet.mesh[1]) == MeshBrillouinZone + +def test_gamma_PP_triplet_value(chi_c, chi_s, U_c, U_s): + gamma = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, -0.5, -0.5) + gamma_triplet = gamma_PP_triplet(chi_c, chi_s, U_c, U_s) + np.testing.assert_equal(gamma.data, gamma_triplet.data) + +if __name__ == "__main__": + p = ParameterCollection( + dim = 2, + norb = 2, + t1 = 1.0, + t2 = 0.5, + t12 = 0.1, + t21 = 0.1, + mu = 0.1, + beta = 1, + U = 1.0, + Up = 0.8, + J = 0.1, + Jp = 0.1, + nk = 3, + nw = 50, + ) + + eliashberg_ingredients = create_eliashberg_ingredients(p) + chi_c = eliashberg_ingredients.chi_c + chi_s = eliashberg_ingredients.chi_s + U_c = eliashberg_ingredients.U_c + U_s = eliashberg_ingredients.U_s + + test_gamma_PP_spin_charge_mesh_types(chi_c, chi_s, U_c, U_s) + test_gamma_PP_spin_charge_zero_input(chi_c, chi_s, U_c, U_s) + test_gamma_PP_spin_charge_only_constant(chi_c, chi_s, U_c, U_s) + test_gamma_PP_singlet_mesh_type(chi_c, chi_s, U_c, U_s) + test_gamma_PP_singlet_value(chi_c, chi_s, U_c, U_s) + test_gamma_PP_triplet_mesh_type(chi_c, chi_s, U_c, U_s) + test_gamma_PP_triplet_value(chi_c, chi_s, U_c, U_s) From 7a633a476adeda729abec9513c05e1684cd80956 Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 12 Aug 2020 12:54:20 +0200 Subject: [PATCH 066/121] [eli] refactor tests --- python/triqs_tprf/utilities.py | 11 ++ test/python/eliashberg/eigenvalue_solver.py | 33 ++-- .../fft_product_constant_vs_full.py | 34 ++-- .../eliashberg/previous_implementation.py | 142 +++++++-------- .../previous_implementation_two_band.py | 133 +++++++-------- .../eliashberg/product_summation_vs_fft.py | 161 ++++++++---------- test/python/eliashberg/symmetrize_delta.py | 139 ++++++++------- 7 files changed, 307 insertions(+), 346 deletions(-) diff --git a/python/triqs_tprf/utilities.py b/python/triqs_tprf/utilities.py index 1f41fa482..a93b9971b 100644 --- a/python/triqs_tprf/utilities.py +++ b/python/triqs_tprf/utilities.py @@ -197,5 +197,16 @@ def create_eliashberg_ingredients(p): gamma = gamma, U_s = U_s, U_c = U_c, + chi_s = chi_s, + chi_c = chi_c, ) return eliashberg_ingredients + +# ---------------------------------------------------------------------- +def assert_parameter_collection_not_equal_model_parameters(p1, p2, model_parameters): + for model_parameter in model_parameters: + value1, value2 = p1[model_parameter], p2[model_parameter] + if value1 != value2: + error = 'The model of the benchmark and the one used now are not the same.\n' + error += '\t\tNow: {0} = {1}, benchmark: {0} = {2}.'.format(model_parameter, value1, value2) + raise AssertionError, error diff --git a/test/python/eliashberg/eigenvalue_solver.py b/test/python/eliashberg/eigenvalue_solver.py index 3d207c061..46cb0b6d2 100644 --- a/test/python/eliashberg/eigenvalue_solver.py +++ b/test/python/eliashberg/eigenvalue_solver.py @@ -23,17 +23,17 @@ # ---------------------------------------------------------------------- -def run_solve_eliashberg(p): - eliashberg_ingredients = create_eliashberg_ingredients(p) - g0_wk = eliashberg_ingredients.g0_wk - gamma = eliashberg_ingredients.gamma - +def test_equality_of_eigenvalue_solvers(g0_wk, gamma): initial_delta = semi_random_initial_delta(g0_wk, seed=1337) - Es, eigen_modes = solve_eliashberg(gamma, g0_wk, - product="FFT", solver=p.solver, initial_delta=initial_delta) - - return Es, eigen_modes + Es_PM, eigen_modes_PM = solve_eliashberg(gamma, g0_wk, product="FFT", solver="PM", initial_delta=initial_delta) + Es_IRAM, eigen_modes_IRAM = solve_eliashberg(gamma, g0_wk, product="FFT", solver="IRAM", initial_delta=initial_delta) + + np.testing.assert_allclose(Es_PM[0], Es_IRAM[0]) + assert allclose_by_scalar_multiplication(eigen_modes_PM[0], eigen_modes_IRAM[0]),\ + "Eigenvectors are not the same." + + print('Both solvers yield the same results.') #================================================================================ if __name__ == '__main__': @@ -52,15 +52,8 @@ def run_solve_eliashberg(p): nw = 200, solver = 'PM', ) + eliashberg_ingredients = create_eliashberg_ingredients(p) + g0_wk = eliashberg_ingredients.g0_wk + gamma = eliashberg_ingredients.gamma - Es_pm, eigen_modes_pm = run_solve_eliashberg(p) - - Es_iram, eigen_modes_iram = run_solve_eliashberg(p.alter(solver='IRAM')) - - print(Es_pm[0], Es_iram[0]) - np.testing.assert_allclose(Es_pm[0], Es_iram[0]) - - assert allclose_by_scalar_multiplication(eigen_modes_pm[0], eigen_modes_iram[0]),\ - "Eigenvectors are not the same." - - print('Both solvers yield the same results.') + test_equality_of_eigenvalue_solvers(g0_wk, gamma) diff --git a/test/python/eliashberg/fft_product_constant_vs_full.py b/test/python/eliashberg/fft_product_constant_vs_full.py index b0f268f27..fc6244eda 100644 --- a/test/python/eliashberg/fft_product_constant_vs_full.py +++ b/test/python/eliashberg/fft_product_constant_vs_full.py @@ -24,6 +24,21 @@ # ---------------------------------------------------------------------- +def test_eliashberg_product_fft_constant(g0_wk, gamma): + gamma.data[:] = np.random.rand(*gamma.data.shape[1:]) + gamma_dyn_tr, gamma_const_r = preprocess_gamma_for_fft(gamma) + + initial_delta = semi_random_initial_delta(g0_wk) + + delta_1 = eliashberg_product_fft_constant(gamma_const_r, g0_wk, initial_delta) + delta_2 = eliashberg_product_fft(gamma_dyn_tr, gamma_const_r, g0_wk, initial_delta) + + np.testing.assert_allclose(delta_1.data, delta_2.data) + + print('The functions eliashberg_product_fft and eliashberg_product_fft_constant' + ' yield the same result for a Gamma that is only constant in momentum space.' + '\nThe function split_into_dynamic_wk_and_constant_k therefore also worked correcty.') + if __name__ == '__main__': p = ParameterCollection( @@ -39,23 +54,8 @@ nk = 4, nw = 200, ) - eliashberg_ingredients = create_eliashberg_ingredients(p) g0_wk = eliashberg_ingredients.g0_wk - - wmesh_boson = MeshImFreq(beta=p.beta, S='Boson', n_max=p.nw) - gamma_pp_wk = Gf(mesh=MeshProduct(wmesh_boson, g0_wk.mesh[1]), - target_shape=g0_wk.target_shape*2) - gamma_pp_wk.data[:] = np.random.rand(p.nk**2, 1, 1, 1, 1) - gamma_pp_dyn_tr, gamma_pp_const_r = preprocess_gamma_for_fft(gamma_pp_wk) - - initial_delta = semi_random_initial_delta(g0_wk) + gamma = eliashberg_ingredients.gamma - delta_1 = eliashberg_product_fft_constant(gamma_pp_const_r, g0_wk, initial_delta) - delta_2 = eliashberg_product_fft(gamma_pp_dyn_tr, gamma_pp_const_r, g0_wk, initial_delta) - - np.testing.assert_allclose(delta_1.data, delta_2.data) - - print('The functions eliashberg_product_fft and eliashberg_product_fft_constant' - ' yield the same result for a Gamma that is only constant in momentum space.' - '\nThe function split_into_dynamic_wk_and_constant_k therefore also worked correcty.') + test_eliashberg_product_fft_constant(g0_wk, gamma) diff --git a/test/python/eliashberg/previous_implementation.py b/test/python/eliashberg/previous_implementation.py index 8834d1cc3..f2f7d98eb 100644 --- a/test/python/eliashberg/previous_implementation.py +++ b/test/python/eliashberg/previous_implementation.py @@ -5,16 +5,10 @@ # ---------------------------------------------------------------------- -import itertools - -# ---------------------------------------------------------------------- - import numpy as np # ---------------------------------------------------------------------- -from pytriqs.gf import MeshImFreq - from triqs_tprf.ParameterCollection import ParameterCollection from triqs_tprf.utilities import create_eliashberg_ingredients from triqs_tprf.lattice import eliashberg_product @@ -22,79 +16,71 @@ # ---------------------------------------------------------------------- -from triqs_tprf.utilities import write_TarGZ_HDFArchive, read_TarGZ_HDFArchive, show_version_info +from triqs_tprf.utilities import assert_parameter_collection_not_equal_model_parameters, write_TarGZ_HDFArchive, read_TarGZ_HDFArchive, show_version_info import triqs_tprf.version as version # ---------------------------------------------------------------------- -p = ParameterCollection( - filename = 'eliashberg_benchmark_new.tar.gz', - dim = 2, - norb = 1, - t = 1.0, - mu = 0.0, - beta = 1, - U = 1.0, - Up = 0.0, - J = 0.0, - Jp = 0.0, - nk = 2, - nw = 100, - version_info = version.info, - ) - -eliashberg_ingredients = create_eliashberg_ingredients(p) -g0_wk = eliashberg_ingredients.g0_wk -gamma = eliashberg_ingredients.gamma -U_c = eliashberg_ingredients.U_c -U_s = eliashberg_ingredients.U_s - -## A bigger w-mesh is needed to construct a Gamma with a twice as big w-mesh than GF -big_nw = 2*p.nw + 1 -eliashberg_ingredients_big = create_eliashberg_ingredients(p.alter(nw=big_nw)) -gamma_big = eliashberg_ingredients_big.gamma - -# -- Setup model, RPA susceptibilities and spin/charge interaction - -# -- The output of the following functions shall be tested -next_delta = eliashberg_product(gamma_big, g0_wk, g0_wk) -E, eigen_modes = solve_eliashberg(gamma_big, g0_wk, product='SUM', solver='IRAM') - -# -- Save results - -p.gamma = gamma -p.next_delta = next_delta -p.E = E[0] -p.eigen_mode = eigen_modes[0] - -write_TarGZ_HDFArchive(p.filename, p=p) - -# -- Load benchmark data - -filename = './eliashberg_benchmark.tar.gz' -p_benchmark = read_TarGZ_HDFArchive(filename)['p'] - -# -- Check if the benchmark data was calculated for the same model, -# -- otherwise a comparison does not make sense. - -model_parameters = ['dim', 'norb', 't', 'mu', 'beta', 'U'] - -for model_parameter in model_parameters: - run_time, benchmark = p[model_parameter], p_benchmark[model_parameter] - if run_time != benchmark: - error = 'The model of the benchmark and the one used now are not the same.\n' - error += '\t\tNow: {0} = {1}, benchmark: {0} = {2}.'.format(model_parameter, run_time, - benchmark) - raise AssertionError, error - -# -- Compare the results. Raise an error if the are not the same within a tolerance. - -print('\nThe benchmark data was obtained with %s.'%show_version_info(p_benchmark.version_info)) - -np.testing.assert_allclose(p_benchmark.gamma.data, p.gamma.data) -np.testing.assert_allclose(p_benchmark.next_delta.data, p.next_delta.data) -np.testing.assert_allclose(p_benchmark.E, p.E) -assert allclose_by_scalar_multiplication(p_benchmark.eigen_mode, p.eigen_mode),\ - "Eigenvectors are not the same." - -print('\nThis (new) version with %s yields the same results!'%show_version_info(p.version_info)) +def save_new_benchmarks(filename, p): + eliashberg_ingredients = create_eliashberg_ingredients(p) + g0_wk = eliashberg_ingredients.g0_wk + big_nw = 2*p.nw + 1 + eliashberg_ingredients_big = create_eliashberg_ingredients(p.alter(nw=big_nw)) + gamma_big = eliashberg_ingredients_big.gamma + + next_delta = eliashberg_product(gamma_big, g0_wk, g0_wk) + Es, eigen_modes = solve_eliashberg(gamma_big, g0_wk, product='SUM', solver='IRAM') + + p.next_delta = next_delta + p.E = Es[0] + p.eigen_mode = eigen_modes[0] + + write_TarGZ_HDFArchive(filename, p=p) + +def test_next_delta(g0_wk, gamma_big, expected_next_delta): + next_delta = eliashberg_product(gamma_big, g0_wk, g0_wk) + np.testing.assert_allclose(next_delta.data, expected_next_delta.data) + +def test_solve_eliashberg(g0_wk, gamma_big, expected_E, expected_eigen_mode): + Es, eigen_modes = solve_eliashberg(gamma_big, g0_wk, product='SUM', solver='IRAM') + np.testing.assert_allclose(Es[0], expected_E) + assert allclose_by_scalar_multiplication(eigen_modes[0], expected_eigen_mode),\ + "Eigenvectors are not the same." + + +if __name__ == "__main__": + p = ParameterCollection( + benchmark_filename = "./eliashberg_benchmark.tar.gz", + filename = 'eliashberg_benchmark_new.tar.gz', + dim = 2, + norb = 1, + t = 1.0, + mu = 0.0, + beta = 1, + U = 1.0, + Up = 0.0, + J = 0.0, + Jp = 0.0, + nk = 2, + nw = 100, + version_info = version.info, + ) + + #save_new_benchmarks(p.filename, p) + + p_benchmark = read_TarGZ_HDFArchive(p.benchmark_filename)['p'] + model_parameters_to_test = ['dim', 'norb', 't', 'mu', 'beta', 'U'] + assert_parameter_collection_not_equal_model_parameters(p, p_benchmark, model_parameters_to_test) + + eliashberg_ingredients = create_eliashberg_ingredients(p) + g0_wk = eliashberg_ingredients.g0_wk + # For the eliashberg SUM procedure a Gamma with a twice as big w-mesh then the GF is needed. + big_nw = 2*p.nw + 1 + eliashberg_ingredients_big = create_eliashberg_ingredients(p.alter(nw=big_nw)) + gamma_big = eliashberg_ingredients_big.gamma + + test_next_delta(g0_wk, gamma_big, p_benchmark.next_delta) + test_solve_eliashberg(g0_wk, gamma_big, p_benchmark.E, p_benchmark.eigen_mode) + + print('\nThe benchmark data was obtained with %s.'%show_version_info(p_benchmark.version_info)) + print('\nThis (new) version with %s yields the same results!'%show_version_info(p.version_info)) diff --git a/test/python/eliashberg/previous_implementation_two_band.py b/test/python/eliashberg/previous_implementation_two_band.py index 1ed48a55f..63113010b 100644 --- a/test/python/eliashberg/previous_implementation_two_band.py +++ b/test/python/eliashberg/previous_implementation_two_band.py @@ -28,77 +28,70 @@ # ---------------------------------------------------------------------- -from triqs_tprf.utilities import write_TarGZ_HDFArchive, read_TarGZ_HDFArchive, show_version_info +from triqs_tprf.utilities import assert_parameter_collection_not_equal_model_parameters, write_TarGZ_HDFArchive, read_TarGZ_HDFArchive, show_version_info import triqs_tprf.version as version # ---------------------------------------------------------------------- -p = ParameterCollection( - filename = 'eliashberg_benchmark_two_band_new.tar.gz', - dim = 2, - norb = 2, - t1 = 1.0, - t2 = 0.5, - t12 = 0.1, - t21 = 0.1, - mu = 0.0, - beta = 1, - U = 1.0, - Up = 0.0, - J = 0.0, - Jp = 0.0, - nk = 2, - nw = 100, - version_info = version.info, - ) - -eliashberg_ingredients = create_eliashberg_ingredients(p) -g0_wk = eliashberg_ingredients.g0_wk -gamma = eliashberg_ingredients.gamma - -Gamma_pp_dyn_tr, Gamma_pp_const_r = preprocess_gamma_for_fft(gamma) -# -- The output of the following functions shall be tested -next_delta = eliashberg_product_fft(Gamma_pp_dyn_tr, Gamma_pp_const_r, g0_wk, g0_wk) -E, eigen_modes = solve_eliashberg(gamma, g0_wk, product='FFT', solver='IRAM') - -# -- Save results - -p.gamma = gamma -p.next_delta = next_delta -p.E = E[0] -p.eigen_mode = eigen_modes[0] - -write_TarGZ_HDFArchive(p.filename, p=p) - -# -- Load benchmark data - -filename = './eliashberg_benchmark_two_band.tar.gz' -p_benchmark = read_TarGZ_HDFArchive(filename)['p'] - -# -- Check if the benchmark data was calculated for the same model, -# -- otherwise a comparison does not make sense. - -model_parameters = ['dim', 'norb', 't1', 't2', 't12', 't21', 'mu', 'beta', 'U'] - -for model_parameter in model_parameters: - try: - run_time, benchmark = p[model_parameter], p_benchmark[model_parameter] - except KeyError: - raise AssertionError, "The model parameter %s does not exist."%model_parameter - if (run_time != benchmark): - error = 'The model of the benchmark and the one used now are not the same.\n' - error += '\t\tNow: {0} = {1}, benchmark: {0} = {2}.'.format(model_parameter, run_time, - benchmark) - raise AssertionError, error - -# -- Compare the results. Raise an error if the are not the same within a tolerance. - -print('\nThe benchmark data was obtained with %s.'%show_version_info(p_benchmark.version_info)) - -np.testing.assert_allclose(p_benchmark.gamma.data, p.gamma.data, atol=1e-9) -np.testing.assert_allclose(p_benchmark.next_delta.data, p.next_delta.data, atol=1e-9) -np.testing.assert_allclose(p_benchmark.E, p.E) -assert allclose_by_scalar_multiplication(p_benchmark.eigen_mode, p.eigen_mode),\ - "Eigenvectors are not the same." - -print('\nThis (new) version with %s yields the same results!'%show_version_info(p.version_info)) +def save_new_benchmarks(filename, p): + eliashberg_ingredients = create_eliashberg_ingredients(p) + g0_wk = eliashberg_ingredients.g0_wk + gamma = eliashberg_ingredients.gamma + + Gamma_pp_dyn_tr, Gamma_pp_const_r = preprocess_gamma_for_fft(gamma) + next_delta = eliashberg_product_fft(Gamma_pp_dyn_tr, Gamma_pp_const_r, g0_wk, g0_wk) + Es, eigen_modes = solve_eliashberg(gamma, g0_wk, product='FFT', solver='IRAM') + + p.next_delta = next_delta + p.E = Es[0] + p.eigen_mode = eigen_modes[0] + + write_TarGZ_HDFArchive(filename, p=p) + +def test_next_delta(g0_wk, gamma, expected_next_delta): + Gamma_pp_dyn_tr, Gamma_pp_const_r = preprocess_gamma_for_fft(gamma) + next_delta = eliashberg_product_fft(Gamma_pp_dyn_tr, Gamma_pp_const_r, g0_wk, g0_wk) + np.testing.assert_allclose(next_delta.data, expected_next_delta.data) + +def test_solve_eliashberg(g0_wk, gamma, expected_E, expected_eigen_mode): + Es, eigen_modes = solve_eliashberg(gamma, g0_wk, product='FFT', solver='IRAM') + np.testing.assert_allclose(Es[0], expected_E) + assert allclose_by_scalar_multiplication(eigen_modes[0], expected_eigen_mode),\ + "Eigenvectors are not the same." + +if __name__ == "__main__": + p = ParameterCollection( + filename = 'eliashberg_benchmark_two_band_new.tar.gz', + benchmark_filename = './eliashberg_benchmark_two_band.tar.gz', + dim = 2, + norb = 2, + t1 = 1.0, + t2 = 0.5, + t12 = 0.1, + t21 = 0.1, + mu = 0.0, + beta = 1, + U = 1.0, + Up = 0.0, + J = 0.0, + Jp = 0.0, + nk = 2, + nw = 100, + version_info = version.info, + ) + + #save_new_benchmarks(p.filename, p) + + p_benchmark = read_TarGZ_HDFArchive(p.benchmark_filename)['p'] + model_parameters_to_test = ['dim', 'norb', 't1', 't2', 't12', 't21', 'mu', 'beta', 'U'] + assert_parameter_collection_not_equal_model_parameters(p, p_benchmark, model_parameters_to_test) + + eliashberg_ingredients = create_eliashberg_ingredients(p) + g0_wk = eliashberg_ingredients.g0_wk + gamma = eliashberg_ingredients.gamma + + test_next_delta(g0_wk, gamma, p_benchmark.next_delta) + test_solve_eliashberg(g0_wk, gamma, p_benchmark.E, p_benchmark.eigen_mode) + + print('\nThe benchmark data was obtained with %s.'%show_version_info(p_benchmark.version_info)) + print('\nThis (new) version with %s yields the same results!'%show_version_info(p.version_info)) diff --git a/test/python/eliashberg/product_summation_vs_fft.py b/test/python/eliashberg/product_summation_vs_fft.py index 786fe6dde..d0b489c7e 100644 --- a/test/python/eliashberg/product_summation_vs_fft.py +++ b/test/python/eliashberg/product_summation_vs_fft.py @@ -6,16 +6,14 @@ # ---------------------------------------------------------------------- -import itertools - -# ---------------------------------------------------------------------- - import numpy as np +from pytriqs.plot.mpl_interface import oplot, plt +import warnings # ---------------------------------------------------------------------- from triqs_tprf.ParameterCollection import ParameterCollection -from pytriqs.gf import Gf, MeshImFreq, Idx +from pytriqs.gf import Idx from triqs_tprf.utilities import create_eliashberg_ingredients from triqs_tprf.lattice import eliashberg_product, eliashberg_product_fft from triqs_tprf.eliashberg import semi_random_initial_delta, preprocess_gamma_for_fft @@ -25,7 +23,6 @@ def compare_deltas(deltas_1, deltas_2=None, static=False): """ Build comparison matrix of list of Gf """ - if not deltas_2: deltas_2 = deltas_1 @@ -45,7 +42,6 @@ def compare_deltas(deltas_1, deltas_2=None, static=False): def print_diff(diff): """ Print output of 'compare_deltas' more readable """ - i_max, j_max = diff.shape s = "" @@ -54,101 +50,96 @@ def print_diff(diff): s += dashes for i in range(i_max): - for j in range(j_max): - s += np.format_float_scientific(diff[i,j], precision=2, pad_left=3) s += "\t" - s += "\n" s += dashes print(s) -def compare_next_delta(p): - eliashberg_ingredients = create_eliashberg_ingredients(p) - g0_wk = eliashberg_ingredients.g0_wk - gamma = eliashberg_ingredients.gamma - U_c = eliashberg_ingredients.U_c - U_s = eliashberg_ingredients.U_s +def test_eliashberg_product_for_same_initital_delta(g0_wk, gamma, gamma_big): + initial_delta = semi_random_initial_delta(g0_wk, seed=1337) - ## A bigger w-mesh is needed to construct a Gamma with a twice as big w-mesh than GF - big_nw = 2*p.nw + 1 - eliashberg_ingredients_big = create_eliashberg_ingredients(p.alter(nw=big_nw)) - gamma_big = eliashberg_ingredients_big.gamma + next_delta_summation = eliashberg_product(gamma_big, g0_wk, initial_delta) - # -- Preprocess gamma for the FFT implementations - if p.fit_const: - gamma_dyn_tr, gamma_const_r = preprocess_gamma_for_fft(gamma, None) - else: - gamma_dyn_tr, gamma_const_r = preprocess_gamma_for_fft(gamma, 0.5*(U_s + U_c)) + gamma_dyn_tr, gamma_const_r = preprocess_gamma_for_fft(gamma) + next_delta_fft = eliashberg_product_fft(gamma_dyn_tr, gamma_const_r, g0_wk, initial_delta) - # -- Creating Semi-Random input Delta - v0 = semi_random_initial_delta(g0_wk, nr_factor=p.nr_factor, seed=1337) - p.v0 = v0 + diff = compare_deltas([next_delta_summation, next_delta_fft]) - # -- Test the Eliashberg product - print('Start the summation') - next_delta = eliashberg_product(gamma_big, g0_wk, p.v0) - print('Start the FFT') - next_delta_fft = eliashberg_product_fft(gamma_dyn_tr, gamma_const_r, g0_wk, p.v0) + print_diff(diff) + np.testing.assert_allclose(diff, 0, atol=p.atol) + print('The summation and FFT implementation of the eliashberg product' + ' both yield the same result.') +def test_eliashberg_product_for_different_initital_delta(g0_wk, gamma, gamma_big): + initial_delta = semi_random_initial_delta(g0_wk, seed=1337) - deltas = [v0, next_delta, next_delta_fft] + next_delta_summation = eliashberg_product(gamma_big, g0_wk, initial_delta) - if p.plot: + gamma_dyn_tr, gamma_const_r = preprocess_gamma_for_fft(gamma) + initial_delta = semi_random_initial_delta(g0_wk, seed=1338) + next_delta_fft = eliashberg_product_fft(gamma_dyn_tr, gamma_const_r, g0_wk, initial_delta) - from pytriqs.plot.mpl_interface import oplot, plt - import warnings - warnings.filterwarnings("ignore") #ignore some matplotlib warnings - subp = [4, 3, 1] - fig = plt.figure(figsize=(18, 15)) + diff = compare_deltas([next_delta_summation, next_delta_fft]) - titles = ['Input', 'Summation', 'FFT'] + print_diff(diff) + try: + np.testing.assert_allclose(diff, 0, atol=p.atol) + raise ValueError + except AssertionError: + print('The summation and FFT implementation of the eliashberg product' + ' both yield DIFFERENT results, as expected when using a different inital delta.') - for k_point in [Idx(0,0,0), Idx(1,0,0)]: +def plot_output(g0_wk, gamma): + initial_delta = semi_random_initial_delta(g0_wk) - ax = plt.subplot(*subp); subp[-1] += 1 - oplot(g0_wk[:, k_point]) - plt.title('GF') + next_delta_summation = eliashberg_product(gamma_big, g0_wk, initial_delta) - ax = plt.subplot(*subp); subp[-1] += 1 - oplot(gamma[:, k_point]) - plt.title('Gamma') + gamma_dyn_tr, gamma_const_r = preprocess_gamma_for_fft(gamma) + next_delta_fft = eliashberg_product_fft(gamma_dyn_tr, gamma_const_r, g0_wk, initial_delta) - ax = plt.subplot(*subp); subp[-1] += 1 - oplot(gamma_dyn_tr[:, k_point]) - plt.title('Gamma dyn tr') + deltas = [initial_delta, next_delta_summation, next_delta_fft] - for delta, title in zip(deltas, titles): + warnings.filterwarnings("ignore") #ignore some matplotlib warnings + subp = [4, 3, 1] + fig = plt.figure(figsize=(18, 15)) - ax = plt.subplot(*subp); subp[-1] += 1 - oplot(delta[:, k_point]) - plt.title(title) + titles = ['Input', 'Summation', 'FFT'] - ax.legend_ = None + for k_point in [Idx(0,0,0), Idx(1,0,0)]: - plt.show() + ax = plt.subplot(*subp); subp[-1] += 1 + oplot(g0_wk[:, k_point]) + plt.title('GF') - diff = compare_deltas(deltas[1:]) + ax = plt.subplot(*subp); subp[-1] += 1 + oplot(gamma[:, k_point]) + plt.title('Gamma') - print_diff(diff) - try: - np.testing.assert_allclose(diff, 0, atol=p.atol) - except AssertionError as e: - print('The test failed for the parameter set:') - p.__dict__.pop("v0") - print(p) - raise e + ax = plt.subplot(*subp); subp[-1] += 1 + oplot(gamma_dyn_tr[:, k_point]) + plt.title('Gamma dyn tr') + + for delta, title in zip(deltas, titles): + + ax = plt.subplot(*subp); subp[-1] += 1 + oplot(delta[:, k_point]) + plt.title(title) - return deltas + ax.legend_ = None + + plt.show() #================================================================================ if __name__ == '__main__': - p = ParameterCollection( dim = 1, - norb = 1, - t = 2.0, + norb = 2, + t1 = 1.0, + t2 = 0.5, + t12 = 0.1, + t21 = 0.1, mu = 0.0, beta = 5, U = 1.0, @@ -157,27 +148,17 @@ def compare_next_delta(p): Jp = 0.1, nk = 3, nw = 150, - nr_factor = 0.5, - fit_const = False, - big_factor = 2, atol = 1e-8, - plot = False, ) - for norb in [1, 2]: - p.norb = norb - deltas = compare_next_delta(p) - - print('The summation and FFT implementation of the eliashberg product' - ' both yield the same result.') - - deltas_with_fit = compare_next_delta(p.alter(fit_const=True)) - - diff = compare_deltas(deltas[2:], deltas_with_fit[2:]) - - print('Compare explicit given constant vs. fit:') - - print_diff(diff) - np.testing.assert_allclose(diff, 0, atol=p.atol) + eliashberg_ingredients = create_eliashberg_ingredients(p) + g0_wk = eliashberg_ingredients.g0_wk + gamma = eliashberg_ingredients.gamma + # For the eliashberg SUM procedure a Gamma with a twice as big w-mesh then the GF is needed. + big_nw = 2*p.nw + 1 + eliashberg_ingredients_big = create_eliashberg_ingredients(p.alter(nw=big_nw)) + gamma_big = eliashberg_ingredients_big.gamma - print('Fitting the constant part works.') + test_eliashberg_product_for_same_initital_delta(g0_wk, gamma, gamma_big) + test_eliashberg_product_for_different_initital_delta(g0_wk, gamma, gamma_big) + #plot_output(g0_wk, gamma) diff --git a/test/python/eliashberg/symmetrize_delta.py b/test/python/eliashberg/symmetrize_delta.py index 675f33ef9..72fd348ec 100644 --- a/test/python/eliashberg/symmetrize_delta.py +++ b/test/python/eliashberg/symmetrize_delta.py @@ -10,6 +10,7 @@ # ---------------------------------------------------------------------- import numpy as np +import matplotlib.pyplot as plt # ---------------------------------------------------------------------- @@ -21,78 +22,74 @@ # ---------------------------------------------------------------------- -import matplotlib.pyplot as plt - -# ---------------------------------------------------------------------- - from triqs_tprf.symmetries import enforce_symmetry, check_symmetry # ---------------------------------------------------------------------- -p = ParameterCollection( - dim = 2, - norb = 2, - t1 = 1.0, - t2 = 0.5, - t12 = 0.1, - t21 = 0.1, - mu = 0.1, - beta = 1, - U = 1.0, - Up = 0.8, - J = 0.1, - Jp = 0.1, - nk = 3, - nw = 50, - plot=False - ) - -# -- Setup non-interacing GF and particle-particle vertex -eliashberg_ingredients = create_eliashberg_ingredients(p) -g0_wk = eliashberg_ingredients.g0_wk -gamma = eliashberg_ingredients.gamma - -# -- Test symmetrizing function on eliashberg -variables=["frequency", "momentum", "orbital"] - -# Use all combinations -symmetry_set = list(itertools.product(["even", "odd"], repeat=3)) - -translate_symmetries = {"even" : +1, "odd" : -1, None : None} - -for symmetries in symmetry_set: - symmetrize = functools.partial(enforce_symmetry, - variables=variables, - symmetries=symmetries) - - E, eigen_modes = solve_eliashberg(gamma, g0_wk, product='FFT', solver='IRAM', - symmetrize_fct=symmetrize) - - expected_symmetries = {variable : translate_symmetries[symmetry] \ - for (variable, symmetry) in zip(variables, symmetries)} - - for delta in eigen_modes: - produced_symmetries = check_symmetry(delta) - if not expected_symmetries == produced_symmetries: - raise AssertionError("Incorrect symmetries were produced.") - - if p.plot: - fig, axes = plt.subplots(3, 3) - - vmax = np.max(np.abs(delta[Idx(0),:].data)) - - for orb1, orb2 in itertools.product(range(p.norb), repeat=2): - shape = (p.nk, p.nk, p.norb, p.norb) - data = delta[Idx(0), :].data.reshape(shape) - plt.sca(axes[orb1,orb2]) - plt.imshow(data[:,:,orb1,orb2].real, cmap="RdBu_r", - vmax=vmax, vmin=-vmax) - plt.colorbar() - - plt.sca(axes[-1,-1]) - for orb1, orb2 in itertools.product(range(p.norb), repeat=2): - plt.plot(delta.data[:, 10, orb1, orb2].real) - plt.plot(delta.data[:, 10, orb1, orb2].imag) - - plt.show() - +def test_symmetry_of_symmetry_enforced_deltas(g0_wk, gamma): + variables = ["frequency", "momentum", "orbital"] + all_symmetries = list(itertools.product(["even", "odd"], repeat=3)) + + for symmetries in all_symmetries: + symmetrize_fct = functools.partial(enforce_symmetry, + variables=variables, + symmetries=symmetries) + + E, eigen_modes = solve_eliashberg(gamma, g0_wk, product='FFT', solver='IRAM', + symmetrize_fct=symmetrize_fct) + + translate_symmetries = {"even" : +1, "odd" : -1, None : None} + expected_symmetries = {variable : translate_symmetries[symmetry] \ + for (variable, symmetry) in zip(variables, symmetries)} + + for delta in eigen_modes: + produced_symmetries = check_symmetry(delta) + if not expected_symmetries == produced_symmetries: + raise AssertionError("Incorrect symmetries were produced.") + + #plot_delta(delta) + +def plot_delta(delta): + fig, axes = plt.subplots(3, 3) + + vmax = np.max(np.abs(delta[Idx(0),:].data)) + + for orb1, orb2 in itertools.product(range(p.norb), repeat=2): + shape = (p.nk, p.nk, p.norb, p.norb) + data = delta[Idx(0), :].data.reshape(shape) + plt.sca(axes[orb1,orb2]) + plt.imshow(data[:,:,orb1,orb2].real, cmap="RdBu_r", + vmax=vmax, vmin=-vmax) + plt.colorbar() + + plt.sca(axes[-1,-1]) + for orb1, orb2 in itertools.product(range(p.norb), repeat=2): + plt.plot(delta.data[:, 1, orb1, orb2].real) + plt.plot(delta.data[:, 1, orb1, orb2].imag) + + plt.show() + +if __name__ == "__main__": + p = ParameterCollection( + dim = 2, + norb = 2, + t1 = 1.0, + t2 = 0.5, + t12 = 0.1, + t21 = 0.1, + mu = 0.1, + beta = 1, + U = 1.0, + Up = 0.8, + J = 0.1, + Jp = 0.1, + nk = 3, + nw = 50, + plot=False + ) + + eliashberg_ingredients = create_eliashberg_ingredients(p) + g0_wk = eliashberg_ingredients.g0_wk + gamma = eliashberg_ingredients.gamma + + test_symmetry_of_symmetry_enforced_deltas(g0_wk, gamma) From 76322b727f9707d0017addd65d1ee1d045ff6fc6 Mon Sep 17 00:00:00 2001 From: Stefan Date: Wed, 12 Aug 2020 12:59:31 +0200 Subject: [PATCH 067/121] [eli] add test for semi_random_initial_delta --- test/python/eliashberg/CMakeLists.txt | 1 + .../eliashberg/semi_random_initial_delta.py | 47 +++++++++++++++++++ 2 files changed, 48 insertions(+) create mode 100644 test/python/eliashberg/semi_random_initial_delta.py diff --git a/test/python/eliashberg/CMakeLists.txt b/test/python/eliashberg/CMakeLists.txt index 23f56b532..b2f36d756 100644 --- a/test/python/eliashberg/CMakeLists.txt +++ b/test/python/eliashberg/CMakeLists.txt @@ -5,6 +5,7 @@ set(PREFIX eliashberg-) add_python_test(preprocessing_gamma ${PREFIX}) add_python_test(gamma_creation ${PREFIX}) +add_python_test(semi_random_initial_delta ${PREFIX}) add_python_test(product_summation_vs_fft ${PREFIX}) add_python_test(eigenvalue_solver ${PREFIX}) add_python_test(previous_implementation ${PREFIX}) diff --git a/test/python/eliashberg/semi_random_initial_delta.py b/test/python/eliashberg/semi_random_initial_delta.py new file mode 100644 index 000000000..b754ab1a1 --- /dev/null +++ b/test/python/eliashberg/semi_random_initial_delta.py @@ -0,0 +1,47 @@ +import numpy as np + +from triqs_tprf.ParameterCollection import ParameterCollection +from triqs_tprf.utilities import create_eliashberg_ingredients + +from triqs_tprf.eliashberg import semi_random_initial_delta + +def test_same_output_for_same_seed(g0_wk): + random_delta1 = semi_random_initial_delta(g0_wk, seed=1) + random_delta2 = semi_random_initial_delta(g0_wk, seed=1) + + np.testing.assert_equal(random_delta1.data, random_delta2.data) + +def test_different_output_for_different_seed(g0_wk): + random_delta1 = semi_random_initial_delta(g0_wk, seed=1) + random_delta2 = semi_random_initial_delta(g0_wk, seed=42) + + try: + np.testing.assert_equal(random_delta1.data, random_delta2.data) + raise ValueError + except AssertionError: + pass + +if __name__ == "__main__": + + p = ParameterCollection( + dim = 2, + norb = 2, + t1 = 1.0, + t2 = 0.5, + t12 = 0.1, + t21 = 0.1, + mu = 0.0, + beta = 1, + U = 0.0, + Up = 0.0, + J = 0.0, + Jp = 0.0, + nk = 2, + nw = 100, + ) + + eliashberg_ingredients = create_eliashberg_ingredients(p) + g0_wk = eliashberg_ingredients.g0_wk + + test_same_output_for_same_seed(g0_wk) + test_different_output_for_different_seed(g0_wk) From 73ab7d05722e15ff9a9519691e8a296feada61d4 Mon Sep 17 00:00:00 2001 From: Stefan Date: Thu, 13 Aug 2020 12:01:55 +0200 Subject: [PATCH 068/121] [cmake] allow `add_python_test` to handle prefixes --- test/CMakeLists.txt | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt index dea80bc45..d3f1270f1 100644 --- a/test/CMakeLists.txt +++ b/test/CMakeLists.txt @@ -3,9 +3,8 @@ # where my_script.py is the script macro(add_python_test test) get_filename_component(test_name ${test} NAME_WE) - get_filename_component(test_dir ${test} DIRECTORY) - add_test(NAME Py_${test_name} COMMAND ${TRIQS_PYTHON_INTERPRETER} ${CMAKE_CURRENT_SOURCE_DIR}/${test_dir}/${test_name}.py WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}/${test_dir}) - set_property(TEST Py_${test_name} APPEND PROPERTY ENVIRONMENT PYTHONPATH=${CMAKE_BINARY_DIR}/python:$ENV{PYTHONPATH} ${SANITIZER_RT_PRELOAD}) + add_test(NAME Py_${ARGN}${test_name} COMMAND ${TRIQS_PYTHON_INTERPRETER} ${CMAKE_CURRENT_SOURCE_DIR}/${test_name}.py WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}) + set_property(TEST Py_${ARGN}${test_name} APPEND PROPERTY ENVIRONMENT PYTHONPATH=${CMAKE_BINARY_DIR}/python:$ENV{PYTHONPATH} ${SANITIZER_RT_PRELOAD}) endmacro(add_python_test) add_subdirectory(c++) From d55c89d36ca6268fe74dc91c8e3ce13c6290e734 Mon Sep 17 00:00:00 2001 From: Stefan Date: Thu, 13 Aug 2020 12:54:14 +0200 Subject: [PATCH 069/121] [eli] update theory --- doc/theory/eliashberg.rst | 428 +++++++++++--------------------------- 1 file changed, 121 insertions(+), 307 deletions(-) diff --git a/doc/theory/eliashberg.rst b/doc/theory/eliashberg.rst index f87362ffd..67a1728b3 100644 --- a/doc/theory/eliashberg.rst +++ b/doc/theory/eliashberg.rst @@ -1,26 +1,34 @@ .. _eliashberg: Linearized Eliashberg Equation -================================ +============================== + +.. note:: + The following is restricted to :math:`SU(2)` symmetric systems. + All indices are purely orbital and superconducting gaps :math:`\Delta` and + particle-particle vertices :math:`\Gamma` are restricted to the singlet/triplet + channel, shown by the superscripts s/t respectively. The linearized Eliashberg equation is a generalization of the linearized Bardeen-Cooper-Schrieffer (BCS) gap equation to frequency dependent gaps. -It can be used to determine the critical temperature :math:`T_\mathrm{c}`, +It can be used to determine the critical (inverse) temperature +:math:`T_\mathrm{c}/\beta_\mathrm{c}`, at which a transition to a superconducting state occurs, -and the symmetry of the corresponding gap function :math:`\Delta`. +and the symmetry of the corresponding superconducting gap function +:math:`\Delta^{\mathrm{s/t}}`. It is given by .. math:: - \Delta_{\bar{a}\bar{b}}(K)= -\frac{1}{2 N_{\mathbf{k}}\beta}\sum_{K'} - \Gamma^{PP}_{c\bar{a}d\bar{b}}(Q=0, K, K') + \Delta^{\mathrm{s/t}}_{\bar{a}\bar{b}}(K)= -\frac{1}{2 N_{\mathbf{k}}\beta_\mathrm{c}}\sum_{K'} + \Gamma^{\mathrm{s/t}}_{c\bar{a}d\bar{b}}(Q=0, K, K') G_{c\bar{e}}(K')G_{d\bar{f}}(-K') - \Delta_{\bar{e}\bar{f}}(K')\,. + \Delta^{\mathrm{s/t}}_{\bar{e}\bar{f}}(K')\,. :label: linearized_eliashberg_1 -where :math:`Q/K` is a combination of bosonic/fermionic Matsubara -frequency and momentum, +where :math:`Q/K` is a combination of bosonic/fermionic Matsubara :math:`i\omega_n/i\nu_n` +frequency and momentum :math:`\mathbf{k}`, :math:`N_{\mathbf{k}}` is the number of momentum points, -:math:`\Gamma^{PP}` is the irreducible particle-particle vertex +:math:`\Gamma^{\mathrm{s/t}}` is the irreducible particle-particle vertex and :math:`G` is the one-particle Green's function. Note, that the bosonic Matsubara frequency and momentum in the particle-particle vertex @@ -28,161 +36,67 @@ is set to zero. This is because we are interested in Cooper-pairs which have a zero transfered momentum-frequency in a scattering process. -Deriving the linearized Eliashberg equation: Normal state and superconducting state ------------------------------------------------------------------------------------ - -The linearized Eliashberg equation can be seen from two perspectives. -On one hand we are in the normal state and want to find the transition -to the superconducting one, -and on the other we are in the superconducting state using the limit of -small gaps :math:`\Delta \ll 1`. +Deriving the linearized Eliashberg equation from the normal state +----------------------------------------------------------------- -Normal state -^^^^^^^^^^^^ - -Generally speaking a transition from the normal state to a superconducting +Generally speaking a transition from the normal state to the superconducting one occurs when the particle-particle susceptibility diverges. .. math:: - \mathbf{\chi}^{PP} = [\mathbf{1}-\mathbf{\Gamma}^{PP} \mathbf{\chi}^{(0),{PP}}]^{-1} + \mathbf{\chi}^{\mathrm{s/t}} = [\mathbf{1}-\mathbf{\Gamma}^{\mathrm{s/t}} + \mathbf{\chi}^{(0),{PP}}]^{-1} \mathbf{\chi}^{(0),{PP}} This is the case when the largest eigenvalue of -:math:`\mathbf{\Gamma}^{PP} \mathbf{\chi}^{(0),{PP}}` becomes unity. +:math:`\mathbf{\Gamma^{\mathrm{s/t}}} \mathbf{\chi}^{(0),{PP}}` becomes unity. For a largest eigenvalues that is smaller than :math:`1` we are still in the normal state, -but we can calculate the corresponding eigenvectors :math:`\Delta`. +but we can calculate the corresponding eigenvectors :math:`\Delta^{\mathrm{s/t}}`. This corresponds to the following eigenvalue equation .. math:: - \lambda\Delta_{\bar{a}\bar{b}}(K)= \frac{T^2_{\mathrm{c}}}{2 N_{\mathbf{k}}^2}\sum_{K', K''} - \Gamma^{PP}_{c\bar{a}d\bar{b}}(Q=0, K, K') + \lambda\Delta^{\mathrm{s/t}}_{\bar{a}\bar{b}}(K) + = + \frac{1}{N_{\mathbf{k}}^2 \beta^2}\sum_{K', K''} + \Gamma^{\mathrm{s/t}}_{c\bar{a}d\bar{b}}(Q=0, K, K') \chi^{(0),{PP}}_{\bar{e}d\bar{f}c}(Q=0, K', K'') - \Delta_{\bar{e}\bar{f}}(K')\,, + \Delta^{\mathrm{s/t}}_{\bar{e}\bar{f}}(K')\,, :label: linearized_eliashberg_2 which we can write like Eq. :eq:`linearized_eliashberg_1` with the definiton -of :math:`\chi^{(0),{PP}}` :eq:`bare_pp_sus_def`, - -.. math:: - \lambda\Delta_{\bar{a}\bar{b}}(K)= -\frac{1}{2 N_{\mathbf{k}}\beta}\sum_{K'} - \Gamma^{PP}_{c\bar{a}d\bar{b}}(Q=0, K, K') - G_{c\bar{e}}(K')G_{d\bar{f}}(-K') - \Delta_{\bar{e}\bar{f}}(K')\,. - -This equation is valid for :math:`\lambda \leq 1` -and yields eigenvectors, which are superconducting gaps that have not manifested yet. -At :math:`\lambda=1` the normal state breaks down and the superconducting -state with the corresponding gap emerges. -The size of eigenvalues is therefore an indicator of how likely the associated gap is -to manifest. - -Superconducting state -^^^^^^^^^^^^^^^^^^^^^ - -For a calculation in the superconducting state we must extend the basis -to accommodate Cooper-pairs. -In addition to the normal one-particle Green's function - -.. math:: - G_{a\bar{b}}(\tau, \mathbf{r}) - \equiv - - \langle \mathcal{T} c_{a\uparrow}(\tau, \mathbf{r}) - c^\dagger_{\bar{b}\uparrow}(0, \mathbf{0}) \rangle \,, - -and its backwards propagating counterpart - -.. math:: - \overline{G}_{\bar{a}b}(\tau, \mathbf{r}) - \equiv - - \langle \mathcal{T} c^\dagger_{\bar{a}\downarrow}(\tau, \mathbf{r}) - c_{b\downarrow}(0, \mathbf{0}) \rangle\,, - -we have to introduce the one-particle anomalous Green's functions -:math:`F` and :math:`\overline{F}`. -These are defined as - -.. math:: - F_{ab}(\tau, \mathbf{r}) - \equiv - \langle \mathcal{T} c_{a\uparrow}(\tau, \mathbf{r}) - c_{b\downarrow}(0, \mathbf{0}) \rangle - \,, - -and - -.. math:: - \overline{F}_{\bar{a}\bar{b}}(\tau, \mathbf{r}) - \equiv - \langle \mathcal{T} c^\dagger_{\bar{a}\downarrow}(\tau, \mathbf{r}) - c^\dagger_{\bar{b}\uparrow}(0, \mathbf{0}) \rangle\,. - -Fourier transforming to Matsubara frequency and momentum space then gives that - -.. math:: - \overline{G}_{\bar{a}b}(i\nu_n, \mathbf{k}) = - -G_{b\bar{a}}(-i\nu_n, -\mathbf{k})\,, - :label: g_bar_to_g - -and - -.. math:: - \overline{F}_{\bar{a}\bar{b}}(i\nu_n, \mathbf{k}) - = - [F_{ab}(i\nu_n, \mathbf{k}) ]^{\dagger}\,. - :label: f_bar_to_f - -All four Green's functions are coupled and given by - -.. math:: - \left( \begin{array}{cc} - \mathbf{G} & \mathbf{F} \\ - \overline{\mathbf{F}} & \overline{\mathbf{G}}\\ - \end{array} \right) - = - \left( \begin{array}{cc} - \left(\mathbf{G}^{(0)}\right)^{-1} - \mathbf{\Sigma} & \mathbf{\Delta} \\ - \overline{\mathbf{\Delta}} & \left(\overline{\mathbf{G}}^{(0)}\right)^{-1} - \overline{\mathbf{\Sigma}} \\ - \end{array} \right)^{-1}\,, - -where :math:`\Sigma/\overline{\Sigma}` are the normal self-energies -and :math:`\Delta/\overline{\Delta}` the anomalous ones. -The anomalous self-energies are equivalent to the superconducting gap and are given by +of :math:`\chi^{(0),{PP}}` .. math:: - \Delta_{\bar{a}\bar{b}}(K) + \chi^{(0),{PP}}_{\bar{a}b\bar{c}d}(Q, K, K') = - \frac{1}{2N_{\mathbf{k}} \beta} \sum_{K'} - \Gamma^{PP}_{c\bar{a}d\bar{b}}(Q=0, K, K') - F_{cd}(K')\,, - :label: anomalous_self_energy + -\frac{N_{\mathbf{k}} \beta}{2} + G_{d\bar{a}}(K)G_{b\bar{c}}(-K')\delta_{K, K'}\,, + :label: chi_0_pp -.. math:: - \overline{\Delta}_{{a}{b}}(K) - = - \frac{1}{2N_{\mathbf{k}} \beta} \sum_{K'} - \Gamma^{PP}_{a\bar{c}b\bar{d}}(Q=0, K, K') - \overline{F}_{\bar{c}\bar{d}}(K')\,. - :label: anomalous_self_energy_2 - -With either of those equations we could calculate the gap for the superconducting state -below :math:`T_\mathrm{c}`. -But note, that this is not trivial, due to the coupling of the Green's functions and -self-energies. -In the limit close to :math:`T_\mathrm{c}` the superconducting gap is very small and -we can approximate the anomalous Green's function with +as .. math:: - \mathbf{F} = - - \left[\left(\mathbf{G}^{(0)}\right)^{-1} - \mathbf{\Sigma}\right]^{-1} - \mathbf{\Delta} - \left[\left(\mathbf{\overline{G}}^{(0)}\right)^{-1} - \mathbf{\overline{\Sigma}}\right]^{-1} - :label: approx_anomalous_gf + \lambda\Delta^{\mathrm{s/t}}_{\bar{a}\bar{b}}(K)= -\frac{1}{2 N_{\mathbf{k}}\beta}\sum_{K'} + \Gamma^{\mathrm{s/t}}_{c\bar{a}d\bar{b}}(Q=0, K, K') + G_{c\bar{e}}(K')G_{d\bar{f}}(-K') + \Delta^{\mathrm{s/t}}_{\bar{e}\bar{f}}(K')\,. + :label: linearized_eliashberg_3 -Plugging this linearized version of the anomalouse Green's function in -Eq. :eq:`anomalous_self_energy` with the help of relation -Eq. :eq:`g_bar_to_g` yields the linearized Eliashberg equation -Eq. :eq:`linearized_eliashberg_1`. +.. note:: + There is an inconsistency with a factor of :math:`\frac{1}{2}` with + Eq. :eq:`chi_0_pp` and Eq. :eq:`bare_pp_sus_def`. + As there is no bare particle-particle bubble implementation yet, + and the Eliashberg implementation is self-consistent, + we don't have any problems. + But for future implementations this needs to be addressed. + +This equation is valid for :math:`\lambda \leq 1` +and yields eigenvectors, which correspond to superconducting gap functions +that have not manifested yet. +At :math:`\lambda=1` the normal state breaks down and the superconducting +state with the corresponding gap emerges. +The size of the eigenvalues is therefore an indicator of how likely the associated gap +is to manifest. Relation to the BCS gap equation ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ @@ -196,14 +110,14 @@ For a one-band case and a non-interacting Green's function with dispersion relat :math:`\epsilon`, this yields .. math:: - \Delta(\mathbf{k}) = -\frac{1}{2 N_{\mathbf{k}}}\sum_{\mathbf{k'}} - \Gamma^{PP}(\mathbf{q}=\mathbf{0}, \mathbf{k}, \mathbf{k'}) + \Delta^{\mathrm{s/t}}(\mathbf{k}) = -\frac{1}{2 N_{\mathbf{k}}}\sum_{\mathbf{k'}} + \Gamma^{\mathrm{s/t}}(\mathbf{q}=\mathbf{0}, \mathbf{k}, \mathbf{k'}) \frac{\tan(\epsilon(\mathbf{k'})\beta/2)}{2\epsilon(\mathbf{k'})} - \Delta(\mathbf{k'})\,, - :label: linearized_eliashberg_3 + \Delta^{\mathrm{s/t}}(\mathbf{k'})\,, + :label: linearized_eliashberg_4 which corresponds to the linearized BCS gap equation. -The non-linear BCS gap equation can be obtained from Eq. :eq:`linearized_eliashberg_3` +The non-linear BCS gap equation can be obtained from Eq. :eq:`linearized_eliashberg_4` by substituting :math:`\epsilon` with :math:`\sqrt{\epsilon(\mathbf{k})^2 + |\Delta(\mathbf{k})|^2}`. @@ -236,7 +150,7 @@ real space (parity) (:math:`\hat{P}`), orbital space (:math:`\hat{O}`), and time (frequency) (:math:`\hat{T}`). While :math:`\Delta` has to be odd under the combined action of the symmetry operations :math:`\hat{S}\hat{P}\hat{O}\hat{T}`, -it can be either even (:math:`+`) or odd (:math:`-`) under each separate operation, +it can either be even (:math:`+`) or odd (:math:`-`) under each separate operation, i.e. .. math:: @@ -254,152 +168,38 @@ i.e. \pm \Delta_{a\alpha;b\beta}(-i\nu, \mathbf{k})\,. A gap function can therefore be classified as even (:math:`+`) or odd (:math:`-`) -under these four degrees of freedom. We list all eight possible combinations -in the table below: +under these four degrees of freedom. By calculating the superconducting gap in the +singlet/triplet channel, we fix the spin symmetry to odd/even respectively. +This leaves us with four symmetry combinations for both singlet and triplet gaps, +which we list in the table below. .. table:: :align: center - :widths: grid - - +-----------------+-----------------+-----------------+-----------------+ - | S | P | O | T | - +=================+=================+=================+=================+ - | :math:`-` | :math:`+` | :math:`+` | :math:`+` | - +-----------------+-----------------+-----------------+-----------------+ - | :math:`-` | :math:`-` | :math:`-` | :math:`+` | - +-----------------+-----------------+-----------------+-----------------+ - | :math:`-` | :math:`-` | :math:`+` | :math:`-` | - +-----------------+-----------------+-----------------+-----------------+ - | :math:`-` | :math:`+` | :math:`-` | :math:`-` | - +-----------------+-----------------+-----------------+-----------------+ - | :math:`+` | :math:`-` | :math:`-` | :math:`-` | - +-----------------+-----------------+-----------------+-----------------+ - | :math:`+` | :math:`+` | :math:`+` | :math:`-` | - +-----------------+-----------------+-----------------+-----------------+ - | :math:`+` | :math:`+` | :math:`-` | :math:`+` | - +-----------------+-----------------+-----------------+-----------------+ - | :math:`+` | :math:`-` | :math:`+` | :math:`+` | - +-----------------+-----------------+-----------------+-----------------+ + + +-----------------------------------------------+-----------------------------------------------+ + | Spin-singlet | Spin-triplet | + +===========+===========+===========+===========+===========+===========+===========+===========+ + | S | P | O | T | S | P | O | T | + +-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+ + | :math:`-` | :math:`+` | :math:`+` | :math:`+` | :math:`+` | :math:`-` | :math:`-` | :math:`-` | + +-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+ + | :math:`-` | :math:`-` | :math:`-` | :math:`+` | :math:`+` | :math:`+` | :math:`+` | :math:`-` | + +-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+ + | :math:`-` | :math:`-` | :math:`+` | :math:`-` | :math:`+` | :math:`+` | :math:`-` | :math:`+` | + +-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+ + | :math:`-` | :math:`+` | :math:`-` | :math:`-` | :math:`+` | :math:`-` | :math:`+` | :math:`+` | + +-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+ Because all other combinations are unphysical it is possible to restrict the gap to the allowed symmetries while solving the linearized Eliashberg equation. +Random phase approximation for the irreducible particle-particle vertex +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -Spin diagonalization -^^^^^^^^^^^^^^^^^^^^ - -For :math:`SU(2)` symmetric systems we can drop the spin dependency -by diagonalizing everything in spin. -This diagonalization splits the superconducting gap :math:`\Delta` -in two channels, -the singlet channel - -.. math:: - \Delta^{\mathrm{s}} - = - \Delta_{\uparrow\downarrow} - - - \Delta_{\downarrow\uparrow}\,, - -and triplet channel - -.. math:: - \Delta^{\mathrm{t}} - = - \Delta_{\uparrow\downarrow} - + - \Delta_{\downarrow\uparrow}\,. - -We can then express Eq. :eq:`linearized_eliashberg_2` in either of those two -channels. -Doing this for the singlet channel, -while suppressing frequency, momentum and orbital indices, yields - -.. math:: - \lambda - \Delta^{\mathrm{s}} - &= - \lambda - \left(\Delta_{\uparrow\downarrow} - \Delta_{\downarrow\uparrow}\right) - \\ - &= - -\left[\Gamma^{PP}_{\uparrow\uparrow\downarrow\downarrow} - \; - G_{\uparrow\uparrow}G_{\downarrow\downarrow} - \Delta_{\uparrow\downarrow} - + - \Gamma^{PP}_{\uparrow\downarrow\downarrow\uparrow} - \; - G_{\downarrow\downarrow}G_{\uparrow\uparrow} - \Delta_{\downarrow\uparrow} - \right] - + - \\ - &\quad\quad - \left[ - \Gamma^{PP}_{\downarrow\downarrow\uparrow\uparrow} - \; - G_{\downarrow\downarrow}G_{\uparrow\uparrow} - \Delta_{\downarrow\uparrow} - - - \Gamma^{PP}_{\downarrow\uparrow\uparrow\downarrow} - \; - G_{\uparrow\uparrow} - G_{\downarrow\downarrow} - \Delta_{\uparrow\downarrow} - \right] - \\ - &= - -\Gamma^{PP}_{\uparrow\uparrow\downarrow\downarrow} - \; - GG - \left( - \Delta_{\uparrow\downarrow} - - - \Delta_{\downarrow\uparrow} - \right) - + - \Gamma^{PP}_{\uparrow\downarrow\downarrow\uparrow} - \; - GG - \left( - \Delta_{\uparrow\downarrow} - - - \Delta_{\downarrow\uparrow} - \right) - \\ - &= - -\left(\Gamma^{PP}_{\uparrow\uparrow\downarrow\downarrow} - -\Gamma^{PP}_{\uparrow\downarrow\downarrow\uparrow} - \; - \right) - GG - \Delta^{\mathrm{s}} - \\ - &= - -\Gamma^{\mathrm{s}} - GG - \Delta^{\mathrm{s}}\,. - -This is analog for the triplet channel and we obtain the spin diagonalized -linearized Eliashberg equation - -.. math:: - \lambda\Delta^{\mathrm{s/t}}_{\bar{a}\bar{b}}(K)= -\frac{1}{2 N_{\mathbf{k}}\beta}\sum_{K'} - \Gamma^{\mathrm{s/t}}_{c\bar{a}d\bar{b}}(Q=0, K, K') - G_{c\bar{e}}(K')G_{d\bar{f}}(-K') - \Delta^{\mathrm{s/t}}_{\bar{e}\bar{f}}(K')\,, - :label: linearized_eliashberg_4 - -with all indices being only orbital ones. - -Random phase approximation for the spin diagonalized irreducible particle-particle vertex -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -To obtain the spin diagonalized irreducible particle-particle vertex in the -random phase approximation (RPA) -one substitutes all vertices with the bare one in the parquet equation. -This yields for the singlet channel +The irreducible particle-particle vertex is given by the parquet equation, +which can be expressed in terms of the fully irreducible vertex :math:`\Lambda` +and the channel reducible vertex-ladder functions :math:`\Phi`. +It is given in the singlet channel by .. math:: \Gamma^{\mathrm{s}}_{a\bar{b}c\bar{d}}(Q=0, K, K') @@ -418,10 +218,10 @@ This yields for the singlet channel \Phi^{\mathrm{d}}_{c\bar{b}a\bar{d}}(K+K') \right] + - U^{\mathrm{s}}_{a\bar{b}c\bar{d}}\,, + \Lambda^{\mathrm{s}}_{a\bar{b}c\bar{d}}\,, :label: singlet_gamma -and for the triplet channel +and in the triplet channel by .. math:: \Gamma^{\mathrm{t}}_{a\bar{b}c\bar{d}}(Q=0, K, K') @@ -440,22 +240,33 @@ and for the triplet channel \Phi^{\mathrm{d}}_{c\bar{b}a\bar{d}}(K+K') \right] + - U^{\mathrm{s}}_{a\bar{b}c\bar{d}}\,, + \Lambda^{\mathrm{t}}_{a\bar{b}c\bar{d}}\,, :label: triplet_gamma -with + +where the vertex-ladder functions are given by .. math:: - \Phi^{\mathrm{d/m}}_{a\bar{b}c\bar{d}} - \equiv - U_{a\bar{b}e\bar{f}}^{\mathrm{d/m}} - \chi_{\bar{f}e\bar{g}h}^{\mathrm{d/m}}(Q) - U^{\mathrm{d/m}}_{h\bar{g}c\bar{d}} - \,. + \Phi^{\text{d/m}}_{a\overline{b}c\overline{d}}(Q) + = + \Lambda^{\text{d/m}} \chi^{\text{d/m}}(Q) \Lambda^{\text{d/m}}\,. + + +Note, that the superscripts :math:`\mathrm{d/m}` indicate the density/magnetic channel. + +Now, in the random phase approximation (RPA) the susceptibilities :math:`\chi^{\text{d/m}}` +are approximated by the RPA bubble susceptibility, +and the vertices are approximated by + +.. math:: + \Lambda^{\text{d/m}} \approx U^{\mathrm{d/m}}\,, + +and + +.. math:: + \Lambda^{\text{s/t}} \approx \frac{1}{2}(U^{\mathrm{d}} + U^{\mathrm{m}})\,. -Note, that the superscripts :math:`\mathrm{d}` and :math:`\mathrm{m}` -indicate the density and magnetic channel. -Here :math:`U^{\mathrm{d/m}}` is the bare local Kanamori interaction given by +Here :math:`U^{\mathrm{d/m}}` is the bare local Kanamori interaction given by .. math:: U^{\mathrm{d/m}}_{a\bar{b}c\bar{d}} = @@ -466,7 +277,7 @@ Here :math:`U^{\mathrm{d/m}}` is the bare local Kanamori interaction given by J/J, & \mathrm{if}\;a=c\neq \bar{b}=\bar{d} \\ 0, & \mathrm{else} \end{cases}\,, - + with the Hubbard interaction :math:`U` and the Hund's :math:`J`. Note, that in both singlet :eq:`singlet_gamma` and @@ -476,48 +287,51 @@ Once without an index flip and a dependence on :math:`K-K'`, :math:`\Phi_{a\overline{b}c\overline{d}}(K-K')`, and another time with an index flip and a dependence on :math:`K+K'`, :math:`\Phi_{c\overline{b}a\overline{d}}(K+K')`. -Inside the linearized Eliashberg equation :eq:`linearized_eliashberg_4` +Inside the linearized Eliashberg equation :eq:`linearized_eliashberg_3` the :math:`\Phi_{c\overline{b}a\overline{d}}(K+K')` term picks up a sign which depends on the frequency, momentum and orbital -symmetry of the gap :math:`\Delta`. +symmetry of the gap :math:`\Delta^{\mathrm{s/t}}`. For all allowed singlet combinations it is positive and for all allowed triplet ones negative. Therefore Eq. :eq:`singlet_gamma` and Eq. :eq:`triplet_gamma` become .. math:: \Gamma^{\text{s}}_{a\overline{b}c\overline{d}}(Q=0, K, K') \equiv - \Lambda^{\text{s}}_{a\overline{b}c\overline{d}} - + 3 \Phi^{\text{m}}_{a\overline{b}c\overline{d}}(K-K') - \Phi^{\text{d}}_{a\overline{b}c\overline{d}}(K-K') + + + \Lambda^{\text{s}}_{a\overline{b}c\overline{d}} \,, :label: singlet_gamma_2 .. math:: \Gamma^{\text{t}}_{a\overline{b}c\overline{d}}(Q=0, K, K') \equiv - \Lambda^{\text{t}}_{a\overline{b}c\overline{d}} - \Phi^{\text{m}}_{a\overline{b}c\overline{d}}(K-K') - \Phi^{\text{d}}_{a\overline{b}c\overline{d}}(K-K') + + + \Lambda^{\text{t}}_{a\overline{b}c\overline{d}} \,. :label: triplet_gamma_2 -Note, that this simplification is only allowed, if the solutions of :math:`\Delta` +Note, that this simplification is only allowed, if the solutions of :math:`\Delta^{\mathrm{s/t}}` are restricted to the allowed symmetries, otherwise unphysical solution can occur. Also note, that the RPA particle-particle vertices in Eq. :eq:`singlet_gamma_2` and :eq:`triplet_gamma_2` only depend on the difference between the two fermionic Matsubara frequencies and momenta. We can therefore write the linearized Eliashberg equation -:eq:`linearized_eliashberg_4` as +:eq:`linearized_eliashberg_3` as .. math:: \lambda\Delta^{\mathrm{s/t}}_{\bar{a}\bar{b}}(K)= -\frac{1}{2 N_{\mathbf{k}}\beta}\sum_{K'} \Gamma^{\mathrm{s/t}}_{c\bar{a}d\bar{b}}(K-K') G_{c\bar{e}}(K')G_{d\bar{f}}(-K') - \Delta^{\mathrm{s/t}}_{\bar{e}\bar{f}}(K')\,. + \Delta^{\mathrm{s/t}}_{\bar{e}\bar{f}}(K')\,, :label: linearized_eliashberg_5 + +which is the form it is implemented as now. This allows us to get rid of the summation by using the convolution theorem From 3ea2a8cd02ca3b7a3f0a2a702829096f9694cdae Mon Sep 17 00:00:00 2001 From: Stefan Date: Fri, 14 Aug 2020 12:39:52 +0200 Subject: [PATCH 070/121] [eli] adjust 1/2 factor in implementation to theory This showed, that there was a missing factor of 1/2 in the constant part of the particle-particle gamma. Luckily, this is very insignificant, as I have checked for previous calculations. Anyways, I have adjusted the data for the previous implementation checks. --- c++/triqs_tprf/lattice/eliashberg.cpp | 12 ++++++------ .../eliashberg/eliashberg_benchmark.tar.gz | Bin 27763 -> 22156 bytes .../eliashberg_benchmark_two_band.tar.gz | Bin 110627 -> 79013 bytes test/python/eliashberg/gamma_creation.py | 4 ++-- .../previous_implementation_two_band.py | 6 +++--- 5 files changed, 11 insertions(+), 11 deletions(-) diff --git a/c++/triqs_tprf/lattice/eliashberg.cpp b/c++/triqs_tprf/lattice/eliashberg.cpp index 93b8ed8c7..02aba6601 100644 --- a/c++/triqs_tprf/lattice/eliashberg.cpp +++ b/c++/triqs_tprf/lattice/eliashberg.cpp @@ -104,9 +104,9 @@ g_wk_t eliashberg_product(chi_wk_vt Gamma_pp, g_wk_vt g_wk, for (const auto [n, q] : delta_wk.mesh()) for (auto [A, a, B, b] : Gamma_pp.target_indices()) delta_wk_out[w, k](a, b) += - Gamma_pp(w-n, k - q)(A, a, B, b) * F_wk[n, q](A, B); + -0.5 * Gamma_pp(w-n, k - q)(A, a, B, b) * F_wk[n, q](A, B); - delta_wk_out /= -(wmesh.domain().beta * kmesh.size()); + delta_wk_out /= (wmesh.domain().beta * kmesh.size()); return delta_wk_out; } @@ -181,7 +181,7 @@ e_r_t eliashberg_constant_gamma_f_product(chi_r_vt Gamma_pp_const_r, g_tr_t F_tr for (const auto r : std::get<1>(F_tr.mesh())) { auto F_t = F_tr[_, r]; for (auto [A, a, B, b] : Gamma_pp_const_r.target_indices()) - delta_r_out[r](a, b) += -Gamma_pp_const_r[r](A, a, B, b) * F_t(0)(A, B); + delta_r_out[r](a, b) += -0.5 * Gamma_pp_const_r[r](A, a, B, b) * F_t(0)(A, B); } return delta_r_out; @@ -223,7 +223,7 @@ g_tr_t eliashberg_dynamic_gamma_f_product(chi_tr_vt Gamma_pp_dyn_tr, g_tr_vt F_t for (const auto t : tmesh) { for (auto [A, a, B, b] : Gamma_pp_dyn_tr.target_indices()) - delta_t[t](a, b) += -Gamma_pp_dyn_t[t](A, a, B, b) * F_t[t](A, B); + delta_t[t](a, b) += -0.5 * Gamma_pp_dyn_t[t](A, a, B, b) * F_t[t](A, B); } delta_tr_out[_, r] = delta_t; } @@ -352,14 +352,14 @@ chi_wk_t gamma_PP_spin_charge(chi_wk_vt chi_c, chi_wk_vt chi_s, \ chi_wk_t gamma_PP_singlet(chi_wk_vt chi_c, chi_wk_vt chi_s, \ array_view, 4> U_c, array_view, 4> U_s) { - auto Gamma_pp_wk = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, -0.5, 1.5); + auto Gamma_pp_wk = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, -1, 3); return Gamma_pp_wk; } chi_wk_t gamma_PP_triplet(chi_wk_vt chi_c, chi_wk_vt chi_s, \ array_view, 4> U_c, array_view, 4> U_s) { - auto Gamma_pp_wk = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, -0.5, -0.5); + auto Gamma_pp_wk = gamma_PP_spin_charge(chi_c, chi_s, U_c, U_s, -1, -1); return Gamma_pp_wk; } diff --git a/test/python/eliashberg/eliashberg_benchmark.tar.gz b/test/python/eliashberg/eliashberg_benchmark.tar.gz index 0a7be411b0a4ba2f475def43d44c4ea46dfbc65c..afdba2b6df7a7e9db8629aea1c10e70416d95d82 100644 GIT binary patch literal 22156 zcma&NRa9GD^e_5RihC*UP@p&z*OXGA6fLwk1S#(Bq&O{B+@X}>?oM!u26wmM9v~zn zxBqd@xaW-fbl>*c4||U}=UQ{m{S&4bT-={_V!&r;D@QwX4_gZ>cN?IEm9wR-lexPC z(Amm|-_zXvztdbi8HyA1L)A2gYQU)O%)1X6GP!IN+$z)EONz^Qsf{0AQn0dcR~ddW zV0$mS#b*N-L;IW!QNoAHLp3?m~NX@jf` 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