E_tot_ref = get_total_energy_mf_ref(t, beta, U, mu, n, m) print('E_tot_ref =', E_tot_ref) print('--> tight binding model') t_r = get_tb_model(t, U, n, m, mu=0.) print('--> dispersion e_k') kmesh = t_r.get_kmesh(n_k) e_k = t_r.fourier(kmesh) #print e_k.data print('--> lattice g0_wk') wmesh = MeshImFreq(beta=beta, S='Fermion', n_max=nw) g0_wk = lattice_dyson_g0_wk(mu=mu, e_k=e_k, mesh=wmesh) E_kin = get_kinetic_energy(e_k, g0_wk) print('E_kin =', E_kin) np.testing.assert_almost_equal(E_kin_ref, E_kin, decimal=6) rho = get_density_matrix(g0_wk) print('rho =\n', rho) n = rho[0, 0] + rho[1, 1] m = 0.5 * (rho[0, 0] - rho[1, 1]) print('n, m =', n, m) E_tot = E_kin - U * (n**2 / 4 - m**2)
def test_square_lattice_chi00(): # ------------------------------------------------------------------ # -- Discretizations n_k = (2, 2, 1) nw_g = 500 nn = 400 nw = 1 # ------------------------------------------------------------------ # -- tight binding parameters beta = 20.0 mu = 0.0 t = 1.0 h_loc = np.array([ [-0.3, -0.5], [-0.5, .4], ]) T = -t * np.array([ [1., 0.23], [0.23, 0.5], ]) # ------------------------------------------------------------------ # -- tight binding print('--> tight binding model') t_r = TBLattice( units=[(1, 0, 0), (0, 1, 0)], hopping={ # nearest neighbour hopping -t (0, 0): h_loc, (0, +1): T, (0, -1): T, (+1, 0): T, (-1, 0): T, }, orbital_positions=[(0, 0, 0)] * 2, orbital_names=['up_0', 'do_0'], ) kmesh = t_r.get_kmesh(n_k) e_k = t_r.fourier(kmesh) wmesh = MeshImFreq(beta=beta, S='Fermion', n_max=nw_g) print('--> g0_wk') g0_wk = lattice_dyson_g0_wk(mu=mu, e_k=e_k, mesh=wmesh) print('--> g0_wr') g0_wr = fourier_wk_to_wr(g0_wk) print('--> g0_tr') g0_tr = fourier_wr_to_tr(g0_wr) # ------------------------------------------------------------------ # -- anaytic chi00 print('--> chi00_wk analytic') chi00_wk_analytic = lindhard_chi00_wk(e_k=e_k, nw=nw, beta=beta, mu=mu) print('--> chi00_wr analytic') chi00_wr_analytic = chi_wr_from_chi_wk(chi00_wk_analytic) # ------------------------------------------------------------------ # -- imtime chi00 print('--> chi0_tr_from_grt_PH') chi00_tr = chi0_tr_from_grt_PH(g0_tr) print('--> chi_wr_from_chi_tr') chi00_wr = chi_wr_from_chi_tr(chi00_tr, nw=1) print('--> chi_w0r_from_chi_tr') chi00_wr_ref = chi_w0r_from_chi_tr(chi00_tr) print('--> chi0_w0r_from_grt_PH') chi00_wr_opt = chi0_w0r_from_grt_PH(g0_tr) print('dchi00_wr =', np.max(np.abs(chi00_wr_analytic.data - chi00_wr.data))) print('dchi00_wr_ref =', np.max(np.abs(chi00_wr_analytic.data - chi00_wr_ref.data))) print('dchi00_wr_opt =', np.max(np.abs(chi00_wr_analytic.data - chi00_wr_opt.data))) np.testing.assert_array_almost_equal(chi00_wr_analytic.data, chi00_wr.data, decimal=8) np.testing.assert_array_almost_equal(chi00_wr_analytic.data, chi00_wr_ref.data, decimal=4) np.testing.assert_array_almost_equal(chi00_wr_analytic.data, chi00_wr_opt.data, decimal=4) print('--> chi_wk_from_chi_wr') chi00_wk_imtime = chi_wk_from_chi_wr(chi00_wr) # ------------------------------------------------------------------ # -- imtime chi00 helper function chi00_wk_imtime_2 = imtime_bubble_chi0_wk(g0_wk, nw=1) # ------------------------------------------------------------------ # -- imfreq chi00 print('--> chi00_wnr') chi00_wnr = chi0r_from_gr_PH(nw=1, nn=nn, g_nr=g0_wr) print('--> chi00_wnk') chi00_wnk = chi0q_from_chi0r(chi00_wnr) # -- Test per k and w calculator for chi0_wnk print('--> chi00_wnk_ref') from triqs_tprf.lattice import chi0q_from_g_wk_PH chi00_wnk_ref = chi0q_from_g_wk_PH(nw=1, nn=nn, g_wk=g0_wk) diff = np.max(np.abs(chi00_wnk.data - chi00_wnk_ref.data)) print('chi00_wnk diff =', diff) np.testing.assert_array_almost_equal(chi00_wnk.data, chi00_wnk_ref.data) print('--> chi00_wk_imfreq') chi00_wk_imfreq = chi0q_sum_nu(chi00_wnk) print('--> chi00_wk_imfreq_tail_corr') chi00_wk_imfreq_tail_corr = chi0q_sum_nu_tail_corr_PH(chi00_wnk) # ------------------------------------------------------------------ # -- Compare results def cf_chi_w0(chi1, chi2, decimal=9): chi1, chi2 = chi1[Idx(0), :].data, chi2[Idx(0), :].data diff = np.linalg.norm(chi1 - chi2) print('|dchi| =', diff) np.testing.assert_array_almost_equal(chi1, chi2, decimal=decimal) print('--> Cf analytic with imtime') cf_chi_w0(chi00_wk_analytic, chi00_wk_imtime, decimal=7) print('--> Cf analytic with imtime 2') cf_chi_w0(chi00_wk_analytic, chi00_wk_imtime_2, decimal=4) print('--> Cf analytic with imfreq') cf_chi_w0(chi00_wk_analytic, chi00_wk_imfreq, decimal=2) print('--> Cf analytic with imfreq (tail corr)') cf_chi_w0(chi00_wk_analytic, chi00_wk_imfreq_tail_corr, decimal=5)
import pytriqs.utility.mpi as mpi from pytriqs.gf import Gf, MeshImFreq, MeshProduct from pytriqs.gf import MeshBrillouinZone, MeshCyclicLattice from pytriqs.lattice import BrillouinZone, BravaisLattice from triqs_tprf.lattice import lattice_dyson_g0_wk from triqs_tprf.lattice import fourier_wk_to_wr from triqs_tprf.lattice import fourier_wr_to_wk bz = BrillouinZone(BravaisLattice([[1, 0], [0, 1]])) periodization_matrix = np.diag(np.array([10, 10, 1], dtype=np.int32)) bzmesh = MeshBrillouinZone(bz, periodization_matrix) lmesh = MeshCyclicLattice(bz.lattice, periodization_matrix) e_k = Gf(mesh=bzmesh, target_shape=[1, 1]) for k in bzmesh: e_k[k] = -2 * (np.cos(k[0]) + np.cos(k[1])) # does not work... mesh = MeshImFreq(beta=1.0, S='Fermion', n_max=1024) g0_wk = lattice_dyson_g0_wk(mu=1.0, e_k=e_k, mesh=mesh) g0_wr = fourier_wk_to_wr(g0_wk) g0_wk_ref = fourier_wr_to_wk(g0_wr) np.testing.assert_array_almost_equal(g0_wk.data, g0_wk_ref.data)
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)
import numpy as np from triqs_tprf.tight_binding import TBLattice import triqs_tprf as trpf from pytriqs.gf import * from triqs_tprf.lattice import lattice_dyson_g0_wk import matplotlib.pyplot as plt t = 1.0 H = TBLattice( units=[(1, 0, 0), (0, 1, 0)], hopping={ # nearest neighbour hopping -t (0, +1): -t * np.eye(2), (0, -1): -t * np.eye(2), (+1, 0): -t * np.eye(2), (-1, 0): -t * np.eye(2), }, orbital_positions=[(0, 0, 0)] * 2, orbital_names=['up', 'do'], ) e_k = H.on_mesh_brillouin_zone(n_k=(32, 32, 1)) beta = 50 n_iw = 130 mu = -5 imesh = MeshImFreq(beta, 'Fermion', n_iw) g = lattice_dyson_g0_wk(mu, e_k, imesh) gm = GfImFreq(mesh=imesh, data=g[(0, 0)].data[:, 0].reshape(-1, 1, 1), beta=50) g_pade = GfReFreq(window=(-2, 2), n_points=200, target_shape=[1, 1]) g_pade.set_from_pade(gm) print(g_pade.data.shape)