def get_chi0_nk_at_specific_w(g_wk, nw_index=1, nwf=None):
r""" Compute the generalized bare lattice susceptibility
:math:`\chi^{0}_{\bar{a}b\bar{c}d}(i\omega_{n=\mathrm{nw\_index}}, i\nu_n, \mathbf{k})` from the single-particle
Green's function :math:`G_{a\bar{b}}(i\nu_n, \mathbf{k})` for a specific :math:`i\omega_{n=\mathrm{nw\_index}}`.
Parameters
----------
g_wk : Gf,
Single-particle Green's function :math:`G_{a\bar{b}}(i\nu_n, \mathbf{k})`.
nw_index : int,
The bosonic Matsubara frequency index :math:`i\omega_{n=\mathrm{nw\_index}}`
at which :math:`\chi^0` is calculated.
nwf : int,
Number of fermionic frequencies in :math:`\chi^0`.
Returns
-------
chi0_nk : Gf,
Generalized bare lattice susceptibility
:math:`\chi^{0}_{\bar{a}b\bar{c}d}(i\omega_{n=\mathrm{nw\_index}}, i\nu_n, \mathbf{k})`.
"""
fmesh = g_wk.mesh.components[0]
kmesh = g_wk.mesh.components[1]
if nwf is None:
nwf = len(fmesh) // 2
mpi.barrier()
mpi.report('g_wk ' + str(g_wk[Idx(2), Idx(0, 1, 2)][0, 0]))
n = np.sum(g_wk.data) // len(kmesh)
mpi.report('n ' + str(n))
mpi.barrier()
mpi.report('--> g_wr from g_wk')
g_wr = fourier_wk_to_wr(g_wk)
mpi.report('--> chi0_wnr from g_wr')
chi0_nr = chi0_nr_from_gr_PH_at_specific_w(nw_index=nw_index,
nn=nwf,
g_nr=g_wr)
del g_wr
mpi.report('--> chi0_wnk from chi0_wnr')
# Create a 'fake' bosonic mesh to be able to use 'chi0q_from_chi0r'
chi0_wnr = add_fake_bosonic_mesh(chi0_nr)
del chi0_nr
chi0_wnk = chi0q_from_chi0r(chi0_wnr)
del chi0_wnr
chi0_nk = chi0_wnk[Idx(0), :, :]
del chi0_wnk
return chi0_nk
def test_solve_lattice_bse_at_specific_w_against_full(g0_wk, gamma_wnn, nw_index):
chi_kw, chi0_kw = solve_lattice_bse(g0_wk, gamma_wnn)
chi_k_at_specific_w, chi0_k_at_specific_w = solve_lattice_bse_at_specific_w(
g0_wk, gamma_wnn, nw_index=nw_index
)
np.testing.assert_allclose(
chi0_kw[:, Idx(nw_index)].data, chi0_k_at_specific_w.data, atol=10e-16
)
np.testing.assert_allclose(
chi_kw[:, Idx(nw_index)].data, chi_k_at_specific_w.data, atol=10e-16
)
def test_add_fake_bosonic_mesh_with_gf_nk(bzmesh):
nmesh = MeshImFreq(beta=1, S="Fermion", n_max=1)
gf_nk = Gf(mesh=MeshProduct(nmesh, bzmesh), target_shape=(2, 2))
gf_wnk = add_fake_bosonic_mesh(gf_nk)
np.testing.assert_allclose(gf_nk.data, gf_wnk[Idx(0), :, :].data)
def test_add_fake_bosonic_mesh_with_gf_k_with_beta(bzmesh):
gf_k = Gf(mesh=bzmesh, target_shape=(2, 2))
beta = 10
gf_wk = add_fake_bosonic_mesh(gf_k, beta=beta)
np.testing.assert_allclose(gf_k.data, gf_wk[Idx(0), :].data)
assert gf_wk.mesh[0].beta == beta
def test_chi0_nk_at_specific_w_against_full(g0_wk, p):
chi0_wnk = get_chi0_wnk(g0_wk, nw=p.nw_chi, nwf=p.nwf)
chi0_nk_at_specific_w = get_chi0_nk_at_specific_w(g0_wk,
nw_index=p.nw_index,
nwf=p.nwf)
np.testing.assert_allclose(chi0_wnk[Idx(p.nw_index), :, :].data,
chi0_nk_at_specific_w.data)
def plot_output(g0_wk, gamma):
from triqs.plot.mpl_interface import oplot, plt
initial_delta = semi_random_initial_delta(g0_wk)
next_delta_summation = eliashberg_product(gamma_big, g0_wk, initial_delta)
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)
deltas = [initial_delta, next_delta_summation, next_delta_fft]
warnings.filterwarnings("ignore") #ignore some matplotlib warnings
subp = [4, 3, 1]
fig = plt.figure(figsize=(18, 15))
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()
def test_chi0_nr_at_specific_w_against_full(g0_wr, p):
chi0_wnr = chi0r_from_gr_PH(nw=p.nw_chi, nn=p.nwf, g_nr=g0_wr)
chi0_nr_at_specific_w = chi0_nr_from_gr_PH_at_specific_w(
nw_index=p.nw_index, nn=p.nwf, g_nr=g0_wr
)
np.testing.assert_allclose(
chi0_wnr[Idx(p.nw_index), :, :].data, chi0_nr_at_specific_w.data
)
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 put_gf_on_mesh(g_in, wmesh):
assert (len(wmesh) <= len(g_in.mesh))
g_out = Gf(mesh=wmesh, target_shape=g_in.target_shape)
for w in wmesh:
index = w.linear_index + wmesh.first_index() # absolute index
g_out[w] = g_in[Idx(index)]
return g_out
def plot_delta(delta):
import matplotlib.pyplot as plt
fig, axes = plt.subplots(3, 3)
vmax = np.max(np.abs(delta[Idx(0), :].data))
for orb1, orb2 in itertools.product(list(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(list(range(p.norb)), repeat=2):
plt.plot(delta.data[:, 1, orb1, orb2].real)
plt.plot(delta.data[:, 1, orb1, orb2].imag)
plt.show()
def plot_g2(G2, cplx=None, idx_labels=None, w=Idx(0), opt={}, title=None):
data = G2[w, :, :].data
if cplx == 're':
data = data.real
elif cplx == 'im':
data = data.imag
n = data.shape[-1]
N = n**2
subp = [N, N, 1]
colorbar_flag = True
import itertools
for idxs in itertools.product(range(n), repeat=4):
i1, i2, i3, i4 = idxs
d = data[:, :, i1, i2, i3, i4]
ax = plt.subplot(*subp)
subp[-1] += 1
if idx_labels is not None:
labels = [idx_labels[idx] for idx in idxs]
sub_title = r'$c^\dagger_{%s} c_{%s} c^\dagger_{%s} c_{%s}$' % tuple(
labels)
else:
sub_title = str(idxs)
plt.title(sub_title, fontsize=8)
#plt.pcolormesh(d, **opt)
if np.max(np.abs(d)) > 1e-10:
plt.imshow(d, **opt)
if colorbar_flag:
if title is not None:
plt.title(title)
plt.colorbar()
colorbar_flag = False
ax.set_xticks([])
ax.set_yticks([])
plt.axis('equal')
plt.tight_layout()
def get_chi_SzSz(chi):
# -- Contract Sz Sz response
Sx = 0.5 * np.array([[0., 1.], [1., 0]])
Sy = 0.5 * np.array([[0., -1.j], [1.j, 0]])
Sz = np.diag([+0.5, -0.5])
N = np.eye(2)
#Op1, Op2 = Sx, Sx
#Op1, Op2 = Sy, Sy
Op1, Op2 = Sz, Sz
#Op1, Op2 = N, N
chi_SzSz = chi[0, 0, 0, 0].copy()
chi_SzSz.data[:] = np.einsum('wqabcd,ab,cd->wq', chi.data, Op1, Op2)[:, :]
chi_SzSz = chi_SzSz[Idx(0), :]
return chi_SzSz
def strip_sigma(nw, beta, sigma_in, debug=False):
np.testing.assert_almost_equal(beta, sigma_in.mesh.beta)
wmesh = MeshImFreq(beta, 'Fermion', n_max=nw)
sigma = Gf(mesh=wmesh, target_shape=sigma_in.target_shape)
for w in wmesh:
index = w.linear_index + wmesh.first_index() # absolute index
sigma[w] = sigma_in[Idx(index)]
if debug:
from triqs.plot.mpl_interface import oplot, plt
oplot(p.Sigmalatt_iw)
oplot(sigma, 'x')
plt.show()
exit()
return sigma
def plot_chi(chi, title):
chi_k = chi[Idx(0), :][0, 0, 0, 0] # zero frequency, and scalar
k = np.linspace(-0.75, 0.75, num=100) * 2. * np.pi
Kx, Ky = np.meshgrid(k, k)
interp = np.vectorize(lambda kx, ky : chi_k([kx, ky, 0]).real)
interp = interp(Kx, Ky)
plt.imshow(
interp, cmap=plt.get_cmap('magma'),
extent=(k.min(), k.max(), k.min(), k.max()),
origin='lower', vmin=0, vmax=interp.max())
plt.title(title)
plt.xlabel(r'$\frac{a}{2\pi} \cdot k_x$')
plt.ylabel(r'$\frac{a}{2\pi} \cdot k_y$')
plt.colorbar()
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)
print('E_tot =', E_tot)
np.testing.assert_almost_equal(E_tot_ref, E_tot, decimal=6)
# ------------------------------------------------------------------
# -- Lattice chi0
print('--> chi00_wk')
chi00_wk = imtime_bubble_chi0_wk(g0_wk, nw=1)
print('chi0_q0 =\n', chi00_wk[Idx(0), Idx(0, 0, 0)].real.reshape((4,4)))
print('--> lindhard_chi00_wk')
chi00_wk_analytic = lindhard_chi00_wk(e_k=e_k, nw=1, beta=beta, mu=mu)
print('chi0_q0_analytic =\n', chi00_wk_analytic[
Idx(0), Idx(0, 0, 0)].real.reshape((4,4)))
np.testing.assert_almost_equal(
chi00_wk.data, chi00_wk_analytic.data, decimal=5)
chi0_q0_ref = chi0_q0_integral(t, beta)
print('chi0_q0 =', chi00_wk[Idx(0), Idx(0, 0, 0)][0,0,0,0].real)
print('chi0_q0_ref =', chi0_q0_ref)
np.testing.assert_almost_equal(
def Idxs(integer_index_list):
from triqs.gf import Idx
return tuple( Idx(i) for i in integer_index_list )
def get_chi0_wnk(g_wk, nw=1, nwf=None):
r""" Compute the generalized bare lattice susceptibility
:math:`\chi^{0}_{\bar{a}b\bar{c}d}(i\omega_n, i\nu_n, \mathbf{k})` from the single-particle
Green's function :math:`G_{a\bar{b}}(i\nu_n, \mathbf{k})`.
Parameters
----------
g_wk : Gf,
Single-particle Green's function :math:`G_{a\bar{b}}(i\nu_n, \mathbf{k})`.
nw : int,
Number of bosonic frequencies in :math:`\chi^0`.
nwf : int,
Number of fermionic frequencies in :math:`\chi^0`.
Returns
-------
chi0_wnk : Gf,
Generalized bare lattice susceptibility
:math:`\chi^{0}_{\bar{a}b\bar{c}d}(i\omega_n, i\nu_n, \mathbf{k})`.
"""
fmesh = g_wk.mesh.components[0]
kmesh = g_wk.mesh.components[1]
if nwf is None:
nwf = len(fmesh) // 2
mpi.barrier()
mpi.report('g_wk ' + str(g_wk[Idx(2), Idx(0, 0, 0)][0, 0]))
n = np.sum(g_wk.data) / len(kmesh)
mpi.report('n ' + str(n))
mpi.barrier()
mpi.report('--> g_wr from g_wk')
g_wr = fourier_wk_to_wr(g_wk)
mpi.barrier()
mpi.report('g_wr ' + str(g_wr[Idx(2), Idx(0, 0, 0)][0, 0]))
n_r = np.sum(g_wr.data, axis=0)[0]
mpi.report('n_r=0 ' + str(n_r[0, 0]))
mpi.barrier()
mpi.report('--> chi0_wnr from g_wr')
chi0_wnr = chi0r_from_gr_PH(nw=nw, nn=nwf, g_nr=g_wr)
#mpi.report('--> chi0_wnr from g_wr (nompi)')
#chi0_wnr_nompi = chi0r_from_gr_PH_nompi(nw=nw, nn=nwf, g_wr=g_wr)
del g_wr
#abs_diff = np.abs(chi0_wnr.data - chi0_wnr_nompi.data)
#mpi.report('shape = ' + str(abs_diff.shape))
#idx = np.argmax(abs_diff)
#mpi.report('argmax = ' + str(idx))
#diff = np.max(abs_diff)
#mpi.report('diff = %6.6f' % diff)
#del chi0_wnr
#chi0_wnr = chi0_wnr_nompi
#exit()
mpi.barrier()
mpi.report('chi0_wnr ' +
str(chi0_wnr[Idx(0), Idx(0), Idx(0, 0, 0)][0, 0, 0, 0]))
chi0_r0 = np.sum(chi0_wnr[:, :, Idx(0, 0, 0)].data)
mpi.report('chi0_r0 ' + str(chi0_r0))
mpi.barrier()
mpi.report('--> chi0_wnk from chi0_wnr')
chi0_wnk = chi0q_from_chi0r(chi0_wnr)
del chi0_wnr
mpi.barrier()
mpi.report('chi0_wnk ' +
str(chi0_wnk[Idx(0), Idx(0), Idx(0, 0, 0)][0, 0, 0, 0]))
chi0 = np.sum(chi0_wnk.data) / len(kmesh)
mpi.report('chi0 = ' + str(chi0))
mpi.barrier()
#if mpi.is_master_node():
if False:
from triqs_tprf.ParameterCollection import ParameterCollection
p = ParameterCollection()
p.g_wk = g_wk
p.g_wr = g_wr
p.chi0_wnr = chi0_wnr
p.chi0_wnk = chi0_wnk
print('--> Writing debug info for BSE')
with HDFArchive('data_debug_bse.h5', 'w') as arch:
arch['p'] = p
mpi.barrier()
return chi0_wnk
hfr.chi0_SzSz = hfr.bare_response(Sz, Sz)
hfr.chi_SzSz = hfr.response(Sz, Sz)
#hfr.chi0_k = hfr.compute_chi0_k()
np.testing.assert_almost_equal(hr.chi0_SzSz, hfr.chi0_SzSz)
np.testing.assert_almost_equal(hr.chi_SzSz, hfr.chi_SzSz)
# ------------------------------------------------------------------
# -- Call TPRF chi0_wk bubble calc
wmesh = MeshImFreq(beta=beta, S='Fermion', n_max=n_w)
g0_wk = lattice_dyson_g0_wk(mu=mu, e_k=e_k, mesh=wmesh)
chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=1)
chi0_abcd = chi0_wk[Idx(0), Idx(0,0,0)].copy()
chi0_ab = hr.extract_dens_dens(chi0_abcd)
chi0_SzSz = np.einsum('ab,abcd,cd->', Sz, chi0_abcd, Sz)
print('chi0_abcd diff =', np.max(np.abs(chi0_abcd - hfr.chi0_abcd)))
np.testing.assert_almost_equal(chi0_abcd, hfr.chi0_abcd, decimal=6)
print('chi0_ab diff =', np.max(np.abs(chi0_ab - hr.chi0_ab)))
np.testing.assert_almost_equal(chi0_ab, hr.chi0_ab)
np.testing.assert_almost_equal(chi0_SzSz, hr.chi0_SzSz)
if False:
chi0_k = chi0_wk[Idx(0), :]
np.set_printoptions(
e_k_interp = e_k_interp(kx, ky, kz)
plt.figure()
plt.plot(k_plot, e_k_interp, '-')
plt.axes().set_xticks(K_plot)
plt.axes().set_xticklabels([r'$\Gamma$', r'$X$', r'$M$', r'$\Gamma$'])
plt.ylabel(r'$\epsilon(\mathbf{k})$')
plt.grid()
plt.tight_layout()
plt.savefig('figure_e_k_bandpath.pdf')
# ------------------------------------------------------------------
chi_k = chi00_wk[Idx(0), :][0, 0, 0, 0] # zero frequency, and scalar
chi_k_interp = np.vectorize(lambda kx, ky, kz: chi_k([kx, ky, kz]).real)
chi_k_interp = chi_k_interp(kx, ky, kz)
plt.figure()
plt.plot(k_plot, chi_k_interp, '-')
plt.axes().set_xticks(K_plot)
plt.axes().set_xticklabels([r'$\Gamma$', r'$X$', r'$M$', r'$\Gamma$'])
plt.ylabel(r'$\chi_0(\mathbf{k}, i\omega_n = 0)$')
plt.grid()
plt.tight_layout()
plt.savefig('figure_chi00_k_bandpath.pdf')
# ----------------------------------------------------------------------
# -- Bare susceptibility from Green's function bubble
nw = 20
beta = 0.544
from triqs.gf import MeshImFreq, Idx
wmesh = MeshImFreq(beta=beta, S='Fermion', n_max=nw)
from triqs_tprf.lattice import lattice_dyson_g0_wk
g0_wk = lattice_dyson_g0_wk(mu=0., e_k=e_k, mesh=wmesh)
from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk
chi00_wk = imtime_bubble_chi0_wk(g0_wk, nw=1)
print()
print('chi0_q0 =\n', chi00_wk[Idx(0), Idx(0, 0, 0)].real.reshape((16,16)))
#print
#import itertools
#for idxs in itertools.product(range(2), repeat=4):
# print idxs, chi00_wk[Idx(0), Idx(0, 0, 0)].real[idxs]
chi0_q0_ref = chi0_q0_integral(t, beta)
print()
print('chi0_q0 =', chi00_wk[Idx(0), Idx(0, 0, 0)][0,0,0,0].real)
print('chi0_q0_ref =', chi0_q0_ref)
print()
# ----------------------------------------------------------------------
# -- Kanamori interaction
# -- Two site super lattice
P = np.array([[2]])
Units_prim = np.array(t_r_prim.Units)
print('Units_prim =\n', Units_prim)
Units = np.dot(P, Units_prim)
print('Units =\n', Units)
t_r = TBSuperLattice(t_r_prim, P)
kmesh = t_r.get_kmesh(n_k)
e_k = t_r.fourier(kmesh)
print(e_k.target_shape)
print('eps(k=0) =\n', e_k[Idx(0, 0, 0)])
# -- Local double occ and spin operators
gf_struct = [[0, 4]]
docc = n(0, 0) * n(0, 2) + n(0, 1) * n(0, 3)
print('docc =', docc)
sigma_x = 0.5 * np.rot90(np.diag([1., 1.]))
sigma_y = 0.5 * np.rot90(np.diag([1.j, -1.j]))
sigma_z = 0.5 * np.diag([1., -1.])
print('sigma_x =\n', sigma_x)
print('sigma_y =\n', sigma_y)
def make_calc():
# ------------------------------------------------------------------
# -- Read precomputed ED data
filename = "bse_and_rpa_loc_vs_latt.tar.gz"
p = read_TarGZ_HDFArchive(filename)['p']
# ------------------------------------------------------------------
# -- RPA tensor
from triqs_tprf.rpa_tensor import get_rpa_tensor
from triqs_tprf.rpa_tensor import fundamental_operators_from_gf_struct
fundamental_operators = fundamental_operators_from_gf_struct(p.gf_struct)
p.U_abcd = get_rpa_tensor(p.H_int, fundamental_operators)
# ------------------------------------------------------------------
# -- Generalized PH susceptibility
loc_bse = ParameterCollection()
loc_bse.chi_wnn = chi_from_gg2_PH(p.G_iw, p.G2_iw_ph)
loc_bse.chi0_wnn = chi0_from_gg2_PH(p.G_iw, p.G2_iw_ph)
loc_bse.gamma_wnn = inverse_PH(loc_bse.chi0_wnn) - inverse_PH(loc_bse.chi_wnn)
loc_bse.chi_wnn_ref = inverse_PH( inverse_PH(loc_bse.chi0_wnn) - loc_bse.gamma_wnn )
np.testing.assert_array_almost_equal(
loc_bse.chi_wnn.data, loc_bse.chi_wnn_ref.data)
from triqs_tprf.bse import solve_local_bse
loc_bse.gamma_wnn_ref = solve_local_bse(loc_bse.chi0_wnn, loc_bse.chi_wnn)
np.testing.assert_array_almost_equal(
loc_bse.gamma_wnn.data, loc_bse.gamma_wnn_ref.data)
loc_bse.chi0_w = trace_nn(loc_bse.chi0_wnn)
loc_bse.chi_w = trace_nn(loc_bse.chi_wnn)
# ------------------------------------------------------------------
# -- RPA, using BSE inverses and constant Gamma
loc_rpa = ParameterCollection()
loc_rpa.chi0_wnn = loc_bse.chi0_wnn
loc_rpa.chi0_w = loc_bse.chi0_w
loc_rpa.U_abcd = p.U_abcd
# -- Build constant gamma
from triqs_tprf.rpa_tensor import get_gamma_rpa
loc_rpa.gamma_wnn = get_gamma_rpa(loc_rpa.chi0_wnn, loc_rpa.U_abcd)
# -- Solve RPA
loc_rpa.chi_wnn = inverse_PH( inverse_PH(loc_rpa.chi0_wnn) - loc_rpa.gamma_wnn )
loc_rpa.chi_w = trace_nn(loc_rpa.chi_wnn)
# ------------------------------------------------------------------
# -- Bubble RPA on lattice
lat_rpa = ParameterCollection()
# -- Setup dummy lattice Green's function equal to local Green's function
bz = BrillouinZone(BravaisLattice(units=np.eye(3), orbital_positions=[(0,0,0)]))
periodization_matrix = np.diag(np.array(list([1]*3), dtype=int))
kmesh = MeshBrZone(bz, periodization_matrix)
wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nwf_gf)
lat_rpa.g_wk = Gf(mesh=MeshProduct(wmesh, kmesh), target_shape=p.G_iw.target_shape)
lat_rpa.g_wk[:, Idx(0, 0, 0)] = p.G_iw
# -- chi0_wk bubble and chi_wk_rpa bubble RPA
from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk
lat_rpa.chi0_wk = imtime_bubble_chi0_wk(lat_rpa.g_wk, nw=1)
from triqs_tprf.lattice import solve_rpa_PH
lat_rpa.chi_wk = solve_rpa_PH(lat_rpa.chi0_wk, p.U_abcd)
lat_rpa.chi0_w = lat_rpa.chi0_wk[:, Idx(0,0,0)]
lat_rpa.chi_w = lat_rpa.chi_wk[:, Idx(0,0,0)]
print('--> cf Tr[chi0] and chi0_wk')
print(loc_rpa.chi0_w.data.reshape((4, 4)).real)
print(lat_rpa.chi0_w.data.reshape((4, 4)).real)
np.testing.assert_array_almost_equal(
loc_rpa.chi0_w.data, lat_rpa.chi0_w.data, decimal=2)
print('ok!')
print('--> cf Tr[chi_rpa] and chi_wk_rpa')
print(loc_rpa.chi_w.data.reshape((4, 4)).real)
print(lat_rpa.chi_w.data.reshape((4, 4)).real)
np.testing.assert_array_almost_equal(
loc_rpa.chi_w.data, lat_rpa.chi_w.data, decimal=2)
print('ok!')
# ------------------------------------------------------------------
# -- Lattice BSE
lat_bse = ParameterCollection()
lat_bse.g_wk = lat_rpa.g_wk
lat_bse.mu = p.mu
lat_bse.e_k = Gf(mesh=kmesh, target_shape=p.G_iw.target_shape)
lat_bse.e_k[Idx(0,0,0)] = np.eye(2)
lat_bse.sigma_w = p.G_iw.copy()
lat_bse.sigma_w << iOmega_n + lat_bse.mu * np.eye(2) - lat_bse.e_k[Idx(0,0,0)] - inverse(p.G_iw)
lat_bse.g_wk_ref = lat_bse.g_wk.copy()
lat_bse.g_wk_ref[:,Idx(0,0,0)] << inverse(
iOmega_n + lat_bse.mu * np.eye(2) - lat_bse.e_k[Idx(0,0,0)] - lat_bse.sigma_w)
np.testing.assert_array_almost_equal(lat_bse.g_wk.data, lat_bse.g_wk_ref.data)
#for w in lat_bse.g_wk.mesh.components[0]:
# print w, lat_bse.g_wk[w, Idx(0,0,0)][0, 0]
from triqs_tprf.lattice import fourier_wk_to_wr
lat_bse.g_wr = fourier_wk_to_wr(lat_bse.g_wk)
from triqs_tprf.lattice import chi0r_from_gr_PH
lat_bse.chi0_wnr = chi0r_from_gr_PH(nw=1, nn=p.nwf, g_nr=lat_bse.g_wr)
from triqs_tprf.lattice import chi0q_from_chi0r
lat_bse.chi0_wnk = chi0q_from_chi0r(lat_bse.chi0_wnr)
#for n in lat_bse.chi0_wnk.mesh.components[1]:
# print n.value, lat_bse.chi0_wnk[Idx(0), n, Idx(0,0,0)][0,0,0,0]
# -- Lattice BSE calc
from triqs_tprf.lattice import chiq_from_chi0q_and_gamma_PH
lat_bse.chi_kwnn = chiq_from_chi0q_and_gamma_PH(lat_bse.chi0_wnk, loc_bse.gamma_wnn)
# -- Lattice BSE calc with built in trace
from triqs_tprf.lattice import chiq_sum_nu_from_chi0q_and_gamma_PH
lat_bse.chi_kw_ref = chiq_sum_nu_from_chi0q_and_gamma_PH(lat_bse.chi0_wnk, loc_bse.gamma_wnn)
# -- Lattice BSE calc with built in trace using g_wk
from triqs_tprf.lattice import chiq_sum_nu_from_g_wk_and_gamma_PH
lat_bse.chi_kw_tail_corr_ref = chiq_sum_nu_from_g_wk_and_gamma_PH(lat_bse.g_wk, loc_bse.gamma_wnn)
# -- Trace results
from triqs_tprf.lattice import chi0q_sum_nu_tail_corr_PH
from triqs_tprf.lattice import chi0q_sum_nu
lat_bse.chi0_wk_tail_corr = chi0q_sum_nu_tail_corr_PH(lat_bse.chi0_wnk)
lat_bse.chi0_wk = chi0q_sum_nu(lat_bse.chi0_wnk)
from triqs_tprf.lattice import chiq_sum_nu, chiq_sum_nu_q
lat_bse.chi_kw = chiq_sum_nu(lat_bse.chi_kwnn)
np.testing.assert_array_almost_equal(lat_bse.chi_kw.data, lat_bse.chi_kw_ref.data)
from triqs_tprf.bse import solve_lattice_bse
lat_bse.chi_kw_tail_corr, tmp = solve_lattice_bse(lat_bse.g_wk, loc_bse.gamma_wnn)
from triqs_tprf.bse import solve_lattice_bse_e_k_sigma_w
lat_bse.chi_kw_tail_corr_new = solve_lattice_bse_e_k_sigma_w(lat_bse.mu, lat_bse.e_k, lat_bse.sigma_w, loc_bse.gamma_wnn)
np.testing.assert_array_almost_equal(lat_bse.chi_kw_tail_corr.data, lat_bse.chi_kw_tail_corr_ref.data)
np.testing.assert_array_almost_equal(lat_bse.chi_kw_tail_corr.data, lat_bse.chi_kw_tail_corr_new.data)
np.testing.assert_array_almost_equal(lat_bse.chi_kw_tail_corr_ref.data, lat_bse.chi_kw_tail_corr_new.data)
lat_bse.chi0_w_tail_corr = lat_bse.chi0_wk_tail_corr[:, Idx(0, 0, 0)]
lat_bse.chi0_w = lat_bse.chi0_wk[:, Idx(0, 0, 0)]
lat_bse.chi_w_tail_corr = lat_bse.chi_kw_tail_corr[Idx(0, 0, 0), :]
lat_bse.chi_w = lat_bse.chi_kw[Idx(0, 0, 0), :]
print('--> cf Tr[chi0_wnk] and chi0_wk')
print(lat_bse.chi0_w_tail_corr.data.reshape((4, 4)).real)
print(lat_bse.chi0_w.data.reshape((4, 4)).real)
print(lat_rpa.chi0_w.data.reshape((4, 4)).real)
np.testing.assert_array_almost_equal(
lat_bse.chi0_w_tail_corr.data, lat_rpa.chi0_w.data)
np.testing.assert_array_almost_equal(
lat_bse.chi0_w.data, lat_rpa.chi0_w.data, decimal=2)
print('ok!')
print('--> cf Tr[chi_kwnn] and chi_wk (without chi0 tail corr)')
print(lat_bse.chi_w.data.reshape((4, 4)).real)
print(loc_bse.chi_w.data.reshape((4, 4)).real)
np.testing.assert_array_almost_equal(
lat_bse.chi_w.data, loc_bse.chi_w.data)
print('ok!')
# ------------------------------------------------------------------
# -- Use chi0 tail corrected trace to correct chi_rpa cf bubble
dchi_wk = lat_bse.chi0_wk_tail_corr - lat_bse.chi0_wk
dchi_w = dchi_wk[:, Idx(0, 0, 0)]
loc_rpa.chi_w_tail_corr = loc_rpa.chi_w + dchi_w
# -- this will be the same, but it will be close to the real physical value
lat_bse.chi_w_tail_corr_ref = lat_bse.chi_w + dchi_w
loc_bse.chi_w_tail_corr_ref = loc_bse.chi_w + dchi_w
print('--> cf Tr[chi_rpa] and chi_wk_rpa')
print(loc_rpa.chi_w.data.reshape((4, 4)).real)
print(loc_rpa.chi_w_tail_corr.data.reshape((4, 4)).real)
print(lat_rpa.chi_w.data.reshape((4, 4)).real)
np.testing.assert_array_almost_equal(
loc_rpa.chi_w_tail_corr.data, lat_rpa.chi_w.data, decimal=3)
print('--> cf Tr[chi_kwnn] with tail corr (from chi0_wnk)')
print(lat_bse.chi_w_tail_corr.data.reshape((4, 4)).real)
print(lat_bse.chi_w_tail_corr_ref.data.reshape((4, 4)).real)
np.testing.assert_array_almost_equal(
lat_bse.chi_w_tail_corr.data, lat_bse.chi_w_tail_corr_ref.data)
print('ok!')
# ------------------------------------------------------------------
# -- Store to hdf5
filename = 'data_bse_rpa.h5'
with HDFArchive(filename,'w') as res:
res['p'] = p
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)
def solve_lattice_bse_at_specific_w(g_wk, gamma_wnn, nw_index):
r""" Compute the generalized lattice susceptibility
:math:`\chi_{\bar{a}b\bar{c}d}(i\omega_{n=\mathrm{nw\_index}}, \mathbf{k})` using the Bethe-Salpeter
equation (BSE) for a specific :math:`i\omega_{n=\mathrm{nw\_index}}`.
Parameters
----------
g_wk : Gf,
Single-particle Green's function :math:`G_{a\bar{b}}(i\nu_n, \mathbf{k})`.
gamma_wnn : Gf,
Local particle-hole vertex function
:math:`\Gamma_{a\bar{b}c\bar{d}}(i\omega_n, i\nu_n, i\nu_n')`.
nw_index : int,
The bosonic Matsubara frequency index :math:`i\omega_{n=\mathrm{nw\_index}}`
at which the BSE is solved.
Returns
-------
chi_k : Gf,
Generalized lattice susceptibility
:math:`\chi_{\bar{a}b\bar{c}d}(i\omega_{n=\mathrm{nw\_index}}, \mathbf{k})`.
chi0_k : Gf,
Generalized bare lattice susceptibility
:math:`\chi^0_{\bar{a}b\bar{c}d}(i\omega_{n=\mathrm{nw\_index}}, \mathbf{k})`.
"""
# Only use \Gamma at the specific \omega
gamma_nn = gamma_wnn[Idx(nw_index), :, :]
# Keep fake bosonic mesh for usability with other functions
gamma_wnn = add_fake_bosonic_mesh(gamma_nn)
fmesh_g = g_wk.mesh.components[0]
kmesh = g_wk.mesh.components[1]
bmesh = gamma_wnn.mesh.components[0]
fmesh = gamma_wnn.mesh.components[1]
nk = len(kmesh)
nwf = len(fmesh) // 2
nwf_g = len(fmesh_g) // 2
if mpi.is_master_node():
print(tprf_banner(), "\n")
print(
'Lattcie BSE with local vertex approximation at specific \omega.\n'
)
print('nk =', nk)
print('nw_index =', nw_index)
print('nwf =', nwf)
print('nwf_g =', nwf_g)
print()
mpi.report('--> chi0_wk_tail_corr')
# Calculate chi0_wk up to the specific \omega
chi0_wk_tail_corr = imtime_bubble_chi0_wk(g_wk,
nw=np.abs(nw_index) + 1,
save_memory=True)
# Only use specific \omega, but put back on fake bosonic mesh
chi0_k_tail_corr = chi0_wk_tail_corr[Idx(nw_index), :]
chi0_wk_tail_corr = add_fake_bosonic_mesh(chi0_k_tail_corr,
beta=bmesh.beta)
chi0_nk = get_chi0_nk_at_specific_w(g_wk, nw_index=nw_index, nwf=nwf)
# Keep fake bosonic mesh for usability with other functions
chi0_wnk = add_fake_bosonic_mesh(chi0_nk)
mpi.report('--> trace chi0_wnk')
chi0_wk = chi0q_sum_nu(chi0_wnk)
dchi_wk = chi0_wk_tail_corr - chi0_wk
chi0_kw = Gf(mesh=MeshProduct(kmesh, bmesh),
target_shape=chi0_wk_tail_corr.target_shape)
chi0_kw.data[:] = chi0_wk_tail_corr.data.swapaxes(0, 1)
del chi0_wk
del chi0_wk_tail_corr
assert (chi0_wnk.mesh.components[0] == bmesh)
assert (chi0_wnk.mesh.components[1] == fmesh)
assert (chi0_wnk.mesh.components[2] == kmesh)
# -- Lattice BSE calc with built in trace
mpi.report('--> chi_kw from BSE')
#mpi.report('DEBUG BSE INACTIVE'*72)
chi_kw = chiq_sum_nu_from_chi0q_and_gamma_PH(chi0_wnk, gamma_wnn)
#chi_kw = chi0_kw.copy()
mpi.barrier()
mpi.report('--> chi_kw from BSE (done)')
del chi0_wnk
mpi.report('--> chi_kw tail corrected (using chi0_wnk)')
for k in kmesh:
chi_kw[
k, :] += dchi_wk[:,
k] # -- account for high freq of chi_0 (better than nothing)
del dchi_wk
mpi.report('--> solve_lattice_bse, done.')
chi_k = chi_kw[:, Idx(0)]
del chi_kw
chi0_k = chi0_kw[:, Idx(0)]
del chi0_kw
return chi_k, chi0_k
def solve_lattice_bse(g_wk, gamma_wnn):
r""" Compute the generalized lattice susceptibility
:math:`\chi_{\bar{a}b\bar{c}d}(\mathbf{k}, \omega_n)` using the Bethe-Salpeter
equation (BSE).
Parameters
----------
g_wk : Gf,
Single-particle Green's function :math:`G_{a\bar{b}}(i\nu_n, \mathbf{k})`.
gamma_wnn : Gf,
Local particle-hole vertex function
:math:`\Gamma_{a\bar{b}c\bar{d}}(i\omega_n, i\nu_n, i\nu_n')`.
Returns
-------
chi_kw : Gf,
Generalized lattice susceptibility
:math:`\chi_{\bar{a}b\bar{c}d}(\mathbf{k}, i\omega_n)`.
chi0_kw : Gf,
Generalized bare lattice susceptibility
:math:`\chi^0_{\bar{a}b\bar{c}d}(\mathbf{k}, i\omega_n)`.
"""
fmesh_g = g_wk.mesh.components[0]
kmesh = g_wk.mesh.components[1]
bmesh = gamma_wnn.mesh.components[0]
fmesh = gamma_wnn.mesh.components[1]
nk = len(kmesh)
nw = (len(bmesh) + 1) // 2
nwf = len(fmesh) // 2
nwf_g = len(fmesh_g) // 2
if mpi.is_master_node():
print(tprf_banner(), "\n")
print('Lattcie BSE with local vertex approximation.\n')
print('nk =', nk)
print('nw =', nw)
print('nwf =', nwf)
print('nwf_g =', nwf_g)
print()
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()
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]))
mpi.barrier()
mpi.report('--> trace chi0_wnk')
chi0_wk = chi0q_sum_nu(chi0_wnk)
mpi.barrier()
mpi.report('D ' + str(chi0_wk[Idx(0), Idx(0, 0, 0)][0, 0, 0, 0]))
mpi.barrier()
dchi_wk = chi0_wk_tail_corr - chi0_wk
chi0_kw = Gf(mesh=MeshProduct(kmesh, bmesh),
target_shape=chi0_wk_tail_corr.target_shape)
chi0_kw.data[:] = chi0_wk_tail_corr.data.swapaxes(0, 1)
del chi0_wk
del chi0_wk_tail_corr
assert (chi0_wnk.mesh.components[0] == bmesh)
assert (chi0_wnk.mesh.components[1] == fmesh)
assert (chi0_wnk.mesh.components[2] == kmesh)
# -- Lattice BSE calc with built in trace
mpi.report('--> chi_kw from BSE')
#mpi.report('DEBUG BSE INACTIVE'*72)
chi_kw = chiq_sum_nu_from_chi0q_and_gamma_PH(chi0_wnk, gamma_wnn)
#chi_kw = chi0_kw.copy()
mpi.barrier()
mpi.report('--> chi_kw from BSE (done)')
del chi0_wnk
mpi.report('--> chi_kw tail corrected (using chi0_wnk)')
for k in kmesh:
chi_kw[
k, :] += dchi_wk[:,
k] # -- account for high freq of chi_0 (better than nothing)
del dchi_wk
mpi.report('--> solve_lattice_bse, done.')
return chi_kw, chi0_kw
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)
print('E_tot =', E_tot)
np.testing.assert_almost_equal(E_tot_ref, E_tot, decimal=6)
# ------------------------------------------------------------------
# -- Lattice chi0
print('--> chi00_wk')
chi00_wk = imtime_bubble_chi0_wk(g0_wk, nw=1)
print('chi0_q0 =\n', chi00_wk[Idx(0), Idx(0, 0, 0)].real.reshape((4, 4)))
print('--> lindhard_chi00_wk')
chi00_wk_analytic = lindhard_chi00_wk(e_k=e_k, nw=1, beta=beta, mu=mu)
print('chi0_q0_analytic =\n', chi00_wk_analytic[Idx(0),
Idx(0, 0, 0)].real.reshape(
(4, 4)))
np.testing.assert_almost_equal(chi00_wk.data,
chi00_wk_analytic.data,
decimal=5)
chi0_q0_ref = chi0_q0_integral(t, beta)
print('chi0_q0 =', chi00_wk[Idx(0), Idx(0, 0, 0)][0, 0, 0, 0].real)
print('chi0_q0_ref =', chi0_q0_ref)
def make_calc():
# ------------------------------------------------------------------
# -- Read precomputed ED data
filename = "data_pomerol.tar.gz"
p = read_TarGZ_HDFArchive(filename)
# ------------------------------------------------------------------
# -- RPA tensor
from triqs_tprf.rpa_tensor import get_rpa_tensor
from triqs_tprf.rpa_tensor import fundamental_operators_from_gf_struct
fundamental_operators = fundamental_operators_from_gf_struct(p.gf_struct)
p.U_abcd = get_rpa_tensor(p.H_int, fundamental_operators)
# ------------------------------------------------------------------
# -- Generalized PH susceptibility
loc_bse = ParameterCollection()
loc_bse.chi_wnn = chi_from_gg2_PH(p.G_iw, p.G2_iw_ph)
loc_bse.chi0_wnn = chi0_from_gg2_PH(p.G_iw, p.G2_iw_ph)
loc_bse.gamma_wnn = inverse_PH(loc_bse.chi0_wnn) - inverse_PH(
loc_bse.chi_wnn)
loc_bse.chi_wnn_ref = inverse_PH(
inverse_PH(loc_bse.chi0_wnn) - loc_bse.gamma_wnn)
np.testing.assert_array_almost_equal(loc_bse.chi_wnn.data,
loc_bse.chi_wnn_ref.data)
loc_bse.chi0_w = trace_nn(loc_bse.chi0_wnn)
loc_bse.chi_w = trace_nn(loc_bse.chi_wnn)
# ------------------------------------------------------------------
# -- RPA, using BSE inverses and constant Gamma
loc_rpa = ParameterCollection()
loc_rpa.U_abcd = p.U_abcd
# -- Build constant gamma
loc_rpa.gamma_wnn = loc_bse.gamma_wnn.copy()
loc_rpa.gamma_wnn.data[:] = loc_rpa.U_abcd[None, None, None, ...]
# Nb! In the three frequency form $\Gamma \propto U/\beta^2$
loc_rpa.gamma_wnn.data[:] /= p.beta**2
loc_rpa.chi0_wnn = loc_bse.chi0_wnn
loc_rpa.chi0_w = loc_bse.chi0_w
# -- Solve RPA
loc_rpa.chi_wnn = inverse_PH(
inverse_PH(loc_rpa.chi0_wnn) - loc_rpa.gamma_wnn)
loc_rpa.chi_w = trace_nn(loc_rpa.chi_wnn)
# ------------------------------------------------------------------
# -- Bubble RPA on lattice
lat_rpa = ParameterCollection()
# -- Setup dummy lattice Green's function equal to local Green's function
bz = BrillouinZone(
BravaisLattice(units=np.eye(3), orbital_positions=[(0, 0, 0)]))
periodization_matrix = np.diag(np.array(list([1] * 3), dtype=np.int32))
kmesh = MeshBrZone(bz, periodization_matrix)
wmesh = MeshImFreq(beta=p.beta, S='Fermion', n_max=p.nwf_gf)
lat_rpa.g_wk = Gf(mesh=MeshProduct(wmesh, kmesh),
target_shape=p.G_iw.target_shape)
lat_rpa.g_wk[:, Idx(0, 0, 0)] = p.G_iw
# -- chi0_wk bubble and chi_wk_rpa bubble RPA
from triqs_tprf.lattice_utils import imtime_bubble_chi0_wk
lat_rpa.chi0_wk = imtime_bubble_chi0_wk(lat_rpa.g_wk, nw=1)
from triqs_tprf.lattice import solve_rpa_PH
lat_rpa.chi_wk = solve_rpa_PH(lat_rpa.chi0_wk, p.U_abcd)
lat_rpa.chi0_w = lat_rpa.chi0_wk[:, Idx(0, 0, 0)]
lat_rpa.chi_w = lat_rpa.chi_wk[:, Idx(0, 0, 0)]
print('--> cf Tr[chi0] and chi0_wk')
print(loc_rpa.chi0_w.data.reshape((4, 4)).real)
print(lat_rpa.chi0_w.data.reshape((4, 4)).real)
np.testing.assert_array_almost_equal(loc_rpa.chi0_w.data,
lat_rpa.chi0_w.data,
decimal=2)
print('ok!')
print('--> cf Tr[chi_rpa] and chi_wk_rpa')
print(loc_rpa.chi_w.data.reshape((4, 4)).real)
print(lat_rpa.chi_w.data.reshape((4, 4)).real)
np.testing.assert_array_almost_equal(loc_rpa.chi_w.data,
lat_rpa.chi_w.data,
decimal=2)
print('ok!')
# ------------------------------------------------------------------
# -- Lattice BSE
lat_bse = ParameterCollection()
lat_bse.g_wk = lat_rpa.g_wk
from triqs_tprf.lattice import fourier_wk_to_wr
lat_bse.g_wr = fourier_wk_to_wr(lat_bse.g_wk)
from triqs_tprf.lattice import chi0r_from_gr_PH
lat_bse.chi0_wnr = chi0r_from_gr_PH(nw=1, nnu=p.nwf, gr=lat_bse.g_wr)
from triqs_tprf.lattice import chi0q_from_chi0r
lat_bse.chi0_wnk = chi0q_from_chi0r(lat_bse.chi0_wnr)
# -- Lattice BSE calc
from triqs_tprf.lattice import chiq_from_chi0q_and_gamma_PH
lat_bse.chi_kwnn = chiq_from_chi0q_and_gamma_PH(lat_bse.chi0_wnk,
loc_bse.gamma_wnn)
# -- Trace results
from triqs_tprf.lattice import chi0q_sum_nu_tail_corr_PH
from triqs_tprf.lattice import chi0q_sum_nu
lat_bse.chi0_wk_tail_corr = chi0q_sum_nu_tail_corr_PH(lat_bse.chi0_wnk)
lat_bse.chi0_wk = chi0q_sum_nu(lat_bse.chi0_wnk)
from triqs_tprf.lattice import chiq_sum_nu, chiq_sum_nu_q
lat_bse.chi_kw = chiq_sum_nu(lat_bse.chi_kwnn)
lat_bse.chi0_w_tail_corr = lat_bse.chi0_wk_tail_corr[:, Idx(0, 0, 0)]
lat_bse.chi0_w = lat_bse.chi0_wk[:, Idx(0, 0, 0)]
lat_bse.chi_w = lat_bse.chi_kw[Idx(0, 0, 0), :]
print('--> cf Tr[chi0_wnk] and chi0_wk')
print(lat_bse.chi0_w_tail_corr.data.reshape((4, 4)).real)
print(lat_bse.chi0_w.data.reshape((4, 4)).real)
print(lat_rpa.chi0_w.data.reshape((4, 4)).real)
np.testing.assert_array_almost_equal(lat_bse.chi0_w_tail_corr.data,
lat_rpa.chi0_w.data)
np.testing.assert_array_almost_equal(lat_bse.chi0_w.data,
lat_rpa.chi0_w.data,
decimal=2)
print('ok!')
print('--> cf Tr[chi_kwnn] and chi_wk')
print(lat_bse.chi_w.data.reshape((4, 4)).real)
print(loc_bse.chi_w.data.reshape((4, 4)).real)
np.testing.assert_array_almost_equal(lat_bse.chi_w.data,
loc_bse.chi_w.data)
print('ok!')
# ------------------------------------------------------------------
# -- Store to hdf5
filename = 'data_bse_rpa.h5'
with HDFArchive(filename, 'w') as res:
res['p'] = p
