def test_square_lattice_chi00():
# ------------------------------------------------------------------
# -- Discretizations
n_k = (2, 2, 1)
nw_g = 500
nnu = 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'],
)
e_k = t_r.on_mesh_brillouin_zone(n_k)
kmesh = e_k.mesh
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, nnu=nnu, gr=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, nnu=nnu, 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)
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(
chi00_wk_analytic[Idx(0), Idx(0, 0, 0)][0, 0, 0, 0], chi0_q0_ref)