def setup_dmft_calculation(p):
p = copy.deepcopy(p)
p.iter = 0
# -- Local Hubbard interaction
from triqs.operators import n
p.solve.h_int = p.U * n('up', 0) * n(
'do', 0) - 0.5 * p.U * (n('up', 0) + n('do', 0))
# -- 2D square lattice w. nearest neighbour hopping t
from triqs_tprf.tight_binding import TBLattice
T = -p.t * np.eye(2)
H = TBLattice(units=[(1, 0, 0), (0, 1, 0)],
orbital_positions=[(0, 0, 0)] * 2,
orbital_names=['up', 'do'],
hopping={
(0, +1): T,
(0, -1): T,
(+1, 0): T,
(-1, 0): T
})
kmesh = H.get_kmesh(n_k=(p.n_k, p.n_k, 1))
p.e_k = H.fourier(kmesh)
# -- Initial zero guess for the self-energy
p.sigma_w = Gf(mesh=MeshImFreq(p.init.beta, 'Fermion', p.init.n_iw),
target_shape=[2, 2])
p.sigma_w.zero()
return p
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)
T = -t * np.eye(1)
t_r = TBLattice(
units=[(1, 0, 0), (0, 1, 0)],
hopping={
# nearest neighbour hopping -t
(0, +1): T,
(0, -1): T,
(+1, 0): T,
(-1, 0): T,
},
orbital_positions=[(0, 0, 0)],
orbital_names=['0'],
)
print('--> dispersion e_k')
kmesh = t_r.get_kmesh(n_k)
e_k = t_r.fourier(kmesh)
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)
# -- Call TPRF chi0_wk bubble calc
chi00_wk = imtime_bubble_chi0_wk(g0_wk, nw=1)
# -- Analytic reference (Lindhard formula in momentum space)
print('--> lindhard_chi00_wk')
kmesh = t_r.get_kmesh(n_k=(32, 32, 1))
e_k = t_r.fourier(kmesh)
chi00_wk_analytic = lindhard_chi00_wk(e_k=e_k, nw=1, beta=beta, mu=mu)
import sys
import numpy as np
from triqs.gf import Gf, MeshImFreq, Idx
from triqs_tprf.tight_binding import TBLattice
from triqs_tprf.lattice import lattice_dyson_g0_wk
norb, nk, nw = [int(ele) for ele in sys.argv[1:]]
t = -2.0 * np.eye(norb)
t_r = TBLattice(
units=[(1, 0, 0)],
hopping={
(+1, ): t,
(-1, ): t,
},
orbital_positions=[(0, 0, 0)] * norb,
orbital_names=[str(ele) for ele in range(norb)],
)
kmesh = t_r.get_kmesh((nk, 1, 1))
e_k = t_r.fourier(kmesh)
wmesh = MeshImFreq(beta=1.0, S='Fermion', n_max=nw)
g0_wk = lattice_dyson_g0_wk(mu=0.0, e_k=e_k, mesh=wmesh)
print(g0_wk.data.shape)
# nearest neighbour hopping -t
(0,): h_loc,
(+1,): T,
(-1,): T,
},
orbital_positions = [(0,0,0)] * norb,
orbital_names = ['up_0', 'do_0'],
)
Sz = np.kron(np.diag([+0.5, -0.5]), np.eye((1)))
print('h_loc =\n', h_loc)
print('T = \n', T)
print('Sz =\n', Sz)
kmesh = t_r.get_kmesh(n_k=(n_k, 1, 1))
e_k = t_r.fourier(kmesh)
# ------------------------------------------------------------------
# -- Hartree solver
hs = HartreeSolver(e_k, beta, H_int, gf_struct)
eps = 1e-9
hr = HartreeResponse(hs, eps=eps)
hr.chi0_SzSz = hr.bare_response(Sz, Sz)
hr.chi_SzSz = hr.response(Sz, Sz)
hfr = HartreeFockResponse(hs, eps=eps)
from triqs_tprf.tight_binding import TBLattice
t_r = TBLattice(
units = [(1, 0, 0)],
hopping = {
# nearest neighbour hopping -t
(0,): h_loc,
(+1,): T,
(-1,): T,
},
orbital_positions = [(0,0,0)] * norb,
orbital_names = ['up_0', 'do_0', 'up_1', 'do_1'],
)
kmesh = t_r.get_kmesh(n_k=(256, 1, 1))
e_k = t_r.fourier(kmesh)
# ----------------------------------------------------------------------
# -- 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
beta = 40.0
full_units = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]
all_nn_hoppings = list(itertools.product([-1, 0, 1], repeat=dim))
non_diagonal_hoppings = [
ele for ele in all_nn_hoppings if sum(np.abs(ele)) == 1
]
t = -1.0 * np.eye(norbs)
H = TBLattice(
units=full_units[:dim],
hopping={hop: t
for hop in non_diagonal_hoppings},
orbital_positions=[(0, 0, 0)] * norbs,
)
kmesh = H.get_kmesh(n_k=[nk] * dim + [1] * (3 - dim))
e_k = H.fourier(kmesh)
wmesh = MeshImFreq(beta=beta, S='Fermion', n_max=nw)
print('--> Dyson g0_wk')
t = time.time()
g0_wk = lattice_dyson_g0_wk(mu=0.0, e_k=e_k, mesh=wmesh)
print(' {} seconds'.format(time.time() - t))
print('--> Bubble chi0_wk')
t = time.time()
chi0_wk = imtime_bubble_chi0_wk(g0_wk, nw=nw)
print(' {} seconds'.format(time.time() - t))
units=[(1, 0, 0), (0, 1, 0)],
hopping={
# nearest neighbour hopping -t
(0, +1):
-t_intra * np.eye(n_orb_spin) - t_inter * inter_orbital_hopping,
(0, -1):
-t_intra * np.eye(n_orb_spin) - t_inter * inter_orbital_hopping,
(+1, 0):
-t_intra * np.eye(n_orb_spin) - t_inter * inter_orbital_hopping,
(-1, 0):
-t_intra * np.eye(n_orb_spin) - t_inter * inter_orbital_hopping,
},
orbital_positions=[(0, 0, 0)] * n_orb_spin,
)
kmesh = H.get_kmesh(n_k=(16, 16, 1))
e_k = H.fourier(kmesh)
print(e_k)
# ----------------------------------------------------------------------
# -- Bare susceptibility from Green's function bubble
from triqs.gf import MeshImFreq
from triqs_tprf.lattice import lattice_dyson_g0_wk
wmesh = MeshImFreq(beta=5.0, S='Fermion', n_max=30)
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)
T = -t * np.eye(2)
t_r = TBLattice(
units=[(1, 0, 0)],
hopping={
# nearest neighbour hopping -t
(
0, ): h_loc,
(+1, ): T,
(-1, ): T,
},
orbital_positions=[(0, 0, 0)] * 2,
orbital_names=['up', 'do'],
)
kmesh = t_r.get_kmesh(n_k)
e_k = t_r.fourier(kmesh)
# -- Local double occupancy operator
gf_struct = [[0, 2]]
docc = n(0, 0) * n(0, 1)
Sz = 0.5 * np.diag([1., -1.])
# -- Sweep in interaction U
U_vec = np.arange(9., -0.5, -1.5)
h_vec = 1e-3 * np.linspace(-1., 1., num=11)