def create_random_gamma_wnn(p):
wmesh_gamma = MeshImFreq(beta=p.beta, S="Boson", n_max=p.nw_gamma)
nmesh_gamma = MeshImFreq(beta=p.beta, S="Fermion", n_max=p.nwf)
gamma_wnn = Gf(
mesh=MeshProduct(wmesh_gamma, nmesh_gamma, nmesh_gamma),
target_shape=2 * g0_wk.target_shape,
)
np.random.seed(p.seed)
gamma_wnn.data[:] = np.random.rand(*gamma_wnn.data.shape)
return gamma_wnn
def fixed_fermionic_window_python_wnk(chi_wnk, nwf):
r""" Helper routine to reduce the number of fermionic Matsubara
frequencies :math:`\nu` in a two frequency and one momenta dependent
generalized susceptibility :math:`\chi_{abcd}(\omega, \nu, \mathbf{k})`.
Parameters
----------
chi_wnk : two frequency and one momenta dependent generalized
susceptibility :math:`\chi_{abcd}(\omega, \nu, \mathbf{k})`.
nwf : number of fermionic frequencies to keep.
Returns
-------
chi_wnk_out : Susceptibility with reduced number of fermionic Matsubara
frequencies.
"""
g2 = chi_wnk
wmesh, nmesh, kmesh = g2.mesh.components
beta = g2.mesh.components[0].beta
nmesh_small = MeshImFreq(beta=beta, S='Fermion', n_max=nwf)
chi_wnk_out = Gf(mesh=MeshProduct(wmesh, nmesh_small, kmesh),
target_shape=g2.target_shape)
n = g2.data.shape[1]
s = n // 2 - nwf
e = n // 2 + nwf
chi_wnk_out.data[:] = g2.data[:, s:e, :]
return chi_wnk_out
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_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 create_eliashberg_ingredients(p):
H = create_model_for_tests(**p)
kmesh = H.get_kmesh(n_k=[p.nk] * p.dim + [1] * (3 - p.dim))
e_k = H.fourier(kmesh)
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_d, U_m = kanamori_charge_and_spin_quartic_interaction_tensors(
p.norb, p.U, p.Up, p.J, p.Jp)
chi_d = solve_rpa_PH(chi0_wk, U_d)
chi_m = solve_rpa_PH(chi0_wk,
-U_m) # Minus for correct charge rpa equation
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_m=U_m,
U_d=U_d,
chi_m=chi_m,
chi_d=chi_d,
)
return eliashberg_ingredients
def w2dyn_ndarray_to_triqs_BlockGF_iw_beta_niw(giw, n_iw, beta, gf_struct):
""" Convert a W2Dynamics ndarray format with indices [wosos] or [wff]
where t is time, o is orbital, s is spin index, f is flavour
to a block Triqs Matsubara response function
Takes:
giw : Green function as numpy array
beta : inverse temperature
niw : number of Matsubaras
gf_struct: desired block structure of triqs GF
Returns:
BlockGF : triqs block Green function the response function data
Author: Hugo U. R. Strand (2019) """
### check number of Matsubaras is correct and as last dimension
### the variable n_iw has only positive Matsubaras, the objects
### have both negative and positive
n_iw_check = giw.shape[-1] / 2
assert n_iw_check == n_iw
### check if giw is 3 or 5 dimensional, and make it 3 dimensional
if len(giw.shape) == 5:
norbs = giw.shape[0]
nspin = giw.shape[1]
nflavour = norbs * nspin
giw = giw.reshape(nflavour, nflavour, 2 * n_iw)
elif len(giw.shape) == 3:
nflavour = giw.shape[0]
else:
raise Exception(
"giw array must be 3 or 5 dimensional with iw as last dimension!")
### generate triqs Green function with same dimension than
### the input; this may not be a good idea if worm is used
### since then the output can have another structure...
from triqs.gf import MeshImFreq, BlockGf
iw_mesh = MeshImFreq(beta, 'Fermion', n_iw)
G_iw = BlockGf(mesh=iw_mesh, gf_struct=gf_struct)
### read out blocks from full w2dyn matrices
offset = 0
for name, g_iw in G_iw:
size1 = G_iw[name].data.shape[-1]
size2 = G_iw[name].data.shape[-2]
assert (size1 == size2)
size_block = size1
giw_block = giw[offset:offset + size_block,
offset:offset + size_block, :]
g_iw.data[:] = giw_block.transpose(2, 0, 1)
offset += size_block
return G_iw
def solve_lattice_bse(parm, momsus=False):
print('--> solve_lattice_bse')
print('nw =', parm.nw)
print('nwf =', parm.nwf)
# ------------------------------------------------------------------
# -- Setup lattice
bl = BravaisLattice([(1,0,0), (0,1,0)])
bz = BrillouinZone(bl)
bzmesh = MeshBrZone(bz, n_k=1) # only one k-point
e_k = Gf(mesh=bzmesh, target_shape=[1, 1])
e_k *= 0.
# ------------------------------------------------------------------
# -- Lattice single-particle Green's function
mesh = MeshImFreq(beta=parm.beta, S='Fermion', n_max=parm.nwf_gf)
parm.Sigma_iw = parm.G_iw.copy()
G0_iw = parm.G_iw.copy()
G0_iw << inverse(iOmega_n + 0.5*parm.U)
parm.Sigma_iw << inverse(G0_iw) - inverse(parm.G_iw)
parm.mu = 0.5*parm.U
g_wk = lattice_dyson_g_wk(mu=parm.mu, e_k=e_k, sigma_w=parm.Sigma_iw)
g_wr = fourier_wk_to_wr(g_wk)
# ------------------------------------------------------------------
# -- Non-interacting generalized lattice susceptibility
chi0_wr = chi0r_from_gr_PH(nw=parm.nw, nnu=parm.nwf, gr=g_wr)
chi0_wk = chi0q_from_chi0r(chi0_wr)
# ------------------------------------------------------------------
# -- Solve lattice BSE
parm.chi_wk = chiq_from_chi0q_and_gamma_PH(chi0_wk, parm.gamma_m)
# ------------------------------------------------------------------
# -- Store results and static results
num = np.squeeze(parm.chi_wk.data.real)
ref = np.squeeze(parm.chi_m.data.real)
diff = np.max(np.abs(num - ref))
print('diff =', diff)
parm.chi_w = chiq_sum_nu_q(parm.chi_wk) # static suscept
return parm
def create_g0_wk_for_test_model(p):
H = create_model_for_tests(**p)
kmesh = H.get_kmesh(n_k=[p.nk] * p.dim + [1] * (3 - p.dim))
e_k = H.fourier(kmesh)
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)
return g0_wk
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 G2_loc_fixed_fermionic_window_python(g2, nwf):
""" Limit the last two fermionic freqiencies of a three
frequency Green's function object :math:`G(\omega, \nu, \nu')`
to ``nwf``. """
nw = (g2.data.shape[0] + 1) // 2
n = g2.data.shape[1]
beta = g2.mesh.components[0].beta
assert (n // 2 >= nwf)
mesh_iw = MeshImFreq(beta=beta, S='Boson', n_max=nw)
mesh_inu = MeshImFreq(beta=beta, S='Fermion', n_max=nwf)
mesh_prod = MeshProduct(mesh_iw, mesh_inu, mesh_inu)
g2_out = Gf(mesh=mesh_prod, target_shape=g2.target_shape)
s = n // 2 - nwf
e = n // 2 + nwf
g2_out.data[:] = g2.data[:, s:e, s:e]
return g2_out
def bubble_setup(beta, mu, tb_lattice, nk, nw, sigma_w=None):
print((tprf_banner(), "\n"))
print(('beta =', beta))
print(('mu =', mu))
print(('sigma =', (not (sigma == None))))
norb = tb_lattice.NOrbitalsInUnitCell
print(('nk =', nk))
print(('nw =', nw))
print(('norb =', norb))
print()
ntau = 4 * nw
ntot = np.prod(nk) * norb**4 + np.prod(nk) * (nw + ntau) * norb**2
nbytes = ntot * np.complex128().nbytes
ngb = nbytes / 1024.**3
print(('Approx. Memory Utilization: %2.2f GB\n' % ngb))
periodization_matrix = np.diag(np.array(list(nk), dtype=int))
#print 'periodization_matrix =\n', periodization_matrix
bz = BrillouinZone(tb_lattice.bl)
bzmesh = MeshBrZone(bz, periodization_matrix)
print('--> ek')
e_k = ek_tb_dispersion_on_bzmesh(tb_lattice, bzmesh, bz)
if sigma is None:
print('--> g0k')
wmesh = MeshImFreq(beta=beta, S='Fermion', n_max=nw)
g_wk = lattice_dyson_g0_wk(mu=mu, e_k=e_k, mesh=wmesh)
else:
print('--> gk')
sigma_w = strip_sigma(nw, beta, sigma)
g_wk = lattice_dyson_g_wk(mu=mu, e_k=e_k, sigma_w=sigma_w)
print('--> gr_from_gk (k->r)')
g_wr = fourier_wk_to_wr(g_wk)
del g_wk
print('--> grt_from_grw (w->tau)')
g_tr = fourier_wr_to_tr(g_wr)
del g_wr
if sigma is None:
return g_tr
else:
return g_tr, sigma_w
def delta_inv(beta, nw, nk=100):
mesh = MeshImFreq(beta, 'Fermion', n_max=nw)
Sigma0, Sigma1 = 1.337, 3.5235
ek = 2.*np.random.random(nk) - 1.
G = Gf(mesh=mesh, target_shape=[1, 1])
Sig = G.copy()
for w in Sig.mesh:
Sig[w][:] = Sigma0 + Sigma1 /w
for e in ek: G << G + inverse(iOmega_n - e - Sig)
G /= nk
Delta = G.copy()
Delta << inverse(G) - iOmega_n + Sig
sum_ek = - np.sum(ek) / nk
Roo = np.abs(Sigma0) + 1.
w = [ w for w in mesh ]
wmax = np.abs(w[-1].value)
tail, err = Delta.fit_tail()
order = len(tail)
trunc_err_anal = (Roo / (0.8 * wmax))**order
ratio = tail[0] / sum_ek
diff = np.abs(1 - ratio)
print('-' * 72)
print('beta =', beta)
print('nw =', nw)
print('wmax =', wmax)
print('tail_fit order =', len(tail))
print('tail_fit err =', err)
print(tail[:3])
#print sum_ek
print('trunc_err_anal =', trunc_err_anal)
print('ratio =', ratio)
print('diff =', diff)
return diff[0, 0]
def test_sumk_discrete(self):
tbl_w90 = TB_from_wannier90(seed='wannier_TB_test',
path='./',
extend_to_spin=False)
SK = SumkDiscreteFromLattice(lattice=tbl_w90, n_points=10)
Sigma_proto = GfImFreq(
mesh=MeshImFreq(beta=40, S='Fermion', n_max=1025),
target_shape=[tbl_w90.n_orbitals, tbl_w90.n_orbitals])
Sigma_iw = BlockGf(name_list=['up', 'down'],
block_list=[Sigma_proto, Sigma_proto],
make_copies=True)
# Sumk only accepts Sigma of MeshImFreq
Gloc = SK(Sigma=Sigma_iw, mu=12.3461)
# check if density is close to 1, not to strict since nkpts is relatively small
assert abs(Gloc.total_density().real - 1.0) < 1e-2
def __init__(self,
beta,
gf_struct,
n_iw=1025,
n_tau=10001,
n_l=30,
delta_interface=False,
complex=False):
"""Constructor setting up response function parameters
Arguments:
beta : inverse temperature
gf_struct : Triqs Green's function block structure
n_iw : number of Matsubara frequencies
n_tau : number of imaginary time points
"""
self.constr_params = {
"beta": beta,
"gf_struct": gf_struct,
"n_iw": n_iw,
"n_tau": n_tau,
"n_l": n_l,
"delta_interface": delta_interface
}
self.beta = beta
self.gf_struct = gf_struct
self.n_iw = n_iw
self.n_tau = n_tau
self.n_l = n_l
self.delta_interface = delta_interface
self.complex = complex
self.tau_mesh = MeshImTime(beta, 'Fermion', n_tau)
self.iw_mesh = MeshImFreq(beta, 'Fermion', n_iw)
if self.delta_interface:
self.Delta_tau = BlockGf(mesh=self.tau_mesh,
gf_struct=self.gf_struct)
else:
self.G0_iw = BlockGf(mesh=self.iw_mesh, gf_struct=gf_struct)
def add_fake_bosonic_mesh(gf, beta=None):
""" Put a one value bosonic mesh as the first mesh argument of a
Green's function object.
Parameters
----------
gf : Gf,
Green's function on some arbitrary mesh. If 'beta' is not given
one mesh needs to be a 'MeshImFreq' to obtain a beta'
beta : float, optional
The inverse temperature used for the fake bosonic mesh.
Returns
-------
gf_w : Gf,
Green's function with an additional one value bosonic mesh
on its first position.
"""
mesh = gf.mesh
if isinstance(mesh, MeshProduct):
meshes = mesh.components
else:
meshes = (mesh, )
# If beta is not given access it from a 'MeshImFreq' of the 'Gf'
if not beta:
betas = [mesh.beta for mesh in meshes if hasattr(mesh, "beta")]
if len(betas) == 0:
raise ValueError(
"No 'beta' was given and the Green's function does not contain"
" a 'MeshImFreq'")
beta = betas[0]
wmesh = MeshImFreq(beta, 'Boson', 1)
mesh = (wmesh, ) + meshes
mesh = MeshProduct(*mesh)
gf_w = Gf(mesh=mesh, target_shape=gf.target_shape)
gf_w.data[0, ...] = gf.data
return gf_w
# 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 may obtain a copy of the License at # https:#www.gnu.org/licenses/gpl-3.0.txt # # Authors: Alexander Hampel, Nils Wentzell import numpy as np from triqs.gf import MeshImFreq, MeshImTime from triqs.gf.tools import discretize_bath, make_delta from triqs.utility.comparison_tests import assert_gfs_are_close # build delta from discretized values mesh = MeshImFreq(beta=40, S='Fermion', n_max=200) hoppings = np.array([[0.2, 0.6]]) energies = np.array([0.0, 0.5]) delta_iw = make_delta(V=hoppings, eps=energies, mesh=mesh) # run bath fitter on this input V_opt, e_opt, delta_disc_iw = discretize_bath(delta_in=delta_iw, Nb=2, eps0=2.5, V0=None, tol=1e-10) # compare to given values , resulting V can be correct up to a global sign assert np.max(np.abs(hoppings) - np.abs(V_opt)) < 1e-6, 'did not achieved requiered accuracy for bath fit \n'+str(V_opt)+' vs \n'+str(hoppings) assert np.max(np.abs(energies - e_opt)) < 1e-6, 'did not achieved requiered accuracy for bath fit \n'+str(e_opt)+' vs \n'+str(energies) assert_gfs_are_close(delta_disc_iw, delta_iw) #try with Nb % n_orb != 0 V_opt, e_opt, delta_disc_iw = discretize_bath(delta_in=delta_iw, Nb=3, eps0=2.5, V0=None, tol=1e-10)
p.diag = 0.5 + p.delta
p.odiag = 0.5 - p.delta
p.solve.alpha = [[[p.diag, p.odiag] for i in indices]
for bl, indices in p.gf_struct]
# -- Total impurity hamiltonian and interaction part
p.H_0 = -p.mu * (n('up', 0) + n('dn', 0)) - p.h * (n('up', 0) - n('dn', 0))
p.H_int = p.U * n('up', 0) * n('dn', 0)
p.H = p.H_0 + p.H_int
p.solve.h_int = p.H_int
# -- Non-Interacting Impurity Green function
iw_mesh = MeshImFreq(p.beta, 'Fermion', p.n_iw)
p.G0_iw = Gf_from_struct(mesh=iw_mesh, struct=p.gf_struct)
h_field_dict = dict(up=p.h, dn=-p.h)
for name, g0_iw in p.G0_iw:
h_field = h_field_dict[name]
g0_iw << inverse(iOmega_n + p.mu + h_field)
# -- CTINT
S = SolverCore(**p.solver_core.dict())
S.G0_iw << p.G0_iw
S.solve(**p.solve.dict())
# -- Store to hdf5 archive
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
-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)
# ----------------------------------------------------------------------
# -- Kanamori interaction
from triqs.operators.util import U_matrix_kanamori, h_int_kanamori
from triqs_tprf.OperatorUtils import fundamental_operators_from_gf_struct
from triqs_tprf.rpa_tensor import get_rpa_tensor
U = 1.0
J = 0.1
def mesh_product_iterator_numpy(mesh):
return [
list(map(np.array, list(zip(*list(x)))))
for x in mesh_product_iterator(chi4_tau.mesh)
]
# ----------------------------------------------------------------------
if __name__ == '__main__':
nw = 20
nt = 45
beta = 2.0
imtime = MeshImTime(beta, 'Fermion', nt)
imfreq = MeshImFreq(beta, 'Fermion', nw)
imtime3 = MeshProduct(imtime, imtime, imtime)
imfreq3 = MeshProduct(imfreq, imfreq, imfreq)
chi4_tau = Gf(name=r'$g(\tau)$', mesh=imtime3, target_shape=[1, 1, 1, 1])
print(dir(chi4_tau.indices))
for i in chi4_tau.indices:
print(i)
exit()
# -- Smooth anti-periodic function
w = 0.5
e1, e2, e3 = w, w, w
E = np.array([e1, e2, e3])
print('E_kin_ref =', E_kin_ref)
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)
nnu = 100
# -- BZ-sampling
bz = BrillouinZone(BravaisLattice([[1, 0], [0, 1]]))
bzmesh = MeshBrZone(bz, n_k=n_k)
q_list = [q for q in bzmesh]
# -- Dispersion
ek = Gf(mesh=bzmesh, target_shape=[1, 1])
for idx, k in enumerate(bzmesh):
#ek[k] = -2*t*(np.cos(k[0]) + np.cos(k[1])) # does not work...
ek.data[idx] = -2 * (np.cos(k[0]) + np.cos(k[1]))
mesh = MeshImFreq(beta=beta, S='Fermion', n_max=nw_g)
bmesh = MeshImFreq(beta=beta, S='Boson', n_max=nw)
iw_list = np.array([iw for iw in bmesh])
iw_zero_idx = np.where(iw_list == 0)[0][0]
# -- Lattice single-particle Green's function
g0k = g0k_from_ek(mu=mu, ek=ek, mesh=mesh)
g0r = gr_from_gk(g0k)
# -- Non-interacting generalized lattice susceptibility
chi0r = chi0r_from_gr_PH(nw=nw, nnu=nnu, gr=g0r)
chi0q = chi0q_from_chi0r(chi0r, bz)
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
from triqs.gf import Gf, MeshImFreq, MeshBrZone, MeshProduct
from triqs.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 = MeshBrZone(bz, p.nk * np.eye(3, dtype=int))
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)
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_r = TBLattice(
units=[(1, 0, 0)],
hopping={
(+1, ): t,
(-1, ): t,
},
orbital_positions=[(0, 0, 0)] * norb,
)
kmesh = t_r.get_kmesh(n_k=(8, 1, 1))
e_k = t_r.fourier(kmesh)
print(e_k.data)
kmesh = e_k.mesh
wmesh = MeshImFreq(beta, 'Fermion', nw)
g_wk = lattice_dyson_g0_wk(mu=mu, e_k=e_k, mesh=wmesh)
V_k = Gf(mesh=kmesh, target_shape=[norb] * 4)
V_k.data[:] = V
print('--> pi_bubble')
PI_wk = bubble_PI_wk(g_wk)
print('--> screened_interaction_W')
Wr_wk = retarded_screened_interaction_Wr_wk(PI_wk, V_k)
print('--> gw_self_energy')
sigma_wk = gw_sigma_wk(Wr_wk, g_wk, fft_flag=True)
sigma_wk_ref = gw_sigma_wk(Wr_wk, g_wk, fft_flag=False)
np.testing.assert_array_almost_equal(sigma_wk.data, sigma_wk_ref.data)
h_bath = sum(c_dag_bath_vec[s] * h_bath_mat * c_bath_vec[s]
for s in spin_names)[0, 0]
h_coup = sum(c_dag_vec[s] * V_mat * c_bath_vec[s] +
c_dag_bath_vec[s] * V_mat.transpose() * c_vec[s]
for s in spin_names)[0, 0] # FIXME Adjoint
# ==== Total impurity hamiltonian ====
h_imp = h_loc + h_coup + h_bath
# ==== Green function structure ====
gf_struct = [[s, orb_names] for s in spin_names]
# ==== Hybridization Function ====
n_iw = int(10 * beta)
iw_mesh = MeshImFreq(beta, 'Fermion', n_iw)
Delta = BlockGf(mesh=iw_mesh, gf_struct=gf_struct)
# FIXME Delta['up'] << V_mat.transpose() * inverse(iOmega_n - h_bath_mat) * V_mat
for bl, iw in product(spin_names, iw_mesh):
Delta[bl][iw] = V_mat * inv(iw.value * eye(len(orb_bath_names)) -
h_bath_mat) * V_mat.transpose()
# ==== Non-Interacting Impurity Green function ====
G0_iw = Delta.copy()
G0_iw['up'] << inverse(
iOmega_n - h_0_mat - Delta['up']) # FIXME Should work for BlockGf
G0_iw['dn'] << inverse(iOmega_n - h_0_mat - Delta['dn'])
# ==== Construct the CTHYB solver using the G0_iw Interface ====
constr_params = {
'beta': beta,
import triqs.utility.mpi as mpi
from triqs.gf import Gf, MeshImFreq, MeshProduct
from triqs.gf import MeshBrZone, MeshCycLat
from triqs.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=int))
bzmesh = MeshBrZone(bz, periodization_matrix)
lmesh = MeshCycLat(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)
