def on_mesh_brillouin_zone(self, n_k):
""" Construct a discretization of the tight binding model in
reciprocal space with given number of k-points.
Parameters
----------
n_k : three-tuple of ints
Number of k-points in every dimension.
Returns
-------
e_k : TRIQS Greens function on a Brillioun zone mesh
Reciprocal space tight binding dispersion.
"""
target_shape = [self.NOrbitalsInUnitCell] * 2
kmesh = self.get_kmesh(n_k)
e_k = Gf(mesh=kmesh, target_shape=target_shape)
k_vec = np.array([k.value for k in kmesh])
k_vec_rel = np.dot(np.linalg.inv(self.bz.units()).T, k_vec.T).T
e_k.data[:] = self.hopping(k_vec_rel.T).transpose(2, 0, 1)
return e_k
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 compute_chi0_k(self):
from pytriqs.gf import Gf
chi0_k = Gf(mesh=self.e_k.mesh, target_shape=self.shape_abcd)
chi0_k.data[:] = self.chi0_kabcd
return chi0_k
def Gf_from_struct(mesh, struct):
# Without block structure
if not isinstance(struct[0], list):
return Gf(mesh=mesh, indices=struct)
# With block structure
G_lst = []
for bl, idx_lst in struct:
G_lst.append(Gf(mesh=mesh, indices=idx_lst))
return BlockGf(name_list=[bl[0] for bl in struct], block_list=G_lst)
def ek_tb_dispersion_on_bzmesh(tb_lattice, bzmesh, bz):
""" Evaluate dispersion on bzmesh from tight binding model. """
n_orb = tb_lattice.NOrbitalsInUnitCell
ek = Gf(mesh=bzmesh, target_shape=[n_orb] * 2)
k_vec = np.array([k.value for k in bzmesh])
k_vec_rel = get_relative_k_from_absolute(k_vec, bz.units())
ek.data[:] = tb_lattice.hopping(k_vec_rel.T).transpose(2, 0, 1)
return ek
def on_mesh_brillouin_zone(self, n_k):
target_shape = [self.NOrbitalsInUnitCell] * 2
kmesh = self.get_kmesh(n_k)
e_k = Gf(mesh=kmesh, target_shape=target_shape)
k_vec = np.array([k.value for k in kmesh])
k_vec_rel = np.dot(np.linalg.inv(self.bz.units()).T, k_vec.T).T
e_k.data[:] = self.hopping(k_vec_rel.T).transpose(2, 0, 1)
return e_k
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 convert_from_ndarray_to_triqs(U_Q, Q, cell, kpts):
from pytriqs.gf import Gf, MeshBrillouinZone
from pytriqs.lattice.lattice_tools import BrillouinZone
from pytriqs.lattice.lattice_tools import BravaisLattice
bl = BravaisLattice(cell, [(0, 0, 0)])
bz = BrillouinZone(bl)
bzmesh = MeshBrillouinZone(bz, np.diag(np.array(kpts, dtype=np.int32)))
u_q = Gf(mesh=bzmesh, target_shape=U_Q.shape[1:])
tmp = np.array(Q * kpts[None, :], dtype=np.int)
I = [tuple(tmp[i]) for i in xrange(Q.shape[0])]
for qidx, i in enumerate(I):
for k in bzmesh:
# -- Generalize this transform absolute to relative k-points
a = cell[0, 0]
q = k * 0.5 * a / np.pi
j = tuple(np.array(kpts * q, dtype=np.int))
if i == j: u_q[k].data[:] = U_Q[qidx]
return u_q
def setup_dmft_calculation(p):
p = copy.deepcopy(p)
p.iter = 0
# -- Local Hubbard interaction
from pytriqs.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})
p.e_k = H.on_mesh_brillouin_zone(n_k = (p.n_k, p.n_k, 1))
# -- 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 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 = MeshBrillouinZone(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 fixed_fermionic_window_python_wnk(g2, nwf):
#nw = (g2.data.shape[0] + 1) / 2
wmesh, nmesh, kmesh = g2.mesh.components
beta = g2.mesh.components[0].beta
nmesh_small = MeshImFreq(beta=beta, S='Fermion', n_max=nwf)
g2_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
g2_out.data[:] = g2.data[:, s:e, :]
return g2_out
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 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)
from pytriqs.gf import Gf, MeshImFreq, MeshProduct
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 __init__(self,
g1_inu,
n_iw,
n_inu,
blocks_to_calculate=[],
blockstructure_to_compare_with="AABB"):
"""
g1_inu has to be a BlockGf of GfImFreq
"""
mb = MeshImFreq(g1_inu.mesh.beta, "Boson", n_iw)
mf = MeshImFreq(g1_inu.mesh.beta, "Fermion", n_inu)
blockmesh = MeshProduct(mb, mf, mf)
blocks = []
self.gf2_struct = dict()
for i in g1_inu.indices:
blocksR = []
for j in g1_inu.indices:
blockindex = (i, j)
m, n = g1_inu[i].data.shape[1], g1_inu[j].data.shape[1]
blockshape = [m, m, n, n]
blocksR.append(Gf(mesh=blockmesh, target_shape=blockshape))
self.gf2_struct[blockindex] = (m, n)
blocks.append(blocksR)
g1_indices = [i for i in g1_inu.indices]
Block2Gf.__init__(self, g1_indices, g1_indices, blocks)
self.beta = g1_inu.mesh.beta
# mesh adjustments for negative frequencies and g1/g2 mesh-offsets
self.n_iw = len(mb)
self.n_inu = len(mf)
self.bosonic_mesh = np.array(
[w for w in self[blockindex].mesh.components[0]])
self.fermionic_mesh = np.array(
[w for w in self[blockindex].mesh.components[1]])
g1_mesh = np.array([w for w in g1_inu.mesh])
fermionic_mesh_offset = np.argwhere(
g1_mesh.imag == self.fermionic_mesh.imag[0])[0, 0]
bosonic_mesh_offset = np.argwhere(0 == self.bosonic_mesh.imag)[0, 0]
self.f_mesh_inds = np.arange(fermionic_mesh_offset,
self.n_inu + fermionic_mesh_offset)
self.b_mesh_inds = np.arange(-bosonic_mesh_offset,
self.n_iw - bosonic_mesh_offset)
if len(blocks_to_calculate) == 0:
blocks_to_calculate = self.indices
self.blockstruct = blockstructure_to_compare_with
contractions = {"direct": [1, 0, 3, 2], "exchange": [1, 2, 3, 0]}
for blockindex in blocks_to_calculate:
self.set_block(g1_inu, blockindex, contractions)
def general_susceptibility_from_charge_and_spin(chi_c, chi_s, spin_fast=True):
"""Construct a general susceptibility (spin dependent) from chi spin and charge
Parameters:
chi_c: Greens function, the charge susceptibility
chi_s: Greens function, the spin susceptibility
spin_fast: bool, True if spin is the fast index, e.g.
xz up, xz down, xy up, xy down, yz up, yz down,
or False if spin is the slow index, e.g.
xz up, xy up, yz up, xz down, xy down, yz down.
"""
norb = chi_c.target_shape[-1]
rank = chi_c.rank
target_rank = chi_c.target_rank
chi_general = Gf(mesh=chi_c.mesh, target_shape=target_rank * (2 * norb, ))
chi_uu = 0.5 * (chi_c + chi_s)
chi_ud = 0.5 * (chi_c - chi_s)
chi_xud = chi_s
idx_rank = rank * (slice(None), )
if spin_fast:
up = slice(None, None, 2)
down = slice(1, None, 2)
else:
up = slice(norb)
down = slice(norb, None)
chi_general.data[idx_rank + (up, up, up, up)] = chi_uu.data
chi_general.data[idx_rank + (down, down, down, down)] = chi_uu.data
chi_general.data[idx_rank + (up, up, down, down)] = chi_ud.data
chi_general.data[idx_rank + (down, down, up, up)] = chi_ud.data
chi_general.data[idx_rank + (up, down, down, up)] = chi_xud.data
chi_general.data[idx_rank + (down, up, up, down)] = chi_xud.data
return chi_general
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 pytriqs.plot.mpl_interface import oplot, plt
oplot(p.Sigmalatt_iw)
oplot(sigma, 'x')
plt.show()
exit()
return sigma
def make_calc(U=10):
# ------------------------------------------------------------------
# -- Hubbard atom with two bath sites, Hamiltonian
params = dict(
beta=2.0,
V1=2.0,
V2=5.0,
epsilon1=0.00,
epsilon2=4.00,
mu=2.0,
U=U,
ntau=40,
niw=15,
)
# ------------------------------------------------------------------
class Dummy():
def __init__(self):
pass
d = Dummy() # storage space
d.params = params
print '--> Solving SIAM with parameters'
for key, value in params.items():
print '%10s = %-10s' % (key, str(value))
globals()[key] = value # populate global namespace
# ------------------------------------------------------------------
up, do = 0, 1
docc = c_dag(up, 0) * c(up, 0) * c_dag(do, 0) * c(do, 0)
nA = c_dag(up, 0) * c(up, 0) + c_dag(do, 0) * c(do, 0)
nB = c_dag(up, 1) * c(up, 1) + c_dag(do, 1) * c(do, 1)
nC = c_dag(up, 2) * c(up, 2) + c_dag(do, 2) * c(do, 2)
d.H = -mu * nA + epsilon1 * nB + epsilon2 * nC + U * docc + \
V1 * (c_dag(up,0)*c(up,1) + c_dag(up,1)*c(up,0) + \
c_dag(do,0)*c(do,1) + c_dag(do,1)*c(do,0) ) + \
V2 * (c_dag(up,0)*c(up,2) + c_dag(up,2)*c(up,0) + \
c_dag(do,0)*c(do,2) + c_dag(do,2)*c(do,0) )
# ------------------------------------------------------------------
# -- Exact diagonalization
fundamental_operators = [
c(up, 0), c(do, 0),
c(up, 1), c(do, 1),
c(up, 2), c(do, 2)
]
ed = TriqsExactDiagonalization(d.H, fundamental_operators, beta)
# ------------------------------------------------------------------
# -- Single-particle Green's functions
Gopt = dict(beta=beta, statistic='Fermion', indices=[1])
d.G_tau = GfImTime(name=r'$G(\tau)$', n_points=ntau, **Gopt)
d.G_iw = GfImFreq(name='$G(i\omega_n)$', n_points=niw, **Gopt)
ed.set_g2_tau(d.G_tau, c(up, 0), c_dag(up, 0))
ed.set_g2_iwn(d.G_iw, c(up, 0), c_dag(up, 0))
# chi2pp = + < c^+_u(\tau^+) c_u(0^+) c^+_d(\tau) c_d(0) >
# = - < c^+_u(\tau^+) c^+_d(\tau) c_u(0^+) c_d(0) >
chi2opt = dict(beta=beta, statistic='Fermion', indices=[1], n_points=ntau)
d.chi2pp_tau = GfImTime(name=r'$\chi^{(2)}_{PP}(\tau)$', **chi2opt)
ed.set_g2_tau(d.chi2pp_tau,
c_dag(up, 0) * c_dag(do, 0),
c(up, 0) * c(do, 0))
d.chi2pp_tau *= -1.0 * -1.0 # commutation sign and gf sign
d.chi2pp_iw = g_iw_from_tau(d.chi2pp_tau, niw)
# chi2ph = < c^+_u(\tau^+) c_u(\tau) c^+_d(0^+) c_d(0) >
d.chi2ph_tau = GfImTime(name=r'$\chi^{(2)}_{PH}(\tau)$', **chi2opt)
#d.chi2ph_tau = Gf(name=r'$\chi^{(2)}_{PH}(\tau)$', **chi2opt)
ed.set_g2_tau(d.chi2ph_tau,
c_dag(up, 0) * c(up, 0),
c_dag(do, 0) * c(do, 0))
d.chi2ph_tau *= -1.0 # gf sign
d.chi2ph_iw = g_iw_from_tau(d.chi2ph_tau, niw)
# ------------------------------------------------------------------
# -- Two particle Green's functions
imtime = MeshImTime(beta, 'Fermion', ntau)
prodmesh = MeshProduct(imtime, imtime, imtime)
G2opt = dict(mesh=prodmesh, target_shape=[1, 1, 1, 1])
d.G02_tau = Gf(name='$G^{(2)}_0(\tau_1, \tau_2, \tau_3)$', **G2opt)
ed.set_g40_tau(d.G02_tau, d.G_tau)
d.G02_iw = chi4_iw_from_tau(d.G02_tau, niw)
d.G2_tau = Gf(name='$G^{(2)}(\tau_1, \tau_2, \tau_3)$', **G2opt)
ed.set_g4_tau(d.G2_tau, c_dag(up, 0), c(up, 0), c_dag(do, 0), c(do, 0))
#ed.set_g4_tau(d.G2_tau, c(up,0), c_dag(up,0), c(do,0), c_dag(do,0)) # <cc^+cc^+>
d.G2_iw = chi4_iw_from_tau(d.G2_tau, niw)
# -- trying to fix the bug in the fft for w2
d.G02_iw.data[:] = d.G02_iw.data[:, ::-1, ...].conj()
d.G2_iw.data[:] = d.G2_iw.data[:, ::-1, ...].conj()
# ------------------------------------------------------------------
# -- 3/2-particle Green's functions (equal times)
prodmesh = MeshProduct(imtime, imtime)
chi3opt = dict(mesh=prodmesh, target_shape=[1, 1, 1, 1])
# chi3pp = <c^+_u(\tau) c_u(0^+) c^+_d(\tau') c_d(0) >
# = - <c^+_u(\tau) c^+_d(\tau') c_u(0^+) c_d(0) >
d.chi3pp_tau = Gf(name='$\Chi^{(3)}_{PP}(\tau_1, \tau_2, \tau_3)$',
**chi3opt)
ed.set_g3_tau(d.chi3pp_tau, c_dag(up, 0), c_dag(do, 0),
c(up, 0) * c(do, 0))
d.chi3pp_tau *= -1.0 # from commutation
d.chi3pp_iw = chi3_iw_from_tau(d.chi3pp_tau, niw)
# chi3ph = <c^+_u(\tau) c_u(\tau') c^+_d(0^+) c_d(0) >
d.chi3ph_tau = Gf(name='$\Chi^{(3)}_{PH}(\tau_1, \tau_2, \tau_3)$',
**chi3opt)
ed.set_g3_tau(d.chi3ph_tau, c_dag(up, 0), c(up, 0),
c_dag(do, 0) * c(do, 0))
d.chi3ph_iw = chi3_iw_from_tau(d.chi3ph_tau, niw)
# ------------------------------------------------------------------
# -- Store to hdf5
filename = 'data_ed.h5'
with HDFArchive(filename, 'w') as res:
for key, value in d.__dict__.items():
res[key] = value
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 = MeshBrillouinZone(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
def trace_nn(G2_wnn):
bmesh = G2_wnn.mesh.components[0]
G2_w = Gf(mesh=bmesh, target_shape=G2_wnn.target_shape)
G2_w.data[:] = np.sum(G2_wnn.data, axis=(1, 2)) / bmesh.beta**2
return G2_w
# ----------------------------------------------------------------------
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])
for idx, tau in mesh_product_iterator_numpy(chi4_tau.mesh):
chi4_tau[idx.tolist()][:] = np.sum(np.cos(np.pi * E * tau))
# -- Test fourier
def solve_lattice_bse(g_wk, gamma_wnn, tail_corr_nwf=None):
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 'tail_corr_nwf =', tail_corr_nwf
print
if tail_corr_nwf is None:
tail_corr_nwf = nwf
mpi.report('--> chi0_wnk_tail_corr')
chi0_wnk_tail_corr = get_chi0_wnk(g_wk, nw=nw, nwf=tail_corr_nwf)
mpi.report('--> trace chi0_wnk_tail_corr (WARNING! NO TAIL FIT. FIXME!)')
chi0_wk_tail_corr = chi0q_sum_nu_tail_corr_PH(chi0_wnk_tail_corr)
#chi0_wk_tail_corr = chi0q_sum_nu(chi0_wnk_tail_corr)
mpi.barrier()
mpi.report('B1 ' +
str(chi0_wk_tail_corr[Idx(0), Idx(0, 0, 0)][0, 0, 0, 0]))
mpi.barrier()
mpi.report('--> chi0_wnk_tail_corr to chi0_wnk')
if tail_corr_nwf != nwf:
mpi.report('--> fixed_fermionic_window_python_wnk')
chi0_wnk = fixed_fermionic_window_python_wnk(chi0_wnk_tail_corr,
nwf=nwf)
else:
chi0_wnk = chi0_wnk_tail_corr.copy()
del chi0_wnk_tail_corr
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
beta=beta,
statistic='Fermion',
n_points=10,
indices=[1])
ed.set_g2_tau(g_tau, c(up, 0), c_dag(up, 0))
ed.set_g2_iwn(g_iwn, c(up, 0), c_dag(up, 0))
# ------------------------------------------------------------------
# -- Two particle Green's functions
ntau = 20
imtime = MeshImTime(beta, 'Fermion', ntau)
prodmesh = MeshProduct(imtime, imtime, imtime)
g40_tau = Gf(name='g40_tau', mesh=prodmesh, target_shape=[1, 1, 1, 1])
g4_tau = Gf(name='g4_tau', mesh=prodmesh, target_shape=[1, 1, 1, 1])
ed.set_g40_tau(g40_tau, g_tau)
ed.set_g4_tau(g4_tau, c(up, 0), c_dag(up, 0), c(up, 0), c_dag(up, 0))
# ------------------------------------------------------------------
# -- Two particle Green's functions (equal times)
prodmesh = MeshProduct(imtime, imtime)
g3pp_tau = Gf(name='g4_tau', mesh=prodmesh, target_shape=[1, 1, 1, 1])
ed.set_g3_tau(g3pp_tau, c(up, 0), c_dag(up, 0), c(up, 0) * c_dag(up, 0))
# ------------------------------------------------------------------
# -- Store to hdf5
beta = 10.0
U = 2.0
mu = 1.0
h = 0.1
#V = 0.5
V = 1.0
epsilon = 2.3
H = U * n('up', 0) * n('do', 0) + \
- mu * (n('up', 0) + n('do', 0)) + \
h * n('up', 0) - h * n('do', 0) + \
epsilon * (n('up', 1) + n('do', 1)) - epsilon * (n('up', 2) + n('do', 2)) + \
V * ( c_dag('up', 0) * c('up', 1) + c_dag('up', 1) * c('up', 0) ) + \
V * ( c_dag('do', 0) * c('do', 1) + c_dag('do', 1) * c('do', 0) ) + \
V * ( c_dag('up', 0) * c('up', 2) + c_dag('up', 2) * c('up', 0) ) + \
V * ( c_dag('do', 0) * c('do', 2) + c_dag('do', 2) * c('do', 0) )
ed = TriqsExactDiagonalization(H, fundamental_operators, beta)
n_tau = 101
G_tau_up = Gf(mesh=MeshImTime(beta, 'Fermion', n_tau), target_shape=[])
G_tau_do = Gf(mesh=MeshImTime(beta, 'Fermion', n_tau), target_shape=[])
ed.set_g2_tau(G_tau_up, c('up', 0), c_dag('up', 0))
ed.set_g2_tau(G_tau_do, c('do', 0), c_dag('do', 0))
with HDFArchive('anderson.pyed.h5', 'w') as Results:
Results['up'] = G_tau_up
Results['dn'] = G_tau_do
beta = 10.0
gf_struct = [['0', [0, 1]]]
target_shape = [2, 2]
nw = 48
nt = 3 * nw
S = SolverCore(beta=beta, gf_struct=gf_struct, n_iw=nw, n_tau=nt)
h_int = n('0', 0) * n('0', 1)
wmesh = MeshImFreq(beta=beta, S='Fermion', n_max=nw)
tmesh = MeshImTime(beta=beta, S='Fermion', n_max=nt)
Delta_iw = Gf(mesh=wmesh, target_shape=target_shape)
Ek = np.array([
[1.00, 0.75],
[0.75, -1.20],
])
E_loc = np.array([
[0.2, 0.3],
[0.3, 0.4],
])
V = np.array([
[1.0, 0.25],
[0.25, -1.0],
])
# ================== TPRF calculations ======================================== # -- Create dispersion relation Green's function object norbs = e_k_ref.shape[-1] units = [(1, 0, 0), (0, 1, 0), (0, 0, 1)] orbital_positions = [(0, 0, 0)] bl = BravaisLattice(units, orbital_positions) bz = BrillouinZone(bl) periodization_matrix = nk * np.eye(3, dtype=np.int32) periodization_matrix[2, 2] = 1 kmesh = MeshBrillouinZone(bz, periodization_matrix) e_k = Gf(mesh=kmesh, target_shape=[norbs, norbs]) e_k.data[:] = e_k_ref.reshape(nk**2, norbs, norbs) # -- Calculate bare Green's function wmesh = MeshImFreq(beta=beta, S='Fermion', n_max=n_max) g0_wk = lattice_dyson_g0_wk(mu=mu, e_k=e_k, mesh=wmesh) # -- Calculate bare bubble chi00_wk = imtime_bubble_chi0_wk(g0_wk, nw=n_max) # -- Calculate chi spin and charge U_c, U_s = kanamori_charge_and_spin_quartic_interaction_tensors(
def solve_lattice_bse(g_wk, gamma_wnn, tail_corr_nwf=None):
r""" Compute the generalized lattice susceptibility
:math:`\chi_{abcd}(\omega, \mathbf{k})` using the Bethe-Salpeter
equation (BSE).
Parameters
----------
g_wk : Single-particle Green's function :math:`G_{ab}(\omega, \mathbf{k})`.
gamma_wnn : Local particle-hole vertex function
:math:`\Gamma_{abcd}(\omega, \nu, \nu')`
tail_corr_nwf : Number of fermionic freqiencies to use in the
tail correction of the sum over fermionic frequencies.
Returns
-------
chi0_wk : Generalized lattice susceptibility
:math:`\chi_{abcd}(\omega, \mathbf{k})`
"""
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 'tail_corr_nwf =', tail_corr_nwf
print
if tail_corr_nwf is None:
tail_corr_nwf = nwf
mpi.report('--> chi0_wnk_tail_corr')
chi0_wnk_tail_corr = get_chi0_wnk(g_wk, nw=nw, nwf=tail_corr_nwf)
mpi.report('--> trace chi0_wnk_tail_corr (WARNING! NO TAIL FIT. FIXME!)')
chi0_wk_tail_corr = chi0q_sum_nu_tail_corr_PH(chi0_wnk_tail_corr)
#chi0_wk_tail_corr = chi0q_sum_nu(chi0_wnk_tail_corr)
mpi.barrier()
mpi.report('B1 ' +
str(chi0_wk_tail_corr[Idx(0), Idx(0, 0, 0)][0, 0, 0, 0]))
mpi.barrier()
mpi.report('--> chi0_wnk_tail_corr to chi0_wnk')
if tail_corr_nwf != nwf:
mpi.report('--> fixed_fermionic_window_python_wnk')
chi0_wnk = fixed_fermionic_window_python_wnk(chi0_wnk_tail_corr,
nwf=nwf)
else:
chi0_wnk = chi0_wnk_tail_corr.copy()
del chi0_wnk_tail_corr
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
noise growing quadratically with the frequency.
Author: Hugo U.R. Strand """
import itertools
import numpy as np
from pytriqs.archive import HDFArchive
from pytriqs.gf import Gf, MeshImFreq, MeshImTime, iOmega_n, inverse, Fourier
nw = 512
beta = 50.0
target_shape = [2, 2]
wmesh = MeshImFreq(beta=beta, S='Fermion', n_max=nw)
Delta_iw = Gf(mesh=wmesh, target_shape=target_shape)
Ek = np.array([
[1.00, 0.5],
[0.5, -1.20],
])
E_loc = np.array([
[0.33, 0.5],
[0.5, -0.1337],
])
V = np.array([
[1.0, 0.25],
[0.25, -1.0],
])
# Quantum numbers (N_up and N_down)
QN = []
for b, idxs in gf_struct: QN.append(n(b,0))
p["partition_method"] = "quantum_numbers"
p["quantum_numbers"] = QN
mpi.report("Constructing the solver...")
# Construct the solver
S = SolverCore(beta=beta, gf_struct=gf_struct, n_tau=n_tau, n_iw=n_iw)
mpi.report("Preparing the hybridization function...")
# Set hybridization function
#for m, b in enumerate(sorted(gf_struct.keys())):
for m, (b, idxs) in enumerate(gf_struct):
delta_w = Gf(mesh=S.G0_iw.mesh, target_shape=[])
delta_w << (V[m]**2) * inverse(iOmega_n - e[m])
S.G0_iw[b][0,0] << inverse(iOmega_n - e[m] - delta_w)
mpi.report("Running the simulation...")
# Solve the problem
S.solve(h_int=H, **p)
# Save results
if mpi.is_master_node():
with HDFArchive('nonint.h5','a') as Results:
Results[str(modes)] = {'G_tau':S.G_tau,'V':V,'e':e}
def five_plus_five(use_interaction=True):
results_file_name = "5_plus_5." + ("int."
if use_interaction else "") + "h5"
# Block structure of GF
L = 2 # d-orbital
spin_names = ("up", "dn")
orb_names = cubic_names(L)
# Input parameters
beta = 40.
mu = 26
U = 4.0
J = 0.7
F0 = U
F2 = J * (14.0 / (1.0 + 0.63))
F4 = F2 * 0.63
# Dump the local Hamiltonian to a text file (set to None to disable dumping)
H_dump = "H.txt"
# Dump Delta parameters to a text file (set to None to disable dumping)
Delta_dump = "Delta_params.txt"
# Hybridization function parameters
# Delta(\tau) is diagonal in the basis of cubic harmonics
# Each component of Delta(\tau) is represented as a list of single-particle
# terms parametrized by pairs (V_k,\epsilon_k).
delta_params = {
"xy": {
'V': 0.2,
'e': -0.2
},
"yz": {
'V': 0.2,
'e': -0.15
},
"z^2": {
'V': 0.2,
'e': -0.1
},
"xz": {
'V': 0.2,
'e': 0.05
},
"x^2-y^2": {
'V': 0.2,
'e': 0.4
}
}
atomic_levels = {
('up_xy', 0): -0.2,
('dn_xy', 0): -0.2,
('up_yz', 0): -0.15,
('dn_yz', 0): -0.15,
('up_z^2', 0): -0.1,
('dn_z^2', 0): -0.1,
('up_xz', 0): 0.05,
('dn_xz', 0): 0.05,
('up_x^2-y^2', 0): 0.4,
('dn_x^2-y^2', 0): 0.4
}
n_iw = 1025
n_tau = 10001
p = {}
p["max_time"] = -1
p["random_name"] = ""
p["random_seed"] = 123 * mpi.rank + 567
p["length_cycle"] = 50
#p["n_warmup_cycles"] = 5000
p["n_warmup_cycles"] = 500
p["n_cycles"] = int(1.e1 / mpi.size)
#p["n_cycles"] = int(5.e5 / mpi.size)
#p["n_cycles"] = int(5.e6 / mpi.size)
p["partition_method"] = "autopartition"
p["measure_G_tau"] = True
p["move_shift"] = True
p["move_double"] = True
p["measure_pert_order"] = False
p["performance_analysis"] = False
p["use_trace_estimator"] = False
mpi.report("Welcome to 5+5 (5 orbitals + 5 bath sites) test.")
gf_struct = set_operator_structure(spin_names, orb_names, False)
mkind = get_mkind(False, None)
H = Operator()
if use_interaction:
# Local Hamiltonian
U_mat = U_matrix(L, [F0, F2, F4], basis='cubic')
H += h_int_slater(spin_names, orb_names, U_mat, False, H_dump=H_dump)
else:
mu = 0.
p["h_int"] = H
# Quantum numbers (N_up and N_down)
QN = [Operator(), Operator()]
for cn in orb_names:
for i, sn in enumerate(spin_names):
QN[i] += n(*mkind(sn, cn))
if p["partition_method"] == "quantum_numbers": p["quantum_numbers"] = QN
mpi.report("Constructing the solver...")
# Construct the solver
S = SolverCore(beta=beta, gf_struct=gf_struct, n_tau=n_tau, n_iw=n_iw)
mpi.report("Preparing the hybridization function...")
H_hyb = Operator()
# Set hybridization function
if Delta_dump: Delta_dump_file = open(Delta_dump, 'w')
for sn, cn in product(spin_names, orb_names):
bn, i = mkind(sn, cn)
V = delta_params[cn]['V']
e = delta_params[cn]['e']
delta_w = Gf(mesh=MeshImFreq(beta, 'Fermion', n_iw), target_shape=[])
delta_w << (V**2) * inverse(iOmega_n - e)
S.G0_iw[bn][i, i] << inverse(iOmega_n + mu - atomic_levels[(bn, i)] -
delta_w)
cnb = cn + '_b' # bath level
a = sn + '_' + cn
b = sn + '_' + cn + '_b'
H_hyb += ( atomic_levels[(bn,i)] - mu ) * n(a, 0) + \
n(b,0) * e + V * ( c(a,0) * c_dag(b,0) + c(b,0) * c_dag(a,0) )
# Dump Delta parameters
if Delta_dump:
Delta_dump_file.write(bn + '\t')
Delta_dump_file.write(str(V) + '\t')
Delta_dump_file.write(str(e) + '\n')
if mpi.is_master_node():
filename_ham = 'data_Ham%s.h5' % ('_int' if use_interaction else '')
with HDFArchive(filename_ham, 'w') as arch:
arch['H'] = H_hyb + H
arch['gf_struct'] = gf_struct
arch['beta'] = beta
mpi.report("Running the simulation...")
# Solve the problem
S.solve(**p)
# Save the results
if mpi.is_master_node():
Results = HDFArchive(results_file_name, 'w')
Results['G_tau'] = S.G_tau
Results['G0_iw'] = S.G0_iw
Results['use_interaction'] = use_interaction
Results['delta_params'] = delta_params
Results['spin_names'] = spin_names
Results['orb_names'] = orb_names
import __main__
Results.create_group("log")
log = Results["log"]
log["version"] = version.version
log["triqs_hash"] = version.triqs_hash
log["cthyb_hash"] = version.cthyb_hash
log["script"] = inspect.getsource(__main__)
for tau in g_tau.mesh:
g_tau[tau] = np.exp(-beta * tau)
for idx, tau in enumerate(g_tau.mesh):
# comparison does not work at beta since the evaluation g_tau() wraps..
if idx == len(g_tau.mesh) - 1: break
#diff_interp = g_tau(tau)[0,0] - g_ref[idx] # FIXME: tau is complex
diff_interp = g_tau(tau.real)[0, 0] - g_ref[idx]
diff_dbrack = g_tau[tau][0, 0] - g_ref[idx]
np.testing.assert_almost_equal(diff_interp, 0.0)
np.testing.assert_almost_equal(diff_dbrack, 0.0)
# -- three imaginary time gf
imtime = MeshImTime(beta=beta, S='Fermion', n_max=ntau)
g4_tau = Gf(name='g4_tau',
mesh=MeshProduct(imtime, imtime, imtime),
indices=[1])
for t1, t2, t3 in g4_tau.mesh:
g4_tau[t1, t2, t3] = g_tau(t1) * g_tau(t3) - g_tau(t1) * g_tau(t3)
for t1, t2, t3 in g4_tau.mesh:
val = g4_tau[t1, t2, t3]
val_ref = g_tau(t1) * g_tau(t3) - g_tau(t1) * g_tau(t3)
np.testing.assert_array_almost_equal(val, val_ref)