def calc_reference():
ref_orbs = [
'%s' % i for i in range(n_orbs * parms['N_x'] * parms['N_y'])
]
ref_gf_struct = op.set_operator_structure(spin_names,
ref_orbs,
off_diag=off_diag)
ref_index_converter = {(sn, o): ("loc", int(o),
"down" if sn == "dn" else "up")
for sn, o in product(spin_names, ref_orbs)}
#print ref_index_converter,ref_orbs
ref_ed = PomerolED(ref_index_converter, verbose=True)
ref_N = sum(
ops.n(sn, o) for sn, o in product(spin_names, ref_orbs))
# 2 3
# 0 1
ref_H = (parms["U"] * (ops.n('up', '0') * ops.n('dn', '0') +
ops.n('up', '1') * ops.n('dn', '1')) -
2. * parms['t1'] *
(ops.c_dag('up', '0') * ops.c('up', '1') +
ops.c_dag('up', '1') * ops.c('up', '0') +
ops.c_dag('dn', '0') * ops.c('dn', '1') +
ops.c_dag('dn', '1') * ops.c('dn', '0')) -
parms['chemical_potential'] * ref_N)
# Run the solver
ref_ed.diagonalize(ref_H)
# Compute G(i\omega)
ref_G_iw = ref_ed.G_iw(ref_gf_struct, parms['beta'], parms['n_iw'])
return ref_G_iw
def __init__(self, beta, gf_struct, n_iw, spin_orbit=False, verbose=True):
self.beta = beta
self.gf_struct = gf_struct
self.n_iw = n_iw
self.spin_orbit = spin_orbit
self.verbose = verbose
if self.verbose and mpi.is_master_node():
print "\n*** Hubbard I solver using Pomerol library"
print "*** gf_struct =", gf_struct
print "*** n_iw =", n_iw
# get spin_name and orb_names from gf_struct
self.__analyze_gf_struct(gf_struct)
if self.verbose and mpi.is_master_node():
print "*** spin_names =", self.spin_names
print "*** orb_names =", self.orb_names
# check spin_names
for sn in self.spin_names:
if not spin_orbit:
assert sn in ('down', 'dn', 'up'
) # become either 'down' or 'up'
if spin_orbit:
assert sn in ('down', 'dn', 'ud') # all become 'down'
# Conversion from TRIQS to Pomerol notation for operator indices
# TRIQS: ('dn', '-2') --> Pomerol: ('atom', 0, 'down')
# NOTE: When spin_orbit is true, only spin 'down' is used.
mkind = get_mkind(True, None)
index_converter = {
mkind(sn, bn):
("atom", bi, "down" if sn == "dn" or sn == "ud" else sn)
for sn, (bi,
bn) in product(self.spin_names, enumerate(self.orb_names))
}
self.__ed = PomerolED(index_converter, verbose, spin_orbit)
# init G_iw
glist = lambda: [
GfImFreq(indices=self.orb_names, beta=beta, n_points=n_iw)
for block, inner in gf_struct.items()
]
self.G_iw = BlockGf(name_list=self.spin_names,
block_list=glist(),
make_copies=False)
self.G_iw.zero()
self.G0_iw = self.G_iw.copy()
self.Sigma_iw = self.G_iw.copy()
def run_test(t1, filename):
dptkeys = [
'verbosity', 'calculate_sigma', 'calculate_sigma1', 'calculate_sigma2'
]
parms = {
# Solver parameters
'n_iw': 100,
# Physical parameters
'U': 0.5,
't1': t1,
'beta': 10,
# DMFT loop control parameters
'calculate_sigma': True,
'calculate_sigma1': True,
'calculate_sigma2': True,
'measure_G2_iw_ph': True,
"measure_G2_n_bosonic": 10,
"measure_G2_n_fermionic": 10,
"verbosity": 4,
}
parms["N_x"] = 2
parms["N_y"] = 1
parms["N_z"] = 1
parms["ksi_delta"] = 1.0
# Chemical potential depends on the definition of H(k) that is used
parms['chemical_potential_bare'] = 0.
parms['chemical_potential'] = parms['U'] / 2. + parms[
'chemical_potential_bare']
n_orbs = 1 # Number of orbitals
off_diag = True
spin_names = ['up', 'dn'] # Outer (non-hybridizing) blocks
orb_names = ['%s' % i for i in range(n_orbs)] # Orbital indices
gf_struct = op.set_operator_structure(spin_names,
orb_names,
off_diag=off_diag)
if haspomerol:
#####
#
# Reference: 4 site cluster, calculate only G, not G2
#
#####
def calc_reference():
ref_orbs = [
'%s' % i for i in range(n_orbs * parms['N_x'] * parms['N_y'])
]
ref_gf_struct = op.set_operator_structure(spin_names,
ref_orbs,
off_diag=off_diag)
ref_index_converter = {(sn, o): ("loc", int(o),
"down" if sn == "dn" else "up")
for sn, o in product(spin_names, ref_orbs)}
#print ref_index_converter,ref_orbs
ref_ed = PomerolED(ref_index_converter, verbose=True)
ref_N = sum(
ops.n(sn, o) for sn, o in product(spin_names, ref_orbs))
# 2 3
# 0 1
ref_H = (parms["U"] * (ops.n('up', '0') * ops.n('dn', '0') +
ops.n('up', '1') * ops.n('dn', '1')) -
2. * parms['t1'] *
(ops.c_dag('up', '0') * ops.c('up', '1') +
ops.c_dag('up', '1') * ops.c('up', '0') +
ops.c_dag('dn', '0') * ops.c('dn', '1') +
ops.c_dag('dn', '1') * ops.c('dn', '0')) -
parms['chemical_potential'] * ref_N)
# Run the solver
ref_ed.diagonalize(ref_H)
# Compute G(i\omega)
ref_G_iw = ref_ed.G_iw(ref_gf_struct, parms['beta'], parms['n_iw'])
return ref_G_iw
ref_G_iw = calc_reference()
ref = ref_G_iw[ref_spin]
g2_blocks = set([("up", "up"), ("up", "dn"), ("dn", "up"),
("dn", "dn")])
index_converter = {(sn, o):
("loc", int(o), "down" if sn == "dn" else "up")
for sn, o in product(spin_names, orb_names)}
# 1 Bath degree of freedom
# Level of the bath sites
epsilon = [
-parms['chemical_potential_bare'],
]
index_converter.update({
("B%i_%s" % (k, sn), 0):
("bath" + str(k), 0, "down" if sn == "dn" else "up")
for k, sn in product(range(len(epsilon)), spin_names)
})
# Make PomerolED solver object
ed = PomerolED(index_converter, verbose=True)
N = sum(ops.n(sn, o) for sn, o in product(spin_names, orb_names))
H_loc = (parms["U"] * (ops.n('up', '0') * ops.n('dn', '0')) -
parms['chemical_potential'] * N)
# Bath Hamiltonian: levels
H_bath = sum(eps * ops.n("B%i_%s" % (k, sn), 0)
for sn, (k,
eps) in product(spin_names, enumerate(epsilon)))
# Hybridization Hamiltonian
# Bath-impurity hybridization
V = [
-2 * bath_prefactor * t1,
]
H_hyb = ops.Operator()
for k, v in enumerate(V):
H_hyb += sum(
v * ops.c_dag("B%i_%s" % (k, sn), 0) * ops.c(sn, '0') +
np.conj(v) * ops.c_dag(sn, '0') * ops.c("B%i_%s" % (k, sn), 0)
for sn in spin_names)
# Obtain bath sites from Delta and create H_ED
H_ED = H_loc + H_bath + H_hyb
# Run the solver
ed.diagonalize(H_ED)
# Compute G(i\omega)
G_iw = ed.G_iw(gf_struct, parms['beta'], parms['n_iw'])
if parms["measure_G2_iw_ph"]:
common_g2_params = {
'gf_struct': gf_struct,
'beta': parms['beta'],
'blocks': g2_blocks,
'n_iw': parms['measure_G2_n_bosonic']
}
G2_iw = ed.G2_iw_inu_inup(channel="PH",
block_order="AABB",
n_inu=parms['measure_G2_n_fermionic'],
**common_g2_params)
if mpi.is_master_node():
with ar.HDFArchive(filename, 'w') as arch:
arch["parms"] = parms
arch["G_iw"] = G_iw
arch["G2_iw"] = G2_iw
arch["ref"] = ref
else: # haspomerol is False
with ar.HDFArchive(filename, 'r') as arch:
ref = arch['ref']
G_iw = arch['G_iw']
G2_iw = arch['G2_iw']
BL = lattice.BravaisLattice(units=[
(1, 0, 0),
]) #linear lattice
kmesh = gf.MeshBrillouinZone(lattice.BrillouinZone(BL), parms["N_x"])
Hk_blocks = [gf.Gf(indices=orb_names, mesh=kmesh) for spin in spin_names]
Hk = gf.BlockGf(name_list=spin_names, block_list=Hk_blocks)
def Hk_f(k):
return -2 * parms['t1'] * (np.cos(k[0])) * np.eye(1)
for spin, _ in Hk:
for k in Hk.mesh:
Hk[spin][k] = Hk_f(k.value)
# Construct the DF2 program
X = dualfermion.Dpt(beta=parms['beta'],
gf_struct=gf_struct,
Hk=Hk,
n_iw=parms['n_iw'],
n_iw2=parms["measure_G2_n_fermionic"],
n_iW=parms["measure_G2_n_bosonic"])
for name, g0 in X.Delta:
X.Delta[name] << gf.inverse(
gf.iOmega_n +
parms['chemical_potential_bare']) * bath_prefactor**2 * 4 * t1**2
X.G2_iw << G2_iw
# Run the dual perturbation theory
X.gimp << G_iw # Load G from impurity solver
dpt_parms = {key: parms[key] for key in parms if key in dptkeys}
X.run(**dpt_parms)
H = H_int + get_quadratic_operator(T, fop)
up, do = spin_names
index_converter = {
(up, 0): ('loc', 0, 'up'),
(do, 0): ('loc', 0, 'down'),
(up, 1): ('loc', 1, 'up'),
(do, 1): ('loc', 1, 'down'),
(up, 2): ('loc', 2, 'up'),
(do, 2): ('loc', 2, 'down'),
(up, 3): ('loc', 3, 'up'),
(do, 3): ('loc', 3, 'down'),
(up, 4): ('loc', 4, 'up'),
(do, 4): ('loc', 4, 'down'),
(up, 5): ('loc', 5, 'up'),
(do, 5): ('loc', 5, 'down'),
}
ed = PomerolED(index_converter, verbose=True)
ed.diagonalize(H)
gf_struct_up = [[up, [0, 1]]]
gf_struct_do = [[do, [0, 1]]]
G_tau_up = ed.G_tau(gf_struct_up, beta, n_tau=100)
G_tau_do = ed.G_tau(gf_struct_do, beta, n_tau=100)
with HDFArchive('kanamori_offdiag.pomerol.h5', 'w') as Results:
Results['up'] = G_tau_up
Results['dn'] = G_tau_do
from pomerol2triqs import PomerolED
# ----------------------------------------------------------------------
if __name__ == '__main__':
if mpi.is_master_node():
with HDFArchive('data_model.h5', 'r') as A:
p = A["p"]
else:
p = None
p = mpi.bcast(p)
p.convert_keys_from_string_to_python('index_converter')
pom = PomerolED(p.index_converter, verbose=True)
pom.diagonalize(p.H)
p.g_iw = pom.G_iw(p.gf_struct, p.beta, n_iw=400)
p.g_tau = pom.G_tau(p.gf_struct, p.beta, n_tau=200)['0']
p.tau = np.array([float(tau) for tau in p.g_tau.mesh])
opt = dict(block_order='AABB',
beta=p.beta,
gf_struct=p.gf_struct,
blocks=set([('0', '0')]),
n_iw=1,
n_inu=10)
p.g4_ph = pom.G2_iw_inu_inup(channel='PH', **opt)['0', '0']
# Block index combinations for G^2 calculations
g2_blocks = set([("up", "up"), ("dn", "dn"), ("up", "dn")])
# GF structure
gf_struct = {'up': [0], 'dn': [0]}
# Conversion from TRIQS to Pomerol notation for operator indices
index_converter = {}
index_converter.update({(sn, 0): ("loc", 0, "down" if sn == "dn" else "up")
for sn in spin_names})
index_converter.update({("B%i_%s" % (k, sn), 0):
("bath" + str(k), 0, "down" if sn == "dn" else "up")
for k, sn in product(range(len(epsilon)), spin_names)})
# Make PomerolED solver object
ed = PomerolED(index_converter, verbose=True)
# Number of particles on the impurity
H_loc = -mu * (n('up', 0) + n('dn', 0)) + U * n('up', 0) * n('dn', 0)
# Bath Hamiltonian
H_bath = sum(eps * n("B%i_%s" % (k, sn), 0)
for sn, (k, eps) in product(spin_names, enumerate(epsilon)))
# Hybridization Hamiltonian
H_hyb = Operator()
for k, v in enumerate(V):
H_hyb += sum(v * c_dag("B%i_%s" % (k, sn), 0) * c(sn, 0) +
np.conj(v) * c_dag(sn, 0) * c("B%i_%s" % (k, sn), 0)
for sn in spin_names)
# Construct the DF2 program
X = dualfermion.Dpt(beta=parms['beta'],
gf_struct=gf_struct,
Hk=Hk,
n_iw=parms['n_iw'],
n_iw2=parms["measure_G2_n_fermionic"],
n_iW=parms["measure_G2_n_bosonic"])
if haspomerol:
g2_blocks = set([("up", "up"), ("up", "dn"), ("dn", "up"), ("dn", "dn")])
index_converter = {(sn, o): ("loc", int(o), "down" if sn == "dn" else "up")
for sn, o in product(spin_names, orb_names)}
# Make PomerolED solver object
ed = PomerolED(index_converter, verbose=True)
N = sum(ops.n(sn, o) for sn, o in product(spin_names, orb_names))
H = (parms["Ua"] * (ops.n('up', '0') * ops.n('dn', '0')) + parms["Ub"] *
(ops.n('up', '1') * ops.n('dn', '1')) + parms['t0'] *
(ops.c_dag('up', '0') * ops.c('up', '1') + ops.c_dag('up', '1') *
ops.c('up', '0') + ops.c_dag('dn', '0') * ops.c('dn', '1') +
ops.c_dag('dn', '1') * ops.c('dn', '0')) -
parms['chemical_potential'] * N)
#####
#
# Reference: 4 site cluster, calculate only G, not G2
#
#####
def calc_reference():
class Solver:
def __init__(self, beta, gf_struct, n_iw, spin_orbit=False, verbose=True):
self.beta = beta
self.gf_struct = gf_struct
self.n_iw = n_iw
self.spin_orbit = spin_orbit
self.verbose = verbose
if self.verbose and mpi.is_master_node():
print "\n*** Hubbard I solver using Pomerol library"
print "*** gf_struct =", gf_struct
print "*** n_iw =", n_iw
# get spin_name and orb_names from gf_struct
self.__analyze_gf_struct(gf_struct)
if self.verbose and mpi.is_master_node():
print "*** spin_names =", self.spin_names
print "*** orb_names =", self.orb_names
# check spin_names
for sn in self.spin_names:
if not spin_orbit:
assert sn in ('down', 'dn', 'up'
) # become either 'down' or 'up'
if spin_orbit:
assert sn in ('down', 'dn', 'ud') # all become 'down'
# Conversion from TRIQS to Pomerol notation for operator indices
# TRIQS: ('dn', '-2') --> Pomerol: ('atom', 0, 'down')
# NOTE: When spin_orbit is true, only spin 'down' is used.
mkind = get_mkind(True, None)
index_converter = {
mkind(sn, bn):
("atom", bi, "down" if sn == "dn" or sn == "ud" else sn)
for sn, (bi,
bn) in product(self.spin_names, enumerate(self.orb_names))
}
self.__ed = PomerolED(index_converter, verbose, spin_orbit)
# init G_iw
glist = lambda: [
GfImFreq(indices=self.orb_names, beta=beta, n_points=n_iw)
for block, inner in gf_struct.items()
]
self.G_iw = BlockGf(name_list=self.spin_names,
block_list=glist(),
make_copies=False)
self.G_iw.zero()
self.G0_iw = self.G_iw.copy()
self.Sigma_iw = self.G_iw.copy()
def solve(self,
H_int,
E_levels,
integrals_of_motion=None,
density_matrix_cutoff=1e-10,
file_quantum_numbers="",
file_eigenvalues=""):
self.__copy_E_levels(E_levels)
H_0 = sum(
self.E_levels[sn][oi1, oi2].real * c_dag(sn, on1) * c(sn, on2)
for sn, (oi1, on1), (
oi2, on2) in product(self.spin_names, enumerate(
self.orb_names), enumerate(self.orb_names)))
if self.verbose and mpi.is_master_node():
print "\n*** compute G_iw and Sigma_iw"
print "*** E_levels =", E_levels
print "*** H_0 =", H_0
# print "*** integrals_of_motion =", integrals_of_motion
N_op = sum(
c_dag(sn, on) * c(sn, on)
for sn, on in product(self.spin_names, self.orb_names))
if integrals_of_motion is None:
if self.spin_orbit:
# use only N op as integrals_of_motion when spin-orbit coupling is included
self.__ed.diagonalize(H_0 + H_int, integrals_of_motion=[N_op])
else:
# use N and S_z as integrals of motion by default
self.__ed.diagonalize(H_0 + H_int)
else:
assert isinstance(integrals_of_motion, list)
# check commutation relation in advance (just for test)
if self.verbose and mpi.is_master_node():
print "*** Integrals of motion:"
for i, op in enumerate(integrals_of_motion):
print " op%d =" % i, op
print "*** commutation relations:"
is_commute = lambda h, op: h * op - op * h
str_if_commute = lambda h, op: "== 0" if is_commute(
h, op).is_zero() else "!= 0"
for i, op in enumerate(integrals_of_motion):
print " [H_0, op%d]" % i, str_if_commute(
H_0,
op), " [H_int, op%d]" % i, str_if_commute(H_int, op)
self.__ed.diagonalize(H_0 + H_int, integrals_of_motion)
# save data
if file_quantum_numbers:
self.__ed.save_quantum_numbers(file_quantum_numbers)
if file_eigenvalues:
self.__ed.save_eigenvalues(file_eigenvalues)
# set density-matrix cutoff
self.__ed.set_density_matrix_cutoff(density_matrix_cutoff)
# Compute G(i\omega)
self.G_iw << self.__ed.G_iw(self.gf_struct, self.beta, self.n_iw)
# Compute G0 and Sigma
E_list = [self.E_levels[sn]
for sn in self.spin_names] # from dict to list
self.G0_iw << iOmega_n
self.G0_iw -= E_list
self.Sigma_iw << self.G0_iw - inverse(self.G_iw)
self.G0_iw.invert()
# *********************************************************************
# TODO: tail
# set tail of Sigma at all zero in the meantime, because tail of G is
# not computed in pomerol solver. This part should be improved.
# *********************************************************************
for s, sig in self.Sigma_iw:
sig.tail.zero()
def __copy_E_levels(self, E_levels):
"""Copy E_levels after checking the data structure"""
# check data structure
assert (isinstance(E_levels, dict))
for key, value in E_levels.items():
assert (isinstance(value, np.ndarray))
assert (value.shape == (len(self.orb_names), len(self.orb_names)))
# copy
self.E_levels = E_levels.copy()
def __analyze_gf_struct(self, gf_struct):
assert (isinstance(gf_struct, dict))
self.spin_names = gf_struct.keys()
self.orb_names = gf_struct.values()[0]
for value in gf_struct.values():
assert (self.orb_names == value
) # check if all spin blocks have the same orbitals
def make_calc(nw=10, beta=2.0, h_field=0.0):
# ------------------------------------------------------------------
# -- Hubbard atom with two bath sites, Hamiltonian
p = ParameterCollection(
beta=beta,
V1=2.0,
V2=5.0,
epsilon1=0.00,
epsilon2=4.00,
h_field=h_field,
mu=2.0,
U=5.0,
ntau=40,
niw=15,
n_inu=nw,
)
# ------------------------------------------------------------------
print '--> Solving SIAM with parameters'
print p
# ------------------------------------------------------------------
up, do = 'up', 'dn'
docc = c_dag(up, 0) * c(up, 0) * c_dag(do, 0) * c(do, 0)
mA = 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)
p.H = -p.mu * nA + p.U * docc + p.h_field * mA + \
p.epsilon1 * nB + p.epsilon2 * nC + \
p.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) ) + \
p.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
# Conversion from TRIQS to Pomerol notation for operator indices
# TRIQS: block_name, inner_index
# Pomerol: site_label, orbital_index, spin_name
index_converter = {
(up, 0): ('loc', 0, 'up'),
(do, 0): ('loc', 0, 'down'),
(up, 1): ('loc', 1, 'up'),
(do, 1): ('loc', 1, 'down'),
(up, 2): ('loc', 2, 'up'),
(do, 2): ('loc', 2, 'down'),
}
# -- Create Exact Diagonalization instance
ed = PomerolED(index_converter, verbose=True)
ed.diagonalize(p.H) # -- Diagonalize H
gf_struct = [[up, [0]], [do, [0]]]
# -- Single-particle Green's functions
p.G_iw = ed.G_iw(gf_struct, beta, n_iw=100)
p.G_tau = ed.G_tau(gf_struct, beta, n_tau=400)
# -- Particle-particle two-particle Matsubara frequency Green's function
opt = dict(block_order='AABB',
beta=beta,
gf_struct=gf_struct,
blocks=set([(up, up), (up, do)]),
n_iw=1,
n_inu=p.n_inu)
p.G2_iw_ph = ed.G2_iw_inu_inup(channel='PH', **opt)
# ------------------------------------------------------------------
# -- Store to hdf5
mpi.barrier()
if mpi.is_master_node():
filename = 'data_pomerol_h_field_%4.4f.h5' % h_field
with HDFArchive(filename, 'w') as res:
res['p'] = p
# Number of Legendre coefficients for G^2 calculations
g2_n_l = 10
# Block index combinations for G^2 calculations
g2_blocks = set([("up", "up"), ("up", "dn"), ("dn", "up")])
gf_struct = {"up": orb_names, "dn": orb_names}
print "Block structure of single-particle Green's functions:", gf_struct
# Conversion from TRIQS to Pomerol notation for operator indices
# TRIQS: block_name, inner_index
# Pomerol: site_label, orbital_index, spin_name
index_converter = {(sn, o): ("loc", o, "down" if sn == "dn" else "up")
for sn, o in product(spin_names, orb_names)}
# Make PomerolED solver object
ed = PomerolED(index_converter, verbose=True)
# Number of particles on the impurity
N = sum(n(sn, o) for sn, o in product(spin_names, orb_names))
# Hamiltonian
H = h_int_kanamori(spin_names, orb_names,
np.array([[0, U - 3 * J], [U - 3 * J, 0]]),
np.array([[U, U - 2 * J], [U - 2 * J, U]]), J, True)
H -= mu * N
# Diagonalize H
ed.diagonalize(H)
# Compute G(i\omega)
G_iw = ed.G_iw(gf_struct, beta, n_iw)
# Conversion from TRIQS to Pomerol notation for operator indices
# TRIQS: block_name, inner_index
# Pomerol: site_label, orbital_index, spin_name
index_converter = {}
# Local degrees of freedom
index_converter.update({(sn, o): ("loc", o, "down" if sn == "dn" else "up")
for sn, o in product(spin_names, orb_names)})
# Bath degrees of freedom
index_converter.update({("B_" + sn, o):
("bath", o, "down" if sn == "dn" else "up")
for sn, o in product(spin_names, orb_names)})
# Make PomerolED solver object
ed = PomerolED(index_converter, verbose=True)
# Density matrix blocks with small diagonal elements will be discarded
ed.rho_threshold = 1e-6
# Number of particles on the impurity
N = sum(n(sn, o) for sn, o in product(spin_names, orb_names))
# Local Hamiltonian
H_loc = h_int_kanamori(spin_names, orb_names,
np.array([[0, U - 3 * J], [U - 3 * J, 0]]),
np.array([[U, U - 2 * J], [U - 2 * J, U]]), J, True)
H_loc -= mu * N
# Bath Hamiltonian
H_bath = sum(epsilon[o] * n("B_" + sn, o)
energy_window = (-5, 5)
# Number of frequency points for real frequency GF calculation
n_w = 1000
# GF structure
gf_struct = set_operator_structure(spin_names, orb_names, False)
mkind = get_mkind(False, None)
# Conversion from TRIQS to Pomerol notation for operator indices
index_converter = {
mkind(sn, bn): ("atom", bi, "down" if sn == "dn" else "up")
for sn, (bi, bn) in product(spin_names, enumerate(orb_names))
}
# Make PomerolED solver object
ed = PomerolED(index_converter, verbose=True)
# Hamiltonian
H = h_int_slater(spin_names, orb_names, U_mat, False)
# Number of particles
N = N_op(spin_names, orb_names, False)
# z-component of spin
Sz = S_op('z', spin_names, orb_names, False)
# z-component of angular momentum
Lz = L_op('z', spin_names, orb_names, off_diag=False, basis='spherical')
# Double check that we are actually using integrals of motion
h_comm = lambda op: H * op - op * H
####################
beta = 10.0 # Inverse temperature
U = 1.0 # Coulomb repulsion
mu = 0.4 # Chemical potential
h_field = 0.01
spin_names = ("up", "dn")
# Conversion from TRIQS to Pomerol notation for operator indices
index_converter = {}
index_converter.update({(sn, 0): ("A", 0, "down" if sn == "dn" else "up")
for sn in spin_names})
# Make PomerolED solver object
ed = PomerolED(index_converter, verbose=True)
# Hamiltonian
H = -mu * (n('up', 0) + n('dn', 0)) - h_field * (n('up', 0) - n('dn', 0))
H += U * n('up', 0) * n('dn', 0)
# Diagonalize H
ed.diagonalize(H)
# Compute reference values of <n('up', 0)> and <n('dn', 0)>
w = np.array([
1.0,
np.exp(beta * (mu + h_field)),
np.exp(beta * (mu - h_field)),
np.exp(-beta * (-2 * mu + U))
])
# Number of frequency points for real frequency GF calculation
n_w = 1000
# GF structure
gf_struct = {'up': [0], 'dn': [0]}
# Conversion from TRIQS to Pomerol notation for operator indices
index_converter = {}
index_converter.update({(sn, 0): ("loc", 0, "down" if sn == "dn" else "up")
for sn in spin_names})
index_converter.update({("B%i_%s" % (k, sn), 0):
("bath" + str(k), 0, "down" if sn == "dn" else "up")
for k, sn in product(range(len(epsilon)), spin_names)})
# Make PomerolED solver object
ed = PomerolED(index_converter, verbose=True)
# Number of particles on the impurity
H_loc = -mu * (n('up', 0) + n('dn', 0)) + U * n('up', 0) * n('dn', 0)
# Bath Hamiltonian
H_bath = sum(eps * n("B%i_%s" % (k, sn), 0)
for sn, (k, eps) in product(spin_names, enumerate(epsilon)))
# Hybridization Hamiltonian
H_hyb = Operator()
for k, v in enumerate(V):
H_hyb += sum(v * c_dag("B%i_%s" % (k, sn), 0) * c(sn, 0) +
np.conj(v) * c_dag(sn, 0) * c("B%i_%s" % (k, sn), 0)
for sn in spin_names)
def make_calc():
# ------------------------------------------------------------------
# -- Hubbard atom with two bath sites, Hamiltonian
p = ParameterCollection(
beta=1.0,
U=5.0,
nw=1,
nwf=20,
)
p.nwf_gf = 4 * p.nwf
p.mu = 0.5 * p.U
# ------------------------------------------------------------------
ca_up, cc_up = c('0', 0), c_dag('0', 0)
ca_do, cc_do = c('0', 1), c_dag('0', 1)
docc = cc_up * ca_up * cc_do * ca_do
nA = cc_up * ca_up + cc_do * ca_do
p.H = -p.mu * nA + p.U * docc
# ------------------------------------------------------------------
# -- Exact diagonalization
# Conversion from TRIQS to Pomerol notation for operator indices
# TRIQS: block_name, inner_index
# Pomerol: site_label, orbital_index, spin_name
index_converter = {
('0', 0): ('loc', 0, 'up'),
('0', 1): ('loc', 0, 'down'),
}
# -- Create Exact Diagonalization instance
ed = PomerolED(index_converter, verbose=True)
ed.diagonalize(p.H) # -- Diagonalize H
gf_struct = [['0', [0, 1]]]
# -- Single-particle Green's functions
p.G_iw = ed.G_iw(gf_struct, p.beta, n_iw=p.nwf_gf)['0']
# -- Particle-particle two-particle Matsubara frequency Green's function
opt = dict(beta=p.beta,
gf_struct=gf_struct,
blocks=set([("0", "0")]),
n_iw=p.nw,
n_inu=p.nwf)
p.G2_iw_ph = ed.G2_iw_inu_inup(channel='PH', **opt)[('0', '0')]
# ------------------------------------------------------------------
# -- Generalized susceptibility in magnetic PH channel
p.chi_m = Gf(mesh=p.G2_iw_ph.mesh, target_shape=[1, 1, 1, 1])
p.chi_m[0, 0, 0, 0] = p.G2_iw_ph[0, 0, 0, 0] - p.G2_iw_ph[0, 0, 1, 1]
p.chi0_m = chi0_from_gg2_PH(p.G_iw, p.chi_m)
p.label = r'Pomerol'
# ------------------------------------------------------------------
# -- Generalized susceptibility in PH channel
p.chi = chi_from_gg2_PH(p.G_iw, p.G2_iw_ph)
p.chi0 = chi0_from_gg2_PH(p.G_iw, p.G2_iw_ph)
p.gamma = inverse_PH(p.chi0) - inverse_PH(p.chi)
# ------------------------------------------------------------------
# -- Store to hdf5
filename = 'data_pomerol.h5'
with HDFArchive(filename, 'w') as res:
res['p'] = p
# Conversion from TRIQS to Pomerol notation for operator indices
# TRIQS: block_name, inner_index
# Pomerol: site_label, orbital_index, spin_name
index_converter = {}
# Local degrees of freedom
index_converter.update({(sn, 0): ("loc", 0, "down" if sn == "dn" else "up")
for sn in spin_names})
# Bath degrees of freedom
index_converter.update({("B%i_%s" % (k, sn), 0):
("bath" + str(k), 0, "down" if sn == "dn" else "up")
for k, sn in product(range(len(epsilon)), spin_names)})
# Make PomerolED solver object
ed = PomerolED(index_converter, verbose=True)
# Number of particles on the impurity
H_loc = -mu * (n('up', 0) + n('dn', 0)) + U * n('up', 0) * n('dn', 0)
# Bath Hamiltonian
H_bath = sum(eps * n("B%i_%s" % (k, sn), 0)
for sn, (k, eps) in product(spin_names, enumerate(epsilon)))
# Hybridization Hamiltonian
H_hyb = Operator()
for k, v in enumerate(V):
H_hyb += sum(v * c_dag("B%i_%s" % (k, sn), 0) * c(sn, 0) +
np.conj(v) * c_dag(sn, 0) * c("B%i_%s" % (k, sn), 0)
for sn in spin_names)
def make_calc():
# ------------------------------------------------------------------
# -- Hamiltonian
p = ParameterCollection(
beta = 0.5,
U = 0.5,
nw = 1,
nwf = 15,
V = 1.0,
eps = 0.2,
)
p.nwf_gf = 4 * p.nwf
p.mu = 0.5*p.U
# ------------------------------------------------------------------
ca_up, cc_up = c('0', 0), c_dag('0', 0)
ca_do, cc_do = c('0', 1), c_dag('0', 1)
ca0_up, cc0_up = c('1', 0), c_dag('1', 0)
ca0_do, cc0_do = c('1', 1), c_dag('1', 1)
docc = cc_up * ca_up * cc_do * ca_do
nA = cc_up * ca_up + cc_do * ca_do
hybridiz = p.V * (cc0_up * ca_up + cc_up * ca0_up + cc0_do * ca_do + cc_do * ca0_do)
bath_lvl = p.eps * (cc0_up * ca0_up + cc0_do * ca0_do)
p.H_int = p.U * docc
p.H = -p.mu * nA + p.H_int + hybridiz + bath_lvl
# ------------------------------------------------------------------
# -- Exact diagonalization
# Conversion from TRIQS to Pomerol notation for operator indices
# TRIQS: block_name, inner_index
# Pomerol: site_label, orbital_index, spin_name
index_converter = {
('0', 0) : ('loc', 0, 'up'),
('0', 1) : ('loc', 0, 'down'),
('1', 0) : ('loc', 1, 'up'),
('1', 1) : ('loc', 1, 'down'),
}
# -- Create Exact Diagonalization instance
ed = PomerolED(index_converter, verbose=True)
ed.diagonalize(p.H) # -- Diagonalize H
p.gf_struct = [['0', [0, 1]]]
# -- Single-particle Green's functions
p.G_iw = ed.G_iw(p.gf_struct, p.beta, n_iw=p.nwf_gf)['0']
# -- Particle-particle two-particle Matsubara frequency Green's function
opt = dict(
beta=p.beta, gf_struct=p.gf_struct,
blocks=set([("0", "0")]),
n_iw=p.nw, n_inu=p.nwf)
p.G2_iw_ph = ed.G2_iw_inu_inup(channel='PH', **opt)[('0', '0')]
filename = 'data_pomerol.h5'
with HDFArchive(filename,'w') as res:
res['p'] = p
import os
os.system('tar czvf data_pomerol.tar.gz data_pomerol.h5')
os.remove('data_pomerol.h5')
def make_calc():
# ------------------------------------------------------------------
# -- 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=5.0,
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 = 'up', 'dn'
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
# Conversion from TRIQS to Pomerol notation for operator indices
# TRIQS: block_name, inner_index
# Pomerol: site_label, orbital_index, spin_name
index_converter = {
(up, 0): ('loc', 0, 'up'),
(do, 0): ('loc', 0, 'down'),
(up, 1): ('loc', 1, 'up'),
(do, 1): ('loc', 1, 'down'),
(up, 2): ('loc', 2, 'up'),
(do, 2): ('loc', 2, 'down'),
}
# -- Create Exact Diagonalization instance
ed = PomerolED(index_converter, verbose=True)
ed.diagonalize(d.H) # -- Diagonalize H
gf_struct = [[up, [0]], [do, [0]]]
# -- Single-particle Green's functions
G_iw = ed.G_iw(gf_struct, beta, n_iw=niw)
G_tau = ed.G_tau(gf_struct, beta, n_tau=ntau)
G_w = ed.G_w(gf_struct,
beta,
energy_window=(-2.5, 2.5),
n_w=100,
im_shift=0.01)
d.G_iw = G_iw['up']
d.G_tau = G_tau['up']
d.G_w = G_w['up']
# -- Particle-particle two-particle Matsubara frequency Green's function
opt = dict(block_order='AABB',
beta=beta,
gf_struct=gf_struct,
blocks=set([("up", "dn")]),
n_iw=niw,
n_inu=niw)
G2_iw = ed.G2_iw_inu_inup(channel='AllFermionic', **opt)
d.G2_iw = G2_iw['up', 'dn']
G2_iw_pp = ed.G2_iw_inu_inup(channel='PP', **opt)
d.G2_iw_pp = G2_iw_pp['up', 'dn']
G2_iw_ph = ed.G2_iw_inu_inup(channel='PH', **opt)
d.G2_iw_ph = G2_iw_ph['up', 'dn']
# ------------------------------------------------------------------
# -- Store to hdf5
filename = 'data_pomerol.h5'
with HDFArchive(filename, 'w') as res:
for key, value in d.__dict__.items():
res[key] = value