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 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)
from triqs.utility.comparison_tests import *
from triqs.utility.h5diff import h5diff
# Basic input parameters
beta = 40
# Init the SumK class
SK = SumkDFT(hdf_file='SrVO3.ref.h5', use_dft_blocks=True)
num_orbitals = SK.corr_shells[0]['dim']
l = SK.corr_shells[0]['l']
spin_names = ['down', 'up']
orb_names = ['%s' % i for i in range(num_orbitals)]
orb_hybridized = False
gf_struct = set_operator_structure(spin_names, orb_names, orb_hybridized)
glist = [GfImFreq(indices=inner, beta=beta) for block, inner in gf_struct]
Sigma_iw = BlockGf(name_list=[block for block, inner in gf_struct],
block_list=glist,
make_copies=False)
SK.set_Sigma([Sigma_iw])
Gloc = SK.extract_G_loc()
if mpi.is_master_node():
with HDFArchive('srvo3_Gloc.out.h5', 'w') as ar:
ar['Gloc'] = Gloc[0]
if mpi.is_master_node():
h5diff("srvo3_Gloc.out.h5", "srvo3_Gloc.ref.h5")
spin_names = ['up', 'down'] # Outer (non-hybridizing) blocks
orb_names = ['%s' % i for i in range(n_orbs)] # Orbital indices
off_diag = False # Include orbital off-diagonal elements?
n_loop = 2 # Number of DMFT self-consistency loops
# Solver parameters
p = {}
p["n_warmup_cycles"] = 10000 # Number of warmup cycles to equilibrate
p["n_cycles"] = 100000 # Number of measurements
p["length_cycle"] = 500 # Number of MC steps between consecutive measures
p["move_double"] = True # Use four-operator moves
# Block structure of Green's functions
# gf_struct = [ ('up',[0,1,2,3,4]), ('down',[0,1,2,3,4]) ]
# This can be computed using the TRIQS function as follows:
gf_struct = op.set_operator_structure(spin_names, orb_names, off_diag=off_diag)
# Construct the 4-index U matrix U_{ijkl}
# The spherically-symmetric U matrix is parametrised by the radial integrals
# F_0, F_2, F_4, which are related to U and J. We use the functions provided
# in the TRIQS library to construct this easily:
U_mat = op.U_matrix(l=l, U_int=U, J_hund=J, basis='spherical')
# Set the interacting part of the local Hamiltonian
# Here we use the full rotationally-invariant interaction parametrised
# by the 4-index tensor U_{ijkl}.
# The TRIQS library provides a function to build this Hamiltonian from the U tensor:
H = op.h_int_slater(spin_names, orb_names, U_mat, off_diag=off_diag)
# Construct the solver
S = Solver(beta=beta, gf_struct=gf_struct)
def test_solver_dry_run():
# Half band width
D = 2.0
mu = 1.0
U = 4.0
J = 1.0
l = 1
n_orbs = 2 * l +1
# Inter-orbital hybridization
off_diag = True
spin_names = ['ud']
orb_names = [i for i in range(2*n_orbs)]
# Block structure of Green's functions
gf_struct = op.set_operator_structure(spin_names, orb_names, off_diag=off_diag)
# Convert to dict
if isinstance(gf_struct, list):
gf_struct = {x[0]: x[1] for x in gf_struct}
# Local interaction Hamiltonian
U_mat = to_spin_full_U_matrix(op.U_matrix(l=l, U_int=U, J_hund=J, basis='spherical'))
s = ALPSCTHYBSolver(beta, gf_struct, U_mat, n_iw=n_iw)
Delta_iw = make_block_gf(GfImFreq, gf_struct, beta, n_iw)
for name, b in Delta_iw:
b << (D/2.0)**2 * SemiCircular(D)
# Random local transfer matrix
H0 = [numpy.random.rand(2*n_orbs, 2*n_orbs) for name, b in Delta_iw]
H0 = [h + h.conjugate().transpose() for h in H0]
G0_iw = make_block_gf(GfImFreq, gf_struct, beta, n_iw)
G0_iw.zero()
for ib, (name, g0) in enumerate(G0_iw):
dim = len(g0.indices)
g0 << inverse(iOmega_n - H0[ib] - Delta_iw[name])
s.set_G0_iw(G0_iw)
#rot = compute_diag_basis(G0_iw)
#s.rotate_basis(rot, direction='forward')
p = {
'exec_path' : './dummy/hybmat',
'work_dir' : './',
'dry_run' : True,
'random_seed_offset' : 20,
'timelimit' : 60,
}
s.solve(None, '', p)
#s.rotate_basis(rot, direction='backward')
# Check Delta(iwn)
diff = s.get_Delta_iw() - Delta_iw
for name, b in diff:
assert numpy.all(numpy.abs(b.data) < 1e-10)