def run_slater(L, is_cubic):
for l in L:
orb_names = range(2 * l + 1)
num_orbitals = len(orb_names)
gf_struct = set_operator_structure(spin_names, orb_names, True)
mkind = get_mkind(True, None)
F = [3.0 * (0.3**k) for k in range(l + 1)]
U_mat = U_matrix(l, F, basis='cubic' if is_cubic else 'spherical')
h_int = h_int_slater(spin_names, orb_names, U_mat, True)
h_k = np.zeros((num_orbitals, num_orbitals))
# Quantum numbers
QN = [
sum([n(*mkind("up", o)) for o in orb_names], Operator()), # N_up
sum([n(*mkind("dn", o)) for o in orb_names], Operator())
] # N_down
eig_qn, time_qn = partition(h_int, h_k, gf_struct, QN)
eig_ap, time_ap = partition(h_int, h_k, gf_struct)
model = "Slater, %i orbitals" % num_orbitals
model += (" (cubic basis)" if is_cubic else " (spherical basis)")
print_line(model, 2**(2 * num_orbitals), (len(eig_qn), time_qn),
(len(eig_ap), time_ap))
def run_kanamori(max_orbitals,orbital_mixing):
for num_orbitals in range(2,max_orbitals+1):
orb_names = range(num_orbitals)
gf_struct = set_operator_structure(spin_names,orb_names,True)
mkind = get_mkind(True,None)
U = 1.0*(np.ones((num_orbitals,num_orbitals))-np.eye(num_orbitals))
Up = 2.0*np.ones((num_orbitals,num_orbitals))
J = 0.2
V = 0.3
h_k = V*np.ones((num_orbitals,num_orbitals)) if orbital_mixing else V*np.eye(num_orbitals)
h_int = h_int_kanamori(spin_names,orb_names,U,Up,J,True)
# Quantum numbers
QN = [sum([n(*mkind("up",o)) for o in orb_names],Operator()), # N_up
sum([n(*mkind("dn",o)) for o in orb_names],Operator())] # N_down
if not orbital_mixing:
# PS quantum number
QN.append(Operator())
for i, o in enumerate(orb_names):
dn = n(*mkind("up",o)) - n(*mkind("dn",o))
QN[2] += (2**i)*dn*dn
eig_qn,time_qn = partition(h_int,h_k,gf_struct,QN)
eig_ap,time_ap = partition(h_int,h_k,gf_struct)
model = "Kanamori, %i orbitals"%num_orbitals
if orbital_mixing: model += " (orbital mixing)"
print_line(model,2**(2*num_orbitals),(len(eig_qn),time_qn),(len(eig_ap),time_ap))
def run_kanamori(max_orbitals, orbital_mixing):
for num_orbitals in range(2, max_orbitals + 1):
orb_names = range(num_orbitals)
gf_struct = set_operator_structure(spin_names, orb_names, True)
mkind = get_mkind(True, None)
U = 1.0 * (np.ones(
(num_orbitals, num_orbitals)) - np.eye(num_orbitals))
Up = 2.0 * np.ones((num_orbitals, num_orbitals))
J = 0.2
V = 0.3
h_k = V * np.ones(
(num_orbitals,
num_orbitals)) if orbital_mixing else V * np.eye(num_orbitals)
h_int = h_int_kanamori(spin_names, orb_names, U, Up, J, True)
# Quantum numbers
QN = [
sum([n(*mkind("up", o)) for o in orb_names], Operator()), # N_up
sum([n(*mkind("dn", o)) for o in orb_names], Operator())
] # N_down
if not orbital_mixing:
# PS quantum number
QN.append(Operator())
for i, o in enumerate(orb_names):
dn = n(*mkind("up", o)) - n(*mkind("dn", o))
QN[2] += (2**i) * dn * dn
eig_qn, time_qn = partition(h_int, h_k, gf_struct, QN)
eig_ap, time_ap = partition(h_int, h_k, gf_struct)
model = "Kanamori, %i orbitals" % num_orbitals
if orbital_mixing: model += " (orbital mixing)"
print_line(model, 2**(2 * num_orbitals), (len(eig_qn), time_qn),
(len(eig_ap), time_ap))
def run_slater(L,is_cubic):
for l in L:
orb_names = range(2*l+1)
num_orbitals = len(orb_names)
gf_struct = set_operator_structure(spin_names,orb_names,True)
mkind = get_mkind(True,None)
F = [3.0*(0.3**k) for k in range(l+1)]
U_mat = U_matrix(l,F,basis='cubic' if is_cubic else 'spherical')
h_int = h_int_slater(spin_names,orb_names,U_mat,True)
h_k = np.zeros((num_orbitals,num_orbitals))
# Quantum numbers
QN = [sum([n(*mkind("up",o)) for o in orb_names],Operator()), # N_up
sum([n(*mkind("dn",o)) for o in orb_names],Operator())] # N_down
eig_qn,time_qn = partition(h_int,h_k,gf_struct,QN)
eig_ap,time_ap = partition(h_int,h_k,gf_struct)
model = "Slater, %i orbitals"%num_orbitals
model += (" (cubic basis)" if is_cubic else " (spherical basis)")
print_line(model,2**(2*num_orbitals),(len(eig_qn),time_qn),(len(eig_ap),time_ap))
num_orbitals = 2
mu = 1.0
U = 2.0
J = 0.2
h = 0.1
# Poles of delta
epsilon = 2.3
# Hybridization matrices
V = 2.0 * np.eye(num_orbitals) + 0.2 * (np.ones(num_orbitals) - np.eye(num_orbitals))
# Block structure of GF
spin_names = ('up','dn')
orb_names = range(num_orbitals)
gf_struct = set_operator_structure(spin_names,orb_names,True)
# Construct solver
S = SolverCore(beta=beta, gf_struct=gf_struct, n_iw=1025, n_tau=2500)
# 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 += h*S_op('z',spin_names,orb_names,True)
# Set hybridization function
delta_w = GfImFreq(indices = orb_names, beta=beta)
delta_w << inverse(iOmega_n - epsilon) + inverse(iOmega_n + epsilon)
delta_w.from_L_G_R(V, delta_w, V)
F0 = 4.0
F2 = 0.5
spin_names = ("up","dn")
cubic_names = map(str,range(2*L+1))
U_mat = U_matrix(L, radial_integrals=[F0,F2], basis="spherical")
# Parameters
p = {}
p["verbosity"] = 0
p["length_cycle"] = 50
p["n_warmup_cycles"] = 0
p["n_cycles"] = 0
# Block structure of GF
gf_struct = set_operator_structure(spin_names,cubic_names,False)
# Local Hamiltonian
H = h_int_slater(spin_names,cubic_names,U_mat,False)
# Observables
N = N_op(spin_names,cubic_names,False)
S2 = S2_op(spin_names,cubic_names,False)
Sz = S_op('z',spin_names,cubic_names,False)
L2 = L2_op(spin_names,cubic_names,False)
Lz = L_op('z',spin_names,cubic_names,False)
LS = LS_op(spin_names,cubic_names,False)
# Additional splitting terms to lift the degeneracies
H += 0.22*Sz
H += 0.33*Lz
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"] = 50000
p["n_cycles"] = 3000000
results_file_name = "kanamori" + (".qn" if use_qn else "") + ".h5"
mpi.report("Welcome to Kanamori benchmark.")
gf_struct = set_operator_structure(spin_names,orb_names,False)
mkind = get_mkind(False,None)
## 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,False)
if use_qn:
QN = [sum([n(*mkind("up",o)) for o in orb_names],Operator()),
sum([n(*mkind("dn",o)) for o in orb_names],Operator())]
for o in orb_names:
dn = n(*mkind("up",o)) - n(*mkind("dn",o))
QN.append(dn*dn)
p["partition_method"] = "quantum_numbers"
p = {}
p["max_time"] = -1
p["random_name"] = ""
p["random_seed"] = 123 * mpi.rank + 567
p["length_cycle"] = 50
p["n_warmup_cycles"] = 50000/10
p["n_cycles"] = 3200000/10
p["use_norm_as_weight"] = True
p["measure_density_matrix"] = False
results_file_name = "kanamori_offdiag." + ("qn." if use_qn else "") + "h5"
mpi.report("Welcome to Kanamori (off-diagonal) benchmark.")
gf_struct = set_operator_structure(spin_names,orb_names,True)
mkind = get_mkind(True,None)
# 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)
if use_qn:
QN = [sum([n(*mkind("up",o)) for o in orb_names],Operator()),
sum([n(*mkind("dn",o)) for o in orb_names],Operator())]
for o in orb_names:
dn = n(*mkind("up",o)) - n(*mkind("dn",o))
QN.append(dn*dn)
p["partition_method"] = "quantum_numbers"
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__)
cubic_names = map(str, range(2 * L + 1))
U_mat = U_matrix(L, radial_integrals=[F0, F2, F4], basis="cubic")
# Parameters
p = {}
p["max_time"] = -1
p["random_name"] = ""
p["random_seed"] = 123 * mpi.rank + 567
p["length_cycle"] = 50
p["n_warmup_cycles"] = 50
p["n_cycles"] = 5000
p["measure_g_l"] = True
p["move_double"] = False
# Block structure of GF
gf_struct = set_operator_structure(spin_names, cubic_names, False)
# Local Hamiltonian
H = h_int_slater(spin_names, cubic_names, U_mat, False)
# Construct the solver
S = SolverCore(beta=beta, gf_struct=gf_struct, n_iw=1025, n_tau=100000)
# Set hybridization function
delta_w = GfImFreq(indices=[0], beta=beta)
delta_w << (half_bandwidth / 2.0)**2 * SemiCircular(half_bandwidth)
for name, g0 in S.G0_iw:
g0 << inverse(iOmega_n + mu - delta_w)
S.solve(h_int=H, **p)
assert( T1.shape == T2.shape )
for idxs in itertools.product(*[ range(x) for x in T1.shape ]):
print idxs, T1[idxs], T2[idxs]
# ----------------------------------------------------------------------
if __name__ == '__main__':
U = 1.0
J = 0.3
orb_names = ['xy', 'xz', 'yz']
spin_names = ['up', 'do']
norb = len(orb_names)
gf_struct = set_operator_structure(spin_names, orb_names, True) # orbital off diag
fundamental_operators = fundamental_operators_from_gf_struct(gf_struct)
U_ab, UPrime_ab = U_matrix_kanamori(
n_orb=len(orb_names), U_int=U, J_hund=J)
H_int = h_int_kanamori(
spin_names, orb_names, U_ab, UPrime_ab, J_hund=J,
off_diag=True, map_operator_structure=None, H_dump=None) # orgital offdiag
U_abcd = get_rpa_tensor(H_int, fundamental_operators)
U_c, U_s = split_quartic_tensor_in_charge_and_spin(U_abcd)
U_abcd_ref = quartic_tensor_from_charge_and_spin(U_c, U_s)
g2_n_wf = 10
#####################
# Input for Pomerol #
#####################
spin_names = ("up", "dn")
orb_names = map(str, range(-L, L + 1))
# orb_names = range(-L, L+1) # This also works
flag_so = True if ls_coupling != 0 else False
# GF and operator structure
if not flag_so:
# ('up', '-2'), ('dn', '-2'), etc
gf_struct = set_operator_structure(spin_names, orb_names, off_diag=True)
map_operator_structure = {(s, o): (s, o)
for s, o in product(spin_names, orb_names)}
else:
# ('ud', 'up_-2'), ('ud', 'dn_-2'), etc
gf_struct = {
'ud':
[str(s) + '_' + str(o) for s, o in product(spin_names, orb_names)]
}
map_operator_structure = {(s, o): ('ud', str(s) + '_' + str(o))
for s, o in product(spin_names, orb_names)}
# print gf_struct
# print map_operator_structure
# Operators
N = N_op(spin_names, orb_names, map_operator_structure=map_operator_structure)
p["random_name"] = ""
p["random_seed"] = 123 * mpi.rank + 567
p["length_cycle"] = 50
p["n_warmup_cycles"] = 1000
p["n_cycles"] = 30000
p["partition_method"] = "autopartition"
p["measure_g_tau"] = True
p["move_shift"] = 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)
# 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)
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
