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
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']
if mpi.is_master_node():
with HDFArchive('data_pomerol.h5', 'w') as A:
A['p'] = p
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
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)
# Compute G(\tau)
G_tau = ed.G_tau(gf_struct, beta, n_tau)
# Compute G(\omega)
G_w = ed.G_w(gf_struct, beta, energy_window, n_w, 0.01)
###########
# G^{(2)} #
###########
common_g2_params = {
'gf_struct': gf_struct,
'beta': beta,
'blocks': g2_blocks,
'n_iw': g2_n_iw
}
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