def setup_dmft_calculation(p):
p = copy.deepcopy(p)
p.iter = 0
# -- Local Hubbard interaction
from triqs.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
})
kmesh = H.get_kmesh(n_k=(p.n_k, p.n_k, 1))
p.e_k = H.fourier(kmesh)
# -- 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 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
chi0_q0_ref = chi0_q0_integral(t, beta)
print('chi0_q0 =', chi00_wk[Idx(0), Idx(0, 0, 0)][0, 0, 0, 0].real)
print('chi0_q0_ref =', chi0_q0_ref)
np.testing.assert_almost_equal(
chi00_wk_analytic[Idx(0), Idx(0, 0, 0)][0, 0, 0, 0], chi0_q0_ref)
# ------------------------------------------------------------------
# -- RPA tensor
gf_struct = [[0, 2]]
from triqs.operators import n, c, c_dag, Operator, dagger
H_int = U * n(0, 0) * n(0, 1)
print('H_int =', H_int)
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(gf_struct)
print(fundamental_operators)
U_abcd = get_rpa_tensor(H_int, fundamental_operators)
print('U_abcd =\n', U_abcd.reshape((4, 4)))
# ------------------------------------------------------------------
# -- RPA
from triqs_tprf.lattice import solve_rpa_PH
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)
# Bath hamiltonian in matrix representation
h_bath_mat = diag(eps_bath) - matrix([[0, t_bath, 0, 0], [t_bath, 0, 0, 0],
[0, 0, 0, t_bath], [0, 0, t_bath, 0]])
# Coupling matrix
V_mat = matrix([[1., 0., 0, 0], [0., 1., 0, 0], [0., 0., 1, 0], [0., 0., 0,
1]])
# ==== Local Hamiltonian ====
c_dag_vec = matrix([[c_dag('bl', o) for o in range(n_orb)]])
c_vec = matrix([[c('bl', o)] for o in range(n_orb)])
h_0 = (c_dag_vec * h_0_mat * c_vec)[0, 0]
h_int = U * n('bl', up_0) * n('bl', dn_0) + \
U * n('bl', up_1) * n('bl', dn_1) + \
U * n('bl', up_0) * n('bl', dn_1) + \
U * n('bl', up_1) * n('bl', dn_0) + \
Up * n('bl', up_0) * n('bl', up_1) + \
Up * n('bl', dn_0) * n('bl', dn_1)
h_imp = h_0 + h_int
# ==== Bath & Coupling hamiltonian ====
c_dag_bath_vec = matrix(
[[c_dag('bl', o) for o in range(n_orb, n_orb + n_orb_bath)]])
c_bath_vec = matrix([[c('bl', o)] for o in range(n_orb, n_orb + n_orb_bath)])
h_bath = (c_dag_bath_vec * h_bath_mat * c_bath_vec)[0, 0]
h_coup = (c_dag_vec * V_mat * c_bath_vec +
from triqs.operators import c, c_dag, n
from itertools import product
# ==== System Parameters ====
beta = 5. # Inverse temperature
mu = 2. # Chemical potential
U = 5. # On-site density-density interaction
h = 0.2 # Local magnetic field
E = [ 0.0, 4.0 ] # Bath-site energies
V = [ 2.0, 5.0 ] # Couplings to Bath-sites
spin_names = ['up', 'dn']
orb_names = [0]
# ==== Local Hamiltonian ====
h_0 = - mu*( n('up',0) + n('dn',0) ) - h*( n('up',0) - n('dn',0) )
h_int = U * n('up',0) * n('dn',0)
h_imp = h_0 + h_int
# ==== Bath & Coupling Hamiltonian ====
h_bath, h_coup = 0, 0
for i, E_i, V_i in zip([0, 1], E, V):
for sig in ['up','dn']:
h_bath += E_i * n(sig,'b_' + str(i))
h_coup += V_i * (c_dag(sig,0) * c(sig,'b_' + str(i)) + c_dag(sig,'b_' + str(i)) * c(sig,0))
# ==== Total impurity hamiltonian and fundamental operators ====
h_tot = h_imp + h_coup + h_bath
# ==== Green function structure ====
gf_struct = [ [s, orb_names] for s 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():
ref_orbs = ['%s' % i for i in range(n_orbs * parms['N_x'])]
from triqs.operators import c, c_dag, n
from itertools import product
from numpy import sign
# ==== System Parameters ====
beta = 5. # Inverse temperature
mu = 2. # Chemical potential
U = 5. # On-site density-density interaction
h = 0.2 # Local magnetic field
Gamma = 1. # Hybridization energy
spin_names = ['up', 'dn']
orb_names = [0]
# ==== Local Hamiltonian ====
h_0 = - mu*( n('up',0) + n('dn',0) ) - h*( n('up',0) - n('dn',0) )
h_int = U * n('up',0) * n('dn',0)
h_imp = h_0 + h_int
# ==== Green function structure ====
gf_struct = [ [s, orb_names] for s in spin_names ]
# ==== Hybridization Function ====
n_iw = int(10 * beta)
iw_mesh = MeshImFreq(beta, 'Fermion', n_iw)
Delta = BlockGf(mesh=iw_mesh, gf_struct=gf_struct)
Delta << 0.;
for iw in Delta['up'].mesh:
Delta['up'][iw] = -1j * Gamma * sign(iw.imag)
Delta['dn'][iw] = -1j * Gamma * sign(iw.imag)
post_process=True,
)
p.version = ParameterCollection()
p.version.grab_attribs(version, ['version', 'ctint_hash', 'triqs_hash'])
# -- The alpha tensor
p.diag = 0.5 + p.delta
p.odiag = 0.5 - p.delta
p.solve.alpha = [[[p.diag, p.odiag] for i in indices]
for bl, indices in p.gf_struct]
# -- Total impurity hamiltonian and interaction part
p.H_0 = -p.mu * (n('up', 0) + n('dn', 0)) - p.h * (n('up', 0) - n('dn', 0))
p.H_int = p.U * n('up', 0) * n('dn', 0)
p.H = p.H_0 + p.H_int
p.solve.h_int = p.H_int
# -- Non-Interacting Impurity Green function
iw_mesh = MeshImFreq(p.beta, 'Fermion', p.n_iw)
p.G0_iw = Gf_from_struct(mesh=iw_mesh, struct=p.gf_struct)
h_field_dict = dict(up=p.h, dn=-p.h)
for name, g0_iw in p.G0_iw:
h_field = h_field_dict[name]
g0_iw << inverse(iOmega_n + p.mu + h_field)
# -- CTINT
0, ): h_loc,
(+1, ): T,
(-1, ): T,
},
orbital_positions=[(0, 0, 0)] * 2,
orbital_names=['up', 'do'],
)
kmesh = t_r.get_kmesh(n_k)
e_k = t_r.fourier(kmesh)
# -- Local double occupancy operator
gf_struct = [[0, 2]]
docc = n(0, 0) * n(0, 1)
Sz = 0.5 * np.diag([1., -1.])
# -- Sweep in interaction U
U_vec = np.arange(9., -0.5, -1.5)
h_vec = 1e-3 * np.linspace(-1., 1., num=11)
res = []
M0 = np.zeros((2, 2))
M = -5.0 * Sz
mu = 0.
for U in U_vec:
Units = np.dot(P, Units_prim)
print('Units =\n', Units)
t_r = TBSuperLattice(t_r_prim, P)
kmesh = t_r.get_kmesh(n_k)
e_k = t_r.fourier(kmesh)
print(e_k.target_shape)
print('eps(k=0) =\n', e_k[Idx(0, 0, 0)])
# -- Local double occ and spin operators
gf_struct = [[0, 4]]
docc = n(0, 0) * n(0, 2) + n(0, 1) * n(0, 3)
print('docc =', docc)
sigma_x = 0.5 * np.rot90(np.diag([1., 1.]))
sigma_y = 0.5 * np.rot90(np.diag([1.j, -1.j]))
sigma_z = 0.5 * np.diag([1., -1.])
print('sigma_x =\n', sigma_x)
print('sigma_y =\n', sigma_y)
print('sigma_z =\n', sigma_z)
Sx1 = np.kron(sigma_x, np.diag([1., 0.]))
Sx2 = np.kron(sigma_x, np.diag([0., 1.]))
Sy1 = np.kron(sigma_y, np.diag([1., 0.]))
n_iW=parms["measure_G2_n_bosonic"],
)
X.Hk[spin] << Hk[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)}
if haspomerol:
with HDFArchive(arname, 'w') as ar:
# 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["U"] * (ops.n('up', '0') * ops.n('dn', '0')) -
parms['chemical_potential'] * N)
#####
#
# Reference: 2 sites, calculate only G, not G2
#
#####
def calc_reference():
ref_orbs = ['%s' % i for i in range(n_orbs * parms['N_x'])]
ref_gf_struct = op.set_operator_structure(spin_names,
ref_orbs,
off_diag=off_diag)
ref_index_converter = {(sn, o): ("loc", int(o),