# Bath hamiltonian in matrix representation
h_bath_mat = diag(eps_bath) - matrix([[0, t_bath],
[t_bath, 0]])
# Coupling matrix
V_mat = matrix([[1., 1.],
[1., 1.]])
# ==== Local Hamiltonian ====
c_dag_vec = { s: matrix([[c_dag(s,o) for o in orb_names]]) for s in spin_names }
c_vec = { s: matrix([[c(s,o)] for o in orb_names]) for s in spin_names }
h_0 = sum(c_dag_vec[s] * h_0_mat * c_vec[s] for s in spin_names)[0,0]
Umat, Upmat = U_matrix_kanamori(n_orb, U_int=U, J_hund=J)
h_int = h_int_kanamori(spin_names, orb_names, Umat, Upmat, J, off_diag=True)
h_imp = h_0 + h_int
# ==== Bath & Coupling hamiltonian ====
orb_bath_names = ['b_' + str(o) for o in orb_names]
c_dag_bath_vec = { s: matrix([[c_dag(s, o) for o in orb_bath_names]]) for s in spin_names }
c_bath_vec = { s: matrix([[c(s, o)] for o in orb_bath_names]) for s in spin_names }
h_bath = sum(c_dag_bath_vec[s] * h_bath_mat * c_bath_vec[s] for s in spin_names)[0,0]
h_coup = sum(c_dag_vec[s] * V_mat * c_bath_vec[s] + c_dag_bath_vec[s] * V_mat * c_vec[s] for s in spin_names)[0,0] # FIXME Adjoint
# ==== Total impurity hamiltonian ====
h_tot = h_imp + h_coup + h_bath
# ==== Green function structure ====
from triqs.operators.util import U_matrix_kanamori, h_int_kanamori
from triqs_tprf.OperatorUtils import fundamental_operators_from_gf_struct
from triqs_tprf.rpa_tensor import get_rpa_tensor
U = 1.0
J = 0.1
spin_names = ['up', 'do']
orb_names = list(range(norb))
# TRIQS uses spin as slow index
gf_struct = [[spin_name, norb] for spin_name in spin_names]
Umat, Upmat = U_matrix_kanamori(n_orb=norb, U_int=U, J_hund=J)
H_int = h_int_kanamori(spin_names,
orb_names,
U=Umat,
Uprime=Upmat,
J_hund=J,
off_diag=True)
fundamental_operators = fundamental_operators_from_gf_struct(gf_struct)
U_abcd = get_rpa_tensor(H_int, fundamental_operators) # given in cc^+cc^+
# ----------------------------------------------------------------------
# -- Lattice susceptbility in the RPA approximation
from triqs_tprf.lattice import solve_rpa_PH
chi_wk = solve_rpa_PH(chi00_wk, U_abcd)
# ======================================================================
# Coupling matrix
V_mat = matrix([[1., 1., 1.], [1., 1., 1.], [1., 1., 1.]])
# ==== Local Hamiltonian ====
c_dag_vec = {
s: matrix([[c_dag(s, o) for o in range(n_orb)]])
for s in block_names
}
c_vec = {s: matrix([[c(s, o)] for o in range(n_orb)]) for s in block_names}
h_0 = sum(c_dag_vec[s] * h_0_mat * c_vec[s] for s in block_names)[0, 0]
Umat, Upmat = U_matrix_kanamori(n_orb, U_int=U, J_hund=J)
h_int = h_int_kanamori(block_names,
range(n_orb),
Umat,
Upmat,
J,
off_diag=True)
h_imp = h_0 + h_int
# ==== Bath & Coupling hamiltonian ====
c_dag_bath_vec = {
s: matrix([[c_dag(s, o) for o in range(n_orb, n_orb + n_orb_bath)]])
for s in block_names
}
c_bath_vec = {
s: matrix([[c(s, o)] for o in range(n_orb, n_orb + n_orb_bath)])
for s in block_names
}
n_idx = len(idx_lst)
# ==== Local Hamiltonian ====
c_dag_vec = matrix([[c_dag('bl', idx) for idx in idx_lst]])
c_vec = matrix([[c('bl', idx)] for idx in idx_lst])
h_0_mat = TBL._hop[(0, 0, 0)]
h_0 = (c_dag_vec * h_0_mat * c_vec)[0, 0]
Umat, Upmat = U_matrix_kanamori(len(orb_names), U_int=U, J_hund=J)
op_map = {(s, o): ('bl', i)
for i, (s, o) in enumerate(product(block_names, orb_names))}
h_int = h_int_kanamori(block_names,
orb_names,
Umat,
Upmat,
J,
off_diag=True,
map_operator_structure=op_map)
h_imp = h_0 + h_int
# ==== Non-Interacting Impurity Green function ====
iw_mesh = MeshImFreq(beta, 'Fermion', n_iw)
k_mesh = MeshBrZone(TBL.bz, n_k)
k_iw_mesh = MeshProduct(k_mesh, iw_mesh)
G0_k_iw = BlockGf(mesh=k_iw_mesh, gf_struct=gf_struct)
G0_iw = BlockGf(mesh=iw_mesh, gf_struct=gf_struct)
iw_vec = array([iw.value * np.eye(n_idx) for iw in iw_mesh])
k_vec = array([k.value for k in k_mesh])