# Diagonalize H
ed.diagonalize(H)
# Compute reference values of <n('up', 0)> and <n('dn', 0)>
w = np.array([
1.0,
np.exp(beta * (mu + h_field)),
np.exp(beta * (mu - h_field)),
np.exp(-beta * (-2 * mu + U))
])
Z = np.sum(w)
w /= Z
n_up_ref, n_dn_ref = complex(w[1] + w[3]), complex(w[2] + w[3])
n_up = ed.ensemble_average(('up', 0), ('up', 0), beta)
n_dn = ed.ensemble_average(('dn', 0), ('dn', 0), beta)
S_p = ed.ensemble_average(('up', 0), ('dn', 0), beta)
S_m = ed.ensemble_average(('dn', 0), ('up', 0), beta)
assert abs(n_up - n_up_ref) < 1e-10
assert abs(n_dn - n_dn_ref) < 1e-10
assert abs(S_p) < 1e-10
assert abs(S_m) < 1e-10
# Compute 3 susceptibilities
# < n_up ; n_up >
# < n_up ; n_dn >
# < S_+ ; S_- >
# Number of Matsubara frequencies for susceptibility calculation
for sn, o in product(spin_names, orb_names))
# Hybridization Hamiltonian
H_hyb = sum(V[o1, o2] * c_dag("B_" + sn, o1) * c(sn, o2) +
np.conj(V[o2, o1]) * c_dag(sn, o1) * c("B_" + sn, o2)
for sn, o1, o2 in product(spin_names, orb_names, orb_names))
# Complete Hamiltonian
H = H_loc + H_hyb + H_bath
# Diagonalize H
ed.diagonalize(H)
# Compute occupations
occ = [
ed.ensemble_average(i, i, beta).real
for i in product(spin_names, orb_names)
]
# 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)
# Compute \chi(\tau) = <n_{up,0}(\tau) n_{dn,0}(0)>
chi_tau = ed.chi_tau(('up', 0), ('up', 0), ('dn', 0), ('dn', 0), beta, n_tau)
# Hybridization Hamiltonian
H_hyb = Operator()
for k, v in enumerate(V):
H_hyb += sum(v * c_dag("B%i_%s" % (k, sn), 0) * c(sn, 0) +
np.conj(v) * c_dag(sn, 0) * c("B%i_%s" % (k, sn), 0)
for sn in spin_names)
# Complete Hamiltonian
H = H_loc + H_hyb + H_bath
# Diagonalize H
ed.diagonalize(H)
# Compute occupations
occ = [ed.ensemble_average((s, 0), (s, 0), beta).real for s in spin_names]
# 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)
# Compute \chi(\tau) = <n_{up}(\tau) n_{dn}(0)>
chi_tau = ed.chi_tau(('up', 0), ('up', 0), ('dn', 0), ('dn', 0), beta, n_tau)
# Compute \chi(i\nu)
chi_inu = ed.chi_inu(('up', 0), ('up', 0), ('dn', 0), ('dn', 0), beta, n_iw)