def loop_u_tp(u_range, tprange, beta, seed='mott gap'):
tau, w_n = gf.tau_wn_setup(dict(BETA=beta, N_MATSUBARA=max(5 * beta, 256)))
giw_d, giw_o = dimer.gf_met(w_n, 0., 0., 0.5, 0.)
if seed == 'mott gap':
giw_d, giw_o = 1 / (1j * w_n + 4j / w_n), np.zeros_like(w_n) + 0j
giw_s = []
sigma_iw = []
ekin, epot = [], []
iterations = []
for u_int, tp in zip(u_range, tprange):
giw_d, giw_o, loops = dimer.ipt_dmft_loop(beta, u_int, tp, giw_d,
giw_o, tau, w_n)
giw_s.append((giw_d, giw_o))
iterations.append(loops)
g0iw_d, g0iw_o = dimer.self_consistency(1j * w_n, 1j * giw_d.imag,
giw_o.real, 0., tp, 0.25)
siw_d, siw_o = ipt.dimer_sigma(u_int, tp, g0iw_d, g0iw_o, tau, w_n)
sigma_iw.append((siw_d.copy(), siw_o.copy()))
ekin.append(dimer.ekin(giw_d, giw_o, w_n, tp, beta))
epot.append(
dimer.epot(giw_d, w_n, beta, u_int**2 / 4 + tp**2, ekin[-1], u_int)
/ 4) # last division because I want per spin epot
print(np.array(iterations))
return np.array(giw_s), np.array(sigma_iw), np.array(ekin), np.array(
epot), w_n
def dmft_solve(giw_d, giw_o, u_int, tp, beta, tau, w_n):
giw_d, giw_o, loops = dimer.ipt_dmft_loop(
beta, u_int, tp, giw_d, giw_o, tau, w_n)
g0iw_d, g0iw_o = dimer.self_consistency(
1j * w_n, 1j * giw_d.imag, giw_o.real, 0., tp, 0.25)
siw_d, siw_o = ipt.dimer_sigma(u_int, tp, g0iw_d, g0iw_o, tau, w_n)
ekin = dimer.ekin(giw_d, giw_o, w_n, tp, beta)
# last division because I want per spin epot
epot = dimer.epot(giw_d, w_n, beta, u_int ** 2 /
4 + tp**2, ekin, u_int) / 4
return (giw_d, giw_o), (siw_d, siw_o), ekin, epot, loops
def loop_urange(urange, tp, beta):
ekin, epot = [], []
tau, w_n = gf.tau_wn_setup(dict(BETA=beta, N_MATSUBARA=2**10))
giw_d, giw_o = dimer.gf_met(w_n, 0., 0., 0.5, 0.)
for u_int in urange:
giw_d, giw_o, _ = dimer.ipt_dmft_loop(beta, u_int, tp, giw_d, giw_o,
tau, w_n, 1e-4)
ekin.append(dimer.ekin(giw_d, giw_o, w_n, tp, beta))
epot.append(
dimer.epot(giw_d, w_n, beta, u_int**2 / 4 + tp**2 + 0.25, ekin[-1],
u_int))
return np.array(ekin), np.array(epot)
def loop_beta(u_int, tp, betarange, seed):
avgH = []
for beta in betarange:
tau, w_n = gf.tau_wn_setup(
dict(BETA=beta, N_MATSUBARA=max(2**ceil(log(8 * beta) / log(2)), 256)))
giw_d, giw_o = dimer.gf_met(w_n, 0., 0., 0.5, 0.)
if seed == 'I':
giw_d, giw_o = 1 / (1j * w_n - 4j / w_n), np.zeros_like(w_n) + 0j
giw_d, giw_o, _ = dimer.ipt_dmft_loop(
beta, u_int, tp, giw_d, giw_o, tau, w_n, 1e-6)
ekin = dimer.ekin(giw_d[:int(8 * beta)], giw_o[:int(8 * beta)],
w_n[:int(8 * beta)], tp, beta)
epot = dimer.epot(giw_d[:int(8 * beta)], w_n[:int(8 * beta)],
beta, u_int ** 2 / 4 + tp**2 + 0.25, ekin, u_int)
avgH.append(ekin + epot)
return np.array(avgH)
def test_dimer_energies(u_int, mu, tp, beta=100):
h_loc, (a_up, b_up, a_dw, b_dw) = dimer.hamiltonian(u_int, mu, tp)
e_imp = (tp * (a_up.T * b_up + a_dw.T * b_dw + b_up.T * a_up +
b_dw.T * a_dw)).todense()
eig_e, eig_v = op.diagonalize(h_loc.todense())
w_n = gf.matsubara_freq(beta, 2**8) # n=2**7=256
gf_di = op.gf_lehmann(eig_e, eig_v, a_up.T, beta, 1j * w_n)
gf_of = op.gf_lehmann(eig_e, eig_v, a_up.T, beta, 1j * w_n, b_up)
ekin_gf = dimer.ekin(gf_di, gf_of, w_n, tp, beta, 0)
ekin_ed = op.expected_value(e_imp, eig_e, eig_v, beta)
assert abs(ekin_ed - ekin_gf) < 5e-4
epot_gf = dimer.epot(gf_di, w_n, beta, u_int**2 / 4 + tp**2, ekin_gf,
u_int)
docc = (a_up.T * a_up * a_dw.T * a_dw +
b_up.T * b_up * b_dw.T * b_dw).todense()
epot_ed = op.expected_value(docc, eig_e, eig_v, beta) * u_int
assert abs(epot_ed - epot_gf) < 1e-3