def loop_u_tp(u_range, tp_range, beta, seed='mott gap'):
"""Solves IPT dimer and return Im Sigma_AA, Re Simga_AB
returns list len(betarange) x 2 Sigma arrays
"""
tau, w_n = gf.tau_wn_setup(
dict(BETA=beta, N_MATSUBARA=max(2**ceil(log(4 * 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
sigma_iw = []
iterations = []
for tp, u_int in zip(tp_range, u_range):
giw_d, giw_o, loops = dimer.ipt_dmft_loop(beta, u_int, tp, giw_d,
giw_o, tau, w_n, 1e-3)
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.imag, siw_o.real))
print(np.array(iterations))
return sigma_iw
def loop_tp_u(tprange, u_range, beta, filestr, seed='mott gap'):
save_dir = filestr.format(beta)
if np.allclose(tprange, tprange[0]) and 'tp' not in save_dir:
save_dir = os.path.join(save_dir, 'tp' + str(tprange[0]))
elif np.allclose(u_range, u_range[0]):
save_dir = os.path.join(save_dir, 'U' + str(u_range[0]))
if not os.path.exists(save_dir):
os.makedirs(save_dir)
setup = {
'beta': beta,
'tprange': tprange.tolist(),
'u_range': u_range.tolist()
}
with open(save_dir + '/setup', 'w') as conf:
json.dump(setup, conf, indent=2)
###############################################################################
tau, w_n = gf.tau_wn_setup(
dict(BETA=beta, N_MATSUBARA=max(2**ceil(log(6 * beta) / log(2)), 256)))
giw_d, giw_o = dimer.gf_met(w_n, 0., tprange[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 = []
for tp, u_int in zip(tprange, u_range):
giw_d, giw_o, loops = dimer.ipt_dmft_loop(beta, u_int, tp, giw_d,
giw_o, tau, w_n,
1 / 5 / beta)
giw_s.append((giw_d.imag, giw_o.real))
np.save(save_dir + '/giw', np.array(giw_s))
def test_ipt_dimer_pm_g(u_int, result, beta=50.):
tau, w_n = tau_wn_setup(dict(BETA=beta, N_MATSUBARA=256))
giw_d, giw_o = dimer.gf_met(w_n, 0., 0, 0.5, 0.)
giw_d = dimer.ipt_dmft_loop(beta, u_int, 0, giw_d, giw_o, tau, w_n,
1e-5)[0][:64]
assert np.allclose(result, giw_d, atol=3e-3)
def dmft_solve(giw_d, giw_o, beta, u_int, tp, tau, w_n):
giw_d, giw_o, loops = dimer.ipt_dmft_loop(BETA, u_int, tp, giw_d, giw_o,
tau, w_n, 1e-12)
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)
return giw_d, giw_o, siw_d, siw_o
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 ipt_u_tp(u_int, tp, beta, seed="ins"):
tau, w_n = gf.tau_wn_setup(dict(BETA=beta, N_MATSUBARA=1024))
giw_d, giw_o = dimer.gf_met(w_n, 0., 0., 0.5, 0.)
if seed == "ins":
giw_d, giw_o = 1 / (1j * w_n + 4j / w_n), np.zeros_like(w_n) + 0j
giw_d, giw_o, loops = dimer.ipt_dmft_loop(
beta, u_int, tp, giw_d, giw_o, tau, w_n, 1e-12)
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)
return giw_d, giw_o, siw_d, siw_o, g0iw_d, g0iw_o, 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 ipt_u_tp(u_int, tp, beta, seed='ins'):
tau, w_n = gf.tau_wn_setup(dict(BETA=beta, N_MATSUBARA=2**8))
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 == 'ins':
giw_d, giw_o = 1 / (1j * w_n + 4j / w_n), np.zeros_like(w_n) + 0j
giw_d, giw_o, loops = dimer.ipt_dmft_loop(
beta, u_int, tp, giw_d, giw_o, tau, w_n, 1e-7)
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)
return giw_d, giw_o, siw_d, siw_o, g0iw_d, g0iw_o, w_n
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
sigma_iw = []
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)
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()))
print(seed, ' U', u_int, ' tp: ', tp, ' loops: ', loops)
return np.array(sigma_iw), w_n
def zero_f_meas(giw_d, giw_o, murange, tp, u_cut):
sd_zew, so_zew = [], []
for u_int in murange:
giw_d, giw_o, _ = dimer.ipt_dmft_loop(BETA, u_int, tp, giw_d, giw_o,
tau, w_n, 1e-3)
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)
sd_zew.append(np.polyfit(w_n[:2], siw_d[:2].imag, 1))
so_zew.append(np.polyfit(w_n[:2], siw_o[:2].real, 1))
sd_zew, so_zew = np.array(sd_zew), np.array(so_zew)
dw_sig11 = np.ma.masked_array(sd_zew[:, 0], murange >= u_cut)
zet = 1 / (1 - dw_sig11.T)
tpp = (TP + so_zew[:, 1].T)
return zet, tpp
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 ipt_u_tp(urange, tp, beta, w):
tau, w_n = gf.tau_wn_setup(dict(BETA=beta, N_MATSUBARA=2**11))
giw_d, giw_o = dimer.gf_met(w_n, 0., tp, 0.5, 0.)
w_set = list(np.arange(0, 120, 2))
w_set = w_set + list(np.arange(120, 512, 8))
imgss = []
for u_int in urange:
giw_d, giw_o, loops = dimer.ipt_dmft_loop(beta, u_int, tp, giw_d,
giw_o, tau, w_n, 1e-9)
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_imag.dimer_sigma(u_int, tp, g0iw_d, g0iw_o, tau,
w_n)
ss = gf.pade_continuation(1j * siw_d.imag + siw_o.real, w_n,
w + 0.0005j, w_set) # A-bond
imgss.append(
gf.semi_circle_hiltrans(w - tp - (ss.real - 1j * np.abs(ss.imag))))
return imgss
ax[1].set_ylim(*ylim)
w = np.linspace(-4, 4, 2**12)
dw = w[1] - w[0]
BETA = 756.
tau, w_n = gf.tau_wn_setup(dict(BETA=BETA, N_MATSUBARA=2**12))
nfp = gf.fermi_dist(w, BETA)
U, tp = 3.4, 0.3
# Matsubara
giw_d, giw_o = dimer.gf_met(w_n, 0., tp, 0.5, 0.)
giw_d, giw_o, _ = dimer.ipt_dmft_loop(BETA, U, tp, giw_d, giw_o, tau, w_n,
5e-4)
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_imag.dimer_sigma(U, tp, g0iw_d, g0iw_o, tau, w_n)
# Continuate sigma with Padé
w_set = np.array([0, 3] + list(range(5, 761, 7)))
ss, _ = dimer.pade_diag(1j * siw_d.imag, siw_o.real, w_n, w_set, w + 0.0005j)
###############################################################################
# Low Energy in Sigma matsubara
# -----------------------------
fig, ax = plt.subplots(2, 1, sharex=True)
plot_spectral(w, tp, ss, ax, (-7, 5), zero_f_meas_mat(siw_d, siw_o))
# ax[1].set_title('Low Energy Matsubara sigma + Padé Sigma for plot')
