Study the behavior of the Dimer Bethe lattice in the Transition¶
Specific Regions of the phase diagram are reviewed to inspect the behavior of the insulating state
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74 73 72 72 71 70 70 69 68 68 67 66 65 65 64 63 63 62]
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90 94 100 111 130 178 749 267 197 163 141 126 114 108 106 105 103 102
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77 76 74 73 72 71 70 69 68 67 66 65 64 63 62 61 61 60]
[ 58 64 70 98 242 57 45 39 36 34 32 31 30 30 29 28 28 28
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65 72 82 95 117 157 275 512 197 142 116 100 89 81 75 70 66 62
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94 85 78 72 67 63 60 57 54 52 50 48 46 45 45 45 45 45]
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import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import axes3d
import dmft.dimer as dimer
import dmft.common as gf
import dmft.ipt_imag as ipt
def loop_u_tp(u_int, tp, betarange, seed='mott gap'):
giw_s = []
sigma_iw = []
ekin, epot = [], []
iterations = []
lwn = []
for beta in betarange:
tau, w_n = gf.tau_wn_setup(dict(BETA=beta, N_MATSUBARA=512))
lwn.append(w_n)
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_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))
print(np.array(iterations))
# last division in energies because I want per spin epot
return np.array(giw_s), np.array(sigma_iw), np.array(ekin) / 4, np.array(epot) / 4, w_n
urange = np.arange(2.8, 3.4, .1)
data = []
temp = np.linspace(0.015, 0.06, 90)
betarange = 1 / temp
for u_int in urange:
giw_s, sigma_iw, ekin, epot, w_n = loop_u_tp(
u_int, .3, betarange, 'mott gap')
data.append((giw_s, sigma_iw, ekin, epot, w_n, u_int))
for u_int in urange:
giw_s, sigma_iw, ekin, epot, w_n = loop_u_tp(
u_int, .3, betarange, 'met')
data.append((giw_s, sigma_iw, ekin, epot, w_n, u_int))
for sim in data:
giw_s, sigma_iw, ekin, epot, w_n, u_int = sim
plt.plot(1 / betarange, 2 * epot / u_int, 'x-', label=u_int)
plt.title(r'Double occupation')
plt.ylabel(r'$\langle n_\uparrow n_\downarrow \rangle$')
plt.xlabel(r'$T/D$')
plt.legend()
plt.show()
Total running time of the script: ( 2 minutes 14.274 seconds)