INSULATOR¶

# Author: Óscar Nájera

from __future__ import (absolute_import, division, print_function,
                        unicode_literals)

import matplotlib.pyplot as plt
import numpy as np

import dmft.common as gf
import dmft.ipt_imag as ipt
from dmft.ipt_real import dimer_dmft as dimer_dmft_real
import dmft.dimer as dimer
from slaveparticles.quantum import dos


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

Insulator¶

u_int = 3.5
BETA = 100.
tp = 0.3
title = "IPT lattice dimer\n" r"$U = {}$, $t_\perp = {}$, $\beta = {}$".format(
    u_int, tp, BETA)
giw_d, giw_o, siw_d, siw_o, g0iw_d, g0iw_o, w_n = ipt_u_tp(
    u_int, tp, BETA, "ins")
w = np.linspace(-3, 3, 800)
eps_k = np.linspace(-1., 1., 61)
w_set = np.concatenate((np.arange(100), np.arange(100, 200, 2)))

plt.figure()
g0wd = gf.pade_continuation(1j * g0iw_d.imag, w_n, w, w_set)
plt.plot(w, g0wd.real, label=r"$\Re e G0_{11}$")
plt.plot(w, g0wd.imag, label=r"$\Im m G0_{11}$")
plt.legend(loc=0)
plt.ylim([-2, 4])
plt.xlabel(r"$\omega$")
plt.ylabel(r"$G0_{11}(\omega)$")
plt.title(title)
plt.xticks(np.linspace(-3, 3, 13))

plt.figure()
g0wo = gf.pade_continuation(g0iw_o.real, w_n, w, w_set)
plt.plot(w, g0wo.real, label=r"$\Re e G0_{12}$")
plt.plot(w, g0wo.imag, label=r"$\Im m G0_{12}$")
plt.legend(loc=0)
plt.ylim([-5, 1])
plt.xlabel(r"$\omega$")
plt.ylabel(r"$G0_{12}(\omega)$")
plt.title(title)
plt.xticks(np.linspace(-3, 3, 13))

plt.figure()
gwd = gf.pade_continuation(1j * giw_d.imag, w_n, w, w_set)
plt.plot(w, gwd.real, label=r"$\Re e G_{11}$")
plt.plot(w, gwd.imag, label=r"$\Im m G_{11}$")
plt.legend(loc=0)
plt.ylim([-2, 2])
plt.xlabel(r"$\omega$")
plt.ylabel(r"$G_{11}(\omega)$")
plt.title(title)
plt.xticks(np.linspace(-3, 3, 13))

plt.figure()
gwo = gf.pade_continuation(giw_o.real, w_n, w, w_set)
plt.plot(w, gwo.real, label=r"$\Re e G_{12}$")
plt.plot(w, gwo.imag, label=r"$\Im m G_{12}$")
plt.legend(loc=0)
plt.ylim([-2, 2])
plt.xlabel(r"$\omega$")
plt.ylabel(r"$G_{12}(\omega)$")
plt.title(title)
plt.xticks(np.linspace(-3, 3, 13))

plt.figure()
swd = gf.pade_continuation(1j * siw_d.imag, w_n, w, w_set)
swd = swd.real - 1j * np.abs(swd.imag)
plt.plot(w, swd.real, label=r"$\Re e \Sigma_{11}$")
plt.plot(w, swd.imag, label=r"$\Im m \Sigma_{11}$")
plt.legend(loc=0)
plt.ylim([-3, 3])
plt.xlabel(r"$\omega$")
plt.ylabel(r"$\Sigma_{11}(\omega)$")
plt.title(title)
plt.xticks(np.linspace(-3, 3, 13))

plt.figure()
swo = gf.pade_continuation(siw_o.real, w_n, w, w_set)
plt.plot(w, swo.real, label=r"$\Re e \Sigma_{12}$")
plt.plot(w, swo.imag, label=r"$\Im m \Sigma_{12}$")
plt.legend(loc=0)
plt.ylim([-3, 3])
plt.xlabel(r"$\omega$")
plt.ylabel(r"$\Sigma_{12}(\omega)$")
plt.title(title)
plt.xticks(np.linspace(-3, 3, 13))

Reconstruction

GAB = gf.semi_circle_hiltrans(w + 1e-2j - tp - (swd + swo))
G_B = gf.semi_circle_hiltrans(w + 1e-2j + tp - (swd - swo))

backl = .5 * (GAB + G_B)
plt.figure()
plt.plot(w, gwd.imag, label=r"$\Im m G_{11} ref$")
plt.plot(w, backl.real, label=r"$\Re e G_{11}$")
plt.plot(w, backl.imag, label=r"$\Im m G_{11}$")
plt.legend(loc=0)
plt.ylim([-2, 2])
plt.xlabel(r"$\omega$")
plt.ylabel(r"$G_{11}(\omega)$")
plt.title(title)
plt.xticks(np.linspace(-3, 3, 13))

backo = .5 * (GAB - G_B)
plt.figure()
plt.plot(w, gwo.imag, label=r"$\Im m G_{12} ref$")
plt.plot(w, backo.real, label=r"$\Re e G_{12}$")
plt.plot(w, backo.imag, label=r"$\Im m G_{12}$")

plt.legend(loc=0)
plt.ylim([-2, 2])
plt.xlabel(r"$\omega$")
plt.ylabel(r"$G_{11}(\omega)$")
plt.title(title)
plt.xticks(np.linspace(-3, 3, 13))

Insulator in IPT Imag¶

plt.close("all")
u_int = 2.5
BETA = 100.
tp = 0.3
title = "IPT lattice dimer\n" r" $U = {}$, $t_\perp = {}$, $\beta = {}$".format(
    u_int, tp, BETA)
giw_d, giw_o, siw_d, siw_o, g0iw_d, g0iw_o, w_n = ipt_u_tp(
    u_int, tp, BETA, "ins")
w = np.linspace(-3, 3, 800)
eps_k = np.linspace(-1., 1., 61)
w_set = np.concatenate((np.arange(100), np.arange(100, 200, 2)))

plt.figure()
gwd = gf.pade_continuation(1j * giw_d.imag, w_n, w, w_set)
plt.plot(w, gwd.real, label=r"$\Re e G_{11}$")
plt.plot(w, -gwd.imag, label=r"$-\Im m G_{11}$")

swd = gf.pade_continuation(1j * siw_d.imag, w_n, w, w_set)
swd = swd.real - 1j * np.abs(swd.imag)
plt.plot(w, swd.real, label=r"$\Re e \Sigma_{11}$")
plt.plot(w, swd.imag, label=r"$\Im m \Sigma_{11}$")
plt.legend(loc=0)
plt.ylim([-3, 3])
plt.xlabel(r"$\omega$")
plt.title("Matsubara " + title)
plt.xticks(np.linspace(-3, 3, 13))
plt.savefig("IPT_imag_Dimer_mott_ins.pdf", transparent=False,
            bbox_inches="tight", pad_inches=0.05)

../_images/sphx_glr_plot_ipt_insulator_009.png

Insulator in IPT Real¶

w = np.linspace(-6, 6, 2**13)
dw = w[1] - w[0]
nfp = dos.fermi_dist(w, BETA)
gwd = gf.pade_continuation(1j * giw_d.imag, w_n, w, w_set)
(gss, gsa), (ss, sa) = dimer_dmft_real(u_int, tp, nfp, w, dw, gwd, gwd)

rgwd = 0.5 * (gss + gsa)
rswd = 0.5 * (ss + sa)

plt.close("all")
plt.plot(w, rgwd.real, label=r"$\Re e G_{11}$")
plt.plot(w, -rgwd.imag, label=r"$-\Im m G_{11}$")
plt.plot(w, rswd.real, label=r"$\Re e \Sigma_{11}$")
plt.plot(w, rswd.imag, label=r"$\Im m \Sigma_{11}$")
plt.legend(loc=0)
plt.xlim([-3, 3])
plt.ylim([-2, 2.5])
plt.xlabel(r"$\omega$")
plt.title("Real " + title)
plt.xticks(np.linspace(-3, 3, 13))
plt.savefig("IPT_real_Dimer_mott_ins.pdf", transparent=False,
            bbox_inches="tight", pad_inches=0.05)

../_images/sphx_glr_plot_ipt_insulator_010.png

Total running time of the script: ( 0 minutes 3.395 seconds)

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