mirror of
https://github.com/triqs/dft_tools
synced 2024-11-01 03:33:50 +01:00
45 lines
1.3 KiB
Python
45 lines
1.3 KiB
Python
import numpy
|
|
from math import pi
|
|
from cmath import sqrt, log
|
|
from pytriqs.gf.local import *
|
|
from pytriqs.gf.local.descriptors import Function
|
|
|
|
beta = 100 # Inverse temperature
|
|
L = 101 # Number of Matsubara frequencies used in the Pade approximation
|
|
eta = 0.01 # Imaginary frequency shift
|
|
|
|
## Test Green's functions ##
|
|
|
|
# Two Lorentzians
|
|
def GLorentz(z):
|
|
return 0.7/(z-2.6+0.3*1j) + 0.3/(z+3.4+0.1*1j)
|
|
|
|
# Semicircle
|
|
def GSC(z):
|
|
return 2.0*(z + sqrt(1-z**2)*(log(1-z) - log(-1+z))/pi)
|
|
|
|
# A superposition of GLorentz(z) and GSC(z) with equal weights
|
|
def G(z):
|
|
return 0.5*GLorentz(z) + 0.5*GSC(z)
|
|
|
|
# Matsubara GF
|
|
gm = GfImFreq(indices = [0], beta = beta, name = "gm")
|
|
gm <<= Function(G)
|
|
gm.tail.zero()
|
|
gm.tail[1] = numpy.array([[1.0]])
|
|
|
|
# Real frequency BlockGf(reference)
|
|
gr = GfReFreq(indices = [0], window = (-5.995, 5.995), n_points = 1200, name = "gr")
|
|
gr <<= Function(G)
|
|
gr.tail.zero()
|
|
gr.tail[1] = numpy.array([[1.0]])
|
|
|
|
# Analytic continuation of gm
|
|
g_pade = GfReFreq(indices = [0], window = (-5.995, 5.995), n_points = 1200, name = "g_pade")
|
|
g_pade.set_from_pade(gm, n_points = L, freq_offset = eta)
|
|
|
|
# Comparison plot
|
|
from pytriqs.plot.mpl_interface import oplot
|
|
oplot(gr[0,0], '-o', RI = 'S', name = "Original DOS")
|
|
oplot(g_pade[0,0], '-x', RI = 'S', name = "Pade-reconstructed DOS")
|