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