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dft_tools/doc/reference/python/lattice/ex_Hilbert.py

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from pytriqs.lattice.tight_binding import *
from pytriqs.dos import HilbertTransform
from pytriqs.gf.local import GfImFreq
# Define a DOS (here on a square lattice)
BL = BravaisLattice(Units = [(1,0,0) , (0,1,0) ], orbital_positions= {"" : (0,0,0)} )
t = -1.00 # First neighbour Hopping
tp = 0.0*t # Second neighbour Hopping
hop= { (1,0) : [[ t]],
(-1,0) : [[ t]],
(0,1) : [[ t]],
(0,-1) : [[ t]],
(1,1) : [[ tp]],
(-1,-1): [[ tp]],
(1,-1) : [[ tp]],
(-1,1) : [[ tp]]}
TB = TightBinding (BL, hop)
d = dos(TB, n_kpts= 500, n_eps = 101, name = 'dos')[0]
#define a Hilbert transform
H = HilbertTransform(d)
#fill a Green function
G = GfImFreq(indices = ['up','down'], beta = 20)
Sigma0 = GfImFreq(indices = ['up','down'], beta = 20); Sigma0.zero()
G <<= H(Sigma = Sigma0,mu=0.)