def get_sigma_eig(self,wlist=None,interp='spline',kk_method='mac'):
'''
kk-relation to get (index1,index2) component of Sigma, we ignored pi factor here, for we will get U*FG^{-1}.
For reference:
* Initial version: J. Phys.: Condens. Matter 10.8365.
* The matrix version: PRB 79.214518
wlist:
the frequency space.
interp:
interpolation method.
* `spline`
* `pchip`
kk_method:
method to calculate kk-relation(Appl. Spectrosc. 42.952).
* `mac` -> using Maclaurin-method.
* `fft` -> using Successive Double Fourier Transformation method.
'''
nband=self.nband
print 'Interpolating A(w),B(w) to get self-energy Sigma(w).'
t0=time.time()
wl,Alist,Blist=self.data
if not wlist is None:
if interp=='pchip':
interpolator=pchip_interpolate
elif interp=='spline':
interpolator=matrix_spline
else:
raise Exception('Undefined interpolation method @get_sigma.')
Alist=interpolator(wl,Alist,wlist)
Blist=interpolator(wl,Blist,wlist)
else:
wlist=wl
Gilist=-pi*Alist
Filist=-pi*Blist
Gievals,Gievecs=eigh_sorted(Gilist)
#Fievals,Fievecs=eig_sorted(Filist)
if kk_method=='fft':
Grevals=kk_fft(Gievals,'i2r',expand=1.5)
Frlist=kk_fft(Filist,'i2r',expand=1.5)
elif kk_method=='mac':
Grevals=kk(Gievals,'i2r',wlist=wlist)
Frlist=kk(Filist,'i2r',wlist=wlist)
else:
raise Exception('Undefined calculation method for kk-relation!')
#Slist=self.U*array([(Br+1j*Bi).dot(inv(Ar+1j*Ai)) for Ar,Ai,Br,Bi in zip(Arlist,Alist,Brlist,Blist)])
#Srlist=(swapaxes(Slist.conj(),1,2)+Slist)/2.
#Silist=(swapaxes(Slist.conj(),1,2)-Slist)*(-1j/2.)
Gevals=Grevals+1j*Gievals
#Fevals=Frevals+1j*Fievals
invG=eigen_combine(1./Gevals,Gievecs)
F=Frlist+1j*Filist
#why here is a minus sign?!
S=-self.U*bcast_dot(F,invG)
t1=time.time()
print 'Elapse -> %s'%(t1-t0)
return S,invG,F
def get_sigma_naive(self,chain,recursive=False):
'''
get the naive self energy by `G0^{-1} - G^{-1}`.
chain:
the chain instance.
recursive:
the recursive approach.
'''
print 'Getting self-energy using Naive Method.'
t0=time.time()
wlist=self.data[0]
if recursive:
G0=chain.get_G0(wlist,geta=0.01)
else:
HL=chain.H0
G0=mean([H2G(w=wlist[:,newaxis,newaxis],h=H0,geta=1e-2)[:,:2,:2] for H0 in HL],axis=0)
Alist=self.data[1]
Arlist=kk(Alist,'i2r',wlist=wlist)
Gr=-pi*(Arlist+1j*Alist)
sigma=inv(G0)-inv(Gr)
t1=time.time()
print 'Elapse -> %s'%(t1-t0)
return sigma