def z2_invariant(h,nk=100):
"""Calculates the Z2 invariant by the path evolution algorithm"""
import klist
kst = klist.tr_klist(nk=nk) # class with the klist
wfs1 = [occ_states2d(h,k) for k in kst.path1] # lower path
wfs2 = [occ_states2d(h,k) for k in kst.path2] # lower path
wfsc1 = [occ_states2d(h,k) for k in kst.common] # lower path
# related with the other by symmetry
wfsc2 = [wfsc1[-i] for i in range(len(wfsc1))] # invert the order
wfs = wfs1 + wfsc1 + wfs2 + wfsc2 # all the paths
phi = 0.0 # initialize phase
# connection contribution
for i in range(len(wfs)):
m = uij(wfs[i-1],wfs[i]) # matrix of wavefunctions
d = lg.det(m) # calculate determinant
phi += np.arctan2(d.imag,d.real) # add contribution
phi = phi/(2.*np.pi)
# curvature contribution
halfc = 0.0
for ik in np.linspace(-.5,.5,nk):
for jk in np.linspace(-.0,.5,nk/2):
halfc += berry_curvature(h,np.array([ik,jk]))
halfc = halfc/(2.*np.pi*nk*nk)
print halfc,phi
return phi-halfc
def z2_invariant(h, nk=100):
"""Calculates the Z2 invariant by the path evolution algorithm"""
import klist
kst = klist.tr_klist(nk=nk) # class with the klist
wfs1 = [occ_states2d(h, k) for k in kst.path1] # lower path
wfs2 = [occ_states2d(h, k) for k in kst.path2] # lower path
wfsc1 = [occ_states2d(h, k) for k in kst.common] # lower path
# related with the other by symmetry
wfsc2 = [wfsc1[-i] for i in range(len(wfsc1))] # invert the order
wfs = wfs1 + wfsc1 + wfs2 + wfsc2 # all the paths
phi = 0.0 # initialize phase
# connection contribution
for i in range(len(wfs)):
m = uij(wfs[i - 1], wfs[i]) # matrix of wavefunctions
d = lg.det(m) # calculate determinant
phi += np.arctan2(d.imag, d.real) # add contribution
phi = phi / (2. * np.pi)
# curvature contribution
halfc = 0.0
for ik in np.linspace(-.5, .5, nk):
for jk in np.linspace(-.0, .5, nk / 2):
halfc += berry_curvature(h, np.array([ik, jk]))
halfc = halfc / (2. * np.pi * nk * nk)
print halfc, phi
return phi - halfc