def majorana4mps(spaceconfig,ket_even,ket_odd,theta=0,ordering=None):
'''
Get wave function of majorana fermion from ground states of even and odd parity.
Parameters:
:spaceconfig: <SuperSpaceConfig>, the configuration of Hilbert space.
:ket_even/ket_odd: <MPS>, the state of even and odd parities.
:theta: float, the relative phase factor of two vectors.
:ordering: '<-'/'->', the ordering of fermionic operators.
Return:
tuple of (pl1,pl2), the wave functions of majorana fermions.
'''
pl1,pl2=[],[]
cl,cl2=[],[]
nsite=ket_even.nsite
if ordering is None: ordering=arange(nsite)
for i in xrange(ket_even.nsite):
print 'Calculating %s-th Site'%i
bra_even=ket_even.tobra(labels=[ket_odd.labels[0],ket_even.labels[1]+"'"])
bra_odd=ket_odd.tobra(labels=[ket_odd.labels[0],ket_odd.labels[1]+"'"])
p1,p2=0,0
for spin in xrange(spaceconfig.nspin):
ci=get_opC(i,spaceconfig,index=spaceconfig.c2ind(spinindex=spin),ordering=ordering,dag=True)
c01=get_expect(ci,ket=ket_odd,bra=bra_even)
c10=get_expect(ci,ket=ket_even,bra=bra_odd)
ph1=exp(1j*theta)*c10+exp(-1j*theta)*c01
ph2=1j*(exp(1j*theta)*c10-exp(-1j*theta)*c01)
p1=p1+ph1*conj(ph1)
p2=p2+ph2*conj(ph2)
cl.append(c01)
cl2.append(c10)
pl1.append(p1)
pl2.append(p2)
return pl1,pl2,cl,cl2
def measure1(siteindex):
if which=='RHO':
op=opunit_N(spaceconfig,index=None,siteindex=siteindex)
else:
raise NotImplementedError()
if isinstance(op,OpCollection):
m=sum([get_expect(opi,ket=ket) for opi in op.ops])
else:
m=get_expect(op,ket=ket)#,bra=ket.tobra(labels=ket.labels))
print 'Get %s for site %s = %s @RANK: %s'%(which,siteindex,m.item(),RANK)
return m
def measure1(siteindex):
if which=='SDW': #cj+ sx cj ~ (-1)^j*m
op=opunit_S(which='x',spaceconfig=spaceconfig,siteindex=siteindex)
elif which=='sPDW': #cjup+ cjdn+ ~ (-1)^j*G
cup_d=opunit_C(dag=True,index=0,spaceconfig=spaceconfig,siteindex=siteindex)
cdn_d=opunit_C(dag=True,index=1,spaceconfig=spaceconfig,siteindex=siteindex)
cup_0=opunit_C(dag=False,index=0,spaceconfig=spaceconfig,siteindex=anchor)
cdn_0=opunit_C(dag=False,index=1,spaceconfig=spaceconfig,siteindex=anchor)
op=(cup_0*cdn_0)*(cup_d*cdn_d)
if isinstance(op,OpString):
op.compactify()
elif which=='bSDW': #cj+ sx cj+1 + h.c. ~ (-1)^j*M
opi=get_bsdw_op(spaceconfig,siteindex,nsite=nsite)
op0=get_bsdw_op(spaceconfig,siteindex=anchor,nsite=nsite)
op=(op0*opi).compactify()
op.insert_Zs(spaceconfig)
elif which=='bSDW1':
op=get_bsdw_op2(spaceconfig,siteindex,nsite=nsite)
op.insert_Zs(spaceconfig)
elif which=='TX': #<S_z^2> - <S_z>^2
op_sz=opunit_S(which='z',spaceconfig=spaceconfig,siteindex=siteindex)
op=op_sz*op_sz
elif which=='CDW':
op_n=opunit_N(spaceconfig,index=None,siteindex=siteindex)
op_n0=opunit_N(spaceconfig,index=None,siteindex=anchor)
op=op_n*op_n0
elif which=='RHO':
op=opunit_N(spaceconfig,index=None,siteindex=siteindex)
elif which=='triplet': #cj+ sx isy (cj+1+)^t
cup_d=opunit_C(dag=True,index=0,spaceconfig=spaceconfig,siteindex=siteindex)
cup_dp=opunit_C(dag=True,index=0,spaceconfig=spaceconfig,siteindex=siteindex+1)
op=cup_d*cup_dp
#raise NotImplementedError()
elif which=='Sx':
op=opunit_S(which='x',spaceconfig=spaceconfig,siteindex=siteindex)
elif which=='SxSx0':
op_Sx=opunit_S(which='x',spaceconfig=spaceconfig,siteindex=siteindex)
op_Sx=opunit_S(which='x',spaceconfig=spaceconfig,siteindex=anchor)
op=op_Sx*op_Sx
elif which=='DBL':
op_n=opunit_N(spaceconfig,index=0,siteindex=siteindex)*opunit_N(spaceconfig,index=1,siteindex=siteindex)
op_n0=opunit_N(spaceconfig,index=0,siteindex=nsite/2)*opunit_N(spaceconfig,index=1,siteindex=anchor)
op=op_n*op_n0
else:
raise NotImplementedError()
if isinstance(op,OpCollection):
m=sum([get_expect(opi,ket=ket) for opi in op.ops])
else:
m=get_expect(op,ket=ket)#,bra=ket.tobra(labels=ket.labels))
print 'Get %s for site %s = %s @RANK: %s'%(which,siteindex,m,RANK)
return m
def measure1(i):
print 'Measuring Majorana fermion at site %s'%i
bra_even=ket_even.tobra(labels=[ket_odd.labels[0],ket_even.labels[1]+"'"])
bra_odd=ket_odd.tobra(labels=[ket_odd.labels[0],ket_odd.labels[1]+"'"])
signl=[]
si=opunit_S(spaceconfig,which='+',siteindex=i)
for j in xrange(i):
spi=copy.copy(sp)
spi.siteindex=j
signl.append(spi)
si=prod(signl+[si])
c01=get_expect(si,ket=ket_odd,bra=bra_even)
c10=get_expect(si,ket=ket_even,bra=bra_odd)
ph1=exp(1j*theta)*c10+exp(-1j*theta)*c01
ph2=1j*(exp(1j*theta)*c10-exp(-1j*theta)*c01)
p1=ph1
p2=ph2
return p1,p2,c01,c10
def test_loc_observe():
nsite = 10
(E, mps), info = get_spec(nsite, trunc_steps=[], return_vecs=True)
model = info['model']
sx = opunit_Sx(spaceconfig=model.spaceconfig)
sz = opunit_Sz(spaceconfig=model.spaceconfig)
sy = opunit_Sy(spaceconfig=model.spaceconfig)
# measure Sx(i)
ion()
for isite in range(nsite):
res = get_expect(sz.as_site(isite), mps)[0, 0].diagonal()
# res=fft.fft(res)
plot(res)
pdb.set_trace()
