def calground(sites,K1,K2,U,dmu=0,override=True):
'''
The perturbation version of calculating fractional charge.
'''
t=1.
blkid=0
target_block=(0,0)
solve_method=lambda nsite:solve1(K1,K2,U,dmu,target_block,nsite,override)
mpido(solve_method,inputlist=sites,bcastouputmesh=False)
def order_scale(which,K1,K2,U,sites,dmu=0,target_block=(0,0),append=False,usempi=False):
'''Get the scaling behavior of order parameters.'''
suffix='W1%s_W2%s_U%s_NN%s_dmu%s_%s.dat'%(K1,K2,U,len(sites),dmu,target_block)
filename='data/%s_%s'%(which,suffix)
if append:
f=open(filename,'r')
mls=cPickle.load(f)
f.close()
else:
t0=time.time()
def solve1(nsite):
ml=measure_order(which,siteindices=None,append=True,K1=K1,K2=K2,U=U,nsite=nsite,dmu=dmu,target_block=target_block,usempi=not usempi)
return ml
if usempi:
mls=mpido(solve1,inputlist=sites,bcastouputmesh=False)
else:
mls=[]
for nsite in sites:
mls.append(solve1(nsite))
if RANK==0:
t1=time.time()
print 'Elapse -> %s, on RANK: %s'%(t1-t0,RANK)
f=open(filename,'w')
cPickle.dump(mls,f)
f.close()
if ONSV: return
if which=='CDW':
rfilename='data/%s_%s'%('RHO',suffix)
if os.path.isfile(rfilename):
rf=open(rfilename,'r')
rhos=cPickle.load(rf)
rf.close()
mls=[ml+1-rho*rho[len(rho)/2] for ml,rho in zip(mls,rhos)]
spl=[]
for nsite,ml in zip(sites,mls):
#ml=cos(arange(nsite)*pi)
ml=array(ml).real
mqsi=fft.fft(ml)
spi=abs(mqsi[nsite/2])
#spi=abs(mqsi[nsite/2-1:nsite/2+1])
spl.append(spi)
vsites=(sites[:-1]+sites[1:])/2.
cindex=log(abs(diff(spl)/diff(sites)))/log(vsites)
print 'The cirtical index is %s'%cindex
pdb.set_trace()
ion()
x=log(vsites)
y=log(abs(diff(spl)/diff(sites)))
plot(x,y)
#plot(log(vsites),log(abs(diff(spl)/diff(sites))))
pdb.set_trace()
def scan_nonlocality(J,h,nsite,angles1,angles2,maxN=140,append=False,token=''):
'''
Scan the non locality on a block sphere.
'''
sites=arange(nsite+1)
suffix=get_name(J=J,h=h,nsite=nsite)
ffile='data/scan_fidelity_%s_s%s%s.dat'%(suffix,len(angles1),token)
def measure1(angles):
(theta1,phi1),(theta2,phi2)=angles
fs=bulk_edge_fidelity(J=J,h=h,nsite=nsite,target_blocks=({'theta':theta1,'phi':phi1},{'theta':theta2,'phi':phi2}),direction='->',maxN=maxN,append=append)
y=fs[nsite/2]
return y
ml=mpido(measure1,inputlist=zip(angles1,angles2))
print 'Fin. ml = %s'%ml
if RANK==0:
savetxt(ffile,ml)
def measure_order(which,J,h,nsite,target_block,siteindices=None,usempi=True,anchor=None,**kwargs):
'''
Get order parameter from ground states.
Parameters:
:which: str,
* 'Sz', <Sz>
:nsite: int, the number of sites.
:siteindices: list, the measure points.
Return:
number, the value of order parameter.
'''
if anchor is None:anchor=nsite/2
if siteindices is None: siteindices=arange(nsite)
siteindices=array(siteindices)
spaceconfig=SpinSpaceConfig([2,1])
suffix=get_name(h=h,J=J,nsite=nsite)
ofile='data/%s_%s.dat'%(which,suffix)
filename='data/mps_%s.dat'%suffix
eng,ket=load_mps(h=h,J=J,nsite=nsite,target_block=target_block,maxN=200)
ml=[]
ordering=arange(nsite)[::-1]
def measure1(siteindex):
if which=='Sz':
op=opunit_S(which='z',siteindex=siteindex,spaceconfig=spaceconfig)
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
if usempi:
ml=mpido(measure1,inputlist=siteindices)
else:
ml=[]
for siteindex in siteindices:
ml.append(measure1(siteindex))
ml=array(ml)
if RANK==0:
savetxt(ofile,ml.real)
return ml
def smajorana4mps(spaceconfig,ket_even,ket_odd,theta=0):
'''
Get wave function of spin-majorana fermion from ground states of even and odd spin-parity.
Parameters:
:spaceconfig: <SuperSpaceConfig>, the configuration of Hilbert space.
:ket_even/ket_odd: <MPS>, the state of even and odd parities.
:theta: number, the overall state.
Return:
tuple of (pl1,pl2), the wave functions of majorana fermions.
'''
#construct spin parity operator.
data=opunit_Sz(spaceconfig).get_data()+0.5*identity(spaceconfig.hndim)
fill_diagonal(data,exp(1j*pi*data.diagonal()))
sp=OpUnit(data=data,label='P')
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
res=mpido(func=measure1,inputlist=arange(ket_even.nsite),bcastouputmesh=True)
res=array(res)
return res[:,0],res[:,1],res[:,2],res[:,3]
def measure_order(which,dmu=0.01,target_block=(0,0),siteindices=None,append=False,usempi=True,anchor=None,**kwargs):
'''
Get order parameter from ground states.
Parameters:
:which: str,
* 'bSDW',
* 'bSDW1',
* 'SDW',
* 'triplet'
* 'sPDW'.
* 'TX'
* 'CDW', <Rho*Rho>-<Rho>*<Rho>
* 'Sx', <Sx>
* 'SxSx0', <Sx*Sx(0)>
:nsite: int, the number of sites.
:siteindices: list, the measure points.
Return:
number, the value of order parameter.
'''
nsite=kwargs.get('nsite')
if anchor is None:anchor=nsite/2
if siteindices is None: siteindices=arange(nsite)
siteindices=array(siteindices)
spaceconfig=SuperSpaceConfig(chorder([2,1,1]))
suffix='W1%s_W2%s_U%s_N%s_dmu%s_%s'%(kwargs.get('K1'),kwargs.get('K2'),kwargs.get('U'),kwargs.get('nsite'),dmu,target_block)
ofile='data/%s_%s.dat'%(which,suffix)
if kwargs.get('ket') is not None:
ket=kwargs.get('ket')
else:
filename='data/mps_%s.dat'%suffix
if append:
#ket=MPS.load(filename)
eng,ket=load_mps(K1=kwargs.get('K1'),K2=kwargs.get('K2'),U=kwargs.get('U'),which=(dmu,target_block),nsite=nsite,maxN=200)
else:
EG,ket=solve('dmrg',periodic=False,method_args={'target_block':target_block,'nlevel':1},**kwargs)
ket.save(filename)
ml=[]
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
if usempi:
ml=mpido(measure1,inputlist=siteindices)
else:
ml=[]
for siteindex in siteindices:
ml.append(measure1(siteindex))
ml=array(ml)
if RANK==0:
savetxt(ofile,ml.real)
return ml
