def get_solving_system(K1,K2,U,nsite,mu=0.,t=1.,evolutor_type='null',periodic=False,perturb=None):
'''
Set the parameters and get the solving system.
Parameters:
:K1,K2,U,mu,t: float, the parameters.
:evolutor_type: str,
* 'null', do not perform any unitary and truncation during expansion of sites.
* 'full', do blockize and unitary but no truncation is allowed.
* 'masked', use kpmask to identify truncation.
Return:
tuple of (model, expander)
'''
assert(evolutor_type in ['null','full','masked'])
model=BizardModel(K1=K1,K2=K2,U=U,t=t,mu=mu,nsite=nsite,periodic=periodic)
if perturb is not None:
if 'bSDW' in perturb.keys():
model.perturb_bSDW(sites=perturb['bSDW'])
elif 'mu' in perturb.keys():
model.perturb_mu(sites=perturb['mu'][0],lamb=perturb['mu'][1])
if evolutor_type=='null':
return model,None
else:
spaceconfig=SuperSpaceConfig(chorder([model.hgen.spaceconfig.nspin,1,model.hgen.spaceconfig.norbit]))
H_serial=op2collection(op=model.hgen.get_opH())
expander=RGHGen(spaceconfig=spaceconfig,H=H_serial,evolutor_type=evolutor_type)
#ion()
#H_serial.show_advanced()
#pdb.set_trace()
return model,expander
def measure_mjsx(K1,K2,U,nsite,dmu=0.01,usempi=True,append=False):
suffix='W1%s_W2%s_U%s_N%s_dmu%s.dat'%(K1,K2,U,nsite,dmu)
mlfile='data/mjsx_%s.npy'%suffix
siteindices=arange(nsite)
if not append:
blocks=[(0,0),(0,1)]
spaceconfig=SuperSpaceConfig(chorder([2,1,1]))
kets=[]
for target_block in blocks:
suffix='W1%s_W2%s_U%s_N%s_dmu%s_%s.dat'%(K1,K2,U,nsite,dmu,target_block)
filename='data/mps_'+suffix
ket=MPS.load(filename)
kets.append(ket)
kets=[1./sqrt(2.)*(kets[0]+kets[1]),1./sqrt(2.)*(kets[0]-kets[1])]
ml=[]
for ket in kets:
ket.compress()
ml.append(measure_order(which='Sx',ket=ket,usempi=usempi,nsite=nsite))
ml=array(ml)
save(mlfile,ml)
else:
ml=load(mlfile)
ion()
plot(siteindices,ml.T.real)
pdb.set_trace()
def load_mps(alpha,Delta,Vz,mu,U,target_block,nsite,maxN=None,fixtail=True):
'''
Load Specific Matrix product state.
Parameters:
:which: tuple of dmu, target_block.
* target_block, int, '+', '-'.
Return:
eng,mps
'''
suf=get_name(Vz,Delta,mu,alpha,nsite,periodic=False,resonance=False)
spaceconfig1=SuperSpaceConfig(chorder([1,2,1,1]))
suffix0=suf+'_%s'%target_block
filename_mps0='data/mps_%s.dat'%suffix0
filename_eng0='data/eng_%s.dat'%suffix0
tblocks=(0,1)
def get1(target_blocki):
suffix=suf+'_%s'%target_blocki
filename_mps='data/mps_%s.dat'%suffix
filename_eng='data/eng_%s.dat'%suffix
mps=MPS.load(filename_mps)
eng=loadtxt(filename_eng)
if target_blocki==1 and fixtail:
mps=fix_tail(mps,spaceconfig=spaceconfig1,parity=-1)
return eng,mps
if os.path.isfile(filename_mps0):
eng,mps=get1(target_block)
if maxN is not None:
mps.compress(maxN=maxN)
return eng,mps
elif isinstance(target_block,str):
eng,mps1=get1(tblocks[0])
eng,mps2=get1(tblocks[1])
if maxN is not None:
mps1.compress(maxN=int(maxN/sqrt(2)))
mps2.compress(maxN=int(maxN/sqrt(2)))
if target_block=='+':
mps=1./sqrt(2.)*(mps1+mps2)
elif target_block=='-':
mps=1./sqrt(2.)*(mps1-mps2)
elif target_block=='+i':
mps=1./sqrt(2.)*(mps1+1j*mps2)
elif target_block=='-i':
mps=1./sqrt(2.)*(mps1-1j*mps2)
else:
raise ValueError('')
if maxN is None:
mps.recanonicalize()
else:
mps.compress(maxN=maxN)
else:
raise Exception('File %s do not exist!'%filename_mps0)
if not os.path.isfile(filename_mps0):
mps.save(filename_mps0)
savetxt(filename_eng0,[eng])
return eng,mps
def entanglement_spec(K1,K2,U,dmu,nsite,target_block,ibond,maxN=200):
'''Get the entanglement spectrum of specific state.'''
eng,mps=load_mps(K1=K1,K2=K2,U=U,which=(dmu,target_block),nsite=nsite,maxN=200)
spaceconfig=SuperSpaceConfig(chorder([2,1,1]))
mps>>ibond-mps.l
spec=mps.S**2
S=-sum(spec*log(spec)/log(2))
print spec
print 'Entropy =',S
pdb.set_trace()
def measure_order(which,delta,t,mu,nsite,polarity,siteindices=None,usempi=True,anchor=None,**kwargs):
'''
Get order parameter from ground states.
Parameters:
:which: str,
* 'RHO', <N(i)>
: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=SuperSpaceConfig(chorder([1,1,1]))
suffix=get_name(t=t,mu=mu,delta=delta,nsite=nsite)
ofile='data/%s_%s_%s.dat'%(which,suffix,polarity)
filename='data/mps_%s.dat'%suffix
eng,ket=load_mps(t=t,mu=mu,delta=delta,nsite=nsite,polarity=polarity,maxN=200,fixtail=True)
ml=[]
ordering=arange(nsite)[::-1]
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
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 get_solving_system(alpha,Vz,Delta,U,nsite,mu=0.,t=1.,evolutor_type='null',periodic=True):
'''
Set the parameters and get the solving system.
Parameters:
:alpha,Vz,Delta,U,mu,t: float, the parameters.
:evolutor_type: str,
* 'null', do not perform any unitary and truncation during expansion of sites.
* 'full', do blockize and unitary but no truncation is allowed.
* 'masked', use kpmask to identify truncation.
Return:
tuple of (model, expander)
'''
assert(evolutor_type in ['null','full','masked'])
model=RashbaModel(alpha=alpha,Vz=Vz,U=U,Delta=Delta,t=t,mu=mu,nsite=nsite,periodic=periodic,occ=True,kspace=False)
spaceconfig=model.hgen.spaceconfig
spaceconfig1=SuperSpaceConfig(chorder([1,spaceconfig.nspin,1,spaceconfig.norbit]))
H_serial=op2collection(op=model.hgen.get_opH())
expander=RGHGen(H=H_serial,spaceconfig=spaceconfig1,evolutor_type=evolutor_type,use_zstring=True)
return model,expander
def solve1(delta,target_block,nsite,override=True,C2parity=None,t=1.,mu=0.):
'''Get and store the eigen vectors and eigen values for ground state.'''
model=SSHModel(delta=delta,t=t,mu=mu,nsite=nsite,manybody=True)
suffix='%s_%s.dat'%(model.get_str(),target_block)
filename_mps='data/mps3_'+suffix
filename_eng='data/eng3_'+suffix
if not override and os.path.isfile(filename_mps):
Ei=loadtxt(filename_eng)[0]
return Ei,MPS.load(filename_mps)
spaceconfig=SuperSpaceConfig(chorder([model.hgen.spaceconfig.nspin,1,model.hgen.spaceconfig.norbit]))
H_serial=op2collection(op=model.hgen.get_opH())
expander=RGHGen(spaceconfig=spaceconfig,H=H_serial,evolutor_type='masked')
t0=time.time()
dmrgegn=DMRGEngine(hgen=expander,tol=1e-7,reflect=False,eigen_solver='JD') #we can not use reflect here, because SOC do not meet reflection condition!
dmrgegn.use_U1_symmetry('PM',target_block=target_block)
Emin,mps=dmrgegn.run_finite(endpoint=(5,'<-',0),maxN=[10,25,50,70,70,70,70],tol=1e-8)
t1=time.time()
print 'The Ground State Energy for %s: %s, Elapse %s.'%(model,Emin,t1-t0)
print 'FIN - CORE:%s'%RANK
mps.save(filename_mps)
savetxt(filename_eng,Emin)
return Emin,mps
def load_mps(t,mu,delta,polarity,nsite,maxN=None,fixtail=True):
'''
Load Specific Matrix product state.
Parameters:
:which: tuple of dmu, polarity.
* polarity, int, '+', '-'.
Return:
eng,mps
'''
suf=get_name(t=t,mu=mu,delta=delta,nsite=nsite)
spaceconfig1=SuperSpaceConfig(chorder([1,1,1,1]))
suffix0='%s_%s'%(suf,polarity)
filename_mps0='data/mps_%s.dat'%suffix0
filename_eng0='data/eng_%s.dat'%suffix0
tblocks=('l','r')
def get1(polarityi):
suffix='%s_%s'%(suf,polarityi)
filename_mps='data/mps_%s.dat'%suffix
filename_eng='data/eng_%s.dat'%suffix
mps=MPS.load(filename_mps)
eng=loadtxt(filename_eng)
if polarityi==(1,0) and fixtail:
mps=fix_tail(mps,spaceconfig=spaceconfig1,parity=-1)
return eng,mps
if os.path.isfile(filename_mps0):
eng,mps=get1(polarity)
if maxN is not None:
mps.compress(maxN=maxN)
return eng,mps
elif isinstance(polarity,str):
eng,mps1=get1(tblocks[0])
eng,mps2=get1(tblocks[1])
if maxN is not None and maxN is not Inf:
mps1.compress(maxN=int(maxN/sqrt(2)))
mps2.compress(maxN=int(maxN/sqrt(2)))
if polarity=='+i':
mps=1./sqrt(2.)*(mps1+1j*mps2)
elif polarity=='-i':
mps=1./sqrt(2.)*(mps1-1j*mps2)
elif polarity=='+':
mps=1./sqrt(2.)*(mps1+mps2)
elif polarity=='-':
mps=1./sqrt(2.)*(mps1-mps2)
elif polarity=='l':
mps=mps1
elif polarity=='r':
mps=mps2
else:
raise ValueError('')
mps.recanonicalize()
if maxN is not None:
mps.compress(maxN=maxN)
else:
raise Exception('File %s do not exist!'%filename_mps0)
if not os.path.isfile(filename_mps0):
mps.save(filename_mps0)
savetxt(filename_eng0,[eng])
return eng,mps
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
def load_mps(K1,K2,U,which,nsite,maxN=None,fixtail=True):
'''
Load Specific Matrix product state.
Parameters:
:which: tuple of dmu, target_block.
* dmu, 'E', 'O', float.
* target_block, (int,int), '+', '-'.
Return:
eng,mps
'''
spaceconfig=SuperSpaceConfig(chorder([2,1,1]))
dmu,target_block=which
tblocks=[(0,0),(0,1)]
dmus=[0.01,-0.01]
suffix0='W1%s_W2%s_U%s_N%s_dmu%s_%s.dat'%(K1,K2,U,nsite,dmu,target_block)
filename_mps0='data/mps_'+suffix0
filename_eng0='data/eng_'+suffix0
def get1(dmui,target_blocki):
suffix='W1%s_W2%s_U%s_N%s_dmu%s_%s.dat'%(K1,K2,U,nsite,dmui,target_blocki)
filename_mps='data/mps_'+suffix
filename_eng='data/eng_'+suffix
mps=MPS.load(filename_mps)
if target_blocki in tblocks and dmui in dmus and fixtail:
mps=fix_tail(mps,spaceconfig,0)
eng=loadtxt(filename_eng)
return eng,mps
if os.path.isfile(filename_mps0):
eng,mps=get1(dmu,target_block)
if maxN is not None:
mps.compress(maxN=maxN)
mps=mps/sqrt(sum(mps.S**2))
return eng,mps
elif isinstance(target_block,str):
eng,mps1=load_mps(K1,K2,U,which=(dmu,tblocks[0]),nsite=nsite,maxN=maxN)
eng,mps2=load_mps(K1,K2,U,which=(dmu,tblocks[1]),nsite=nsite,maxN=maxN)
if target_block=='+':
mps=1./sqrt(2.)*(mps1+mps2)
elif target_block=='-':
mps=1./sqrt(2.)*(mps1-mps2)
elif target_block=='+i':
mps=1./sqrt(2.)*(mps1+1j*mps2)
elif target_block=='-i':
mps=1./sqrt(2.)*(mps1-1j*mps2)
elif target_block=='0':
mps=mps1
elif target_block=='1':
mps=mps2
else:
print target_block
raise ValueError('')
mps.recanonicalize()
elif isinstance(dmu,str):
eng,mps1=load_mps(K1,K2,U,which=(dmus[0],target_block),nsite=nsite,maxN=maxN)
eng,mps2=load_mps(K1,K2,U,which=(dmus[1],target_block),nsite=nsite,maxN=maxN)
if dmu=='E':
mps=1./sqrt(2.)*(mps1+mps2)
elif dmu=='O':
mps=1./sqrt(2.)*(mps1-mps2)
elif dmu=='Ei':
mps=1./sqrt(2.)*(mps1+1j*mps2)
elif dmu=='Oi':
mps=1./sqrt(2.)*(mps1-1j*mps2)
elif dmu=='L':
mps=mps1
elif dmu=='R':
mps=mps2
else:
print dmu
raise ValueError('')
mps.recanonicalize()
if maxN is not None:
mps.compress(maxN=maxN)
mps=mps/sqrt(sum(mps.S**2))
if not os.path.isfile(filename_mps0):
mps.save(filename_mps0)
savetxt(filename_eng0,[eng])
return eng,mps