def test_overlap(dmu_mag=0.01,target_block=(0,0),**kwargs):
'''
Show the fractional charge wave functions.
'''
model,expander=get_solving_system(evolutor_type='masked',periodic=False,**kwargs)
filename='data/frac_W1%s_W2%s_U%s_N%s'%(kwargs.get('K1'),kwargs.get('K2'),kwargs.get('U'),kwargs.get('nsite'))
filename_ket1='data/mps_W1%s_W2%s_U%s_N%s_dmu%s_%s.dat'%(kwargs.get('K1'),kwargs.get('K2'),kwargs.get('U'),kwargs.get('nsite'),dmu_mag,target_block)
filename_ket2='data/mps_W1%s_W2%s_U%s_N%s_dmu%s_%s.dat'%(kwargs.get('K1'),kwargs.get('K2'),kwargs.get('U'),kwargs.get('nsite'),-dmu_mag,target_block)
ket1=MPS.load(filename_ket1)
ket2=MPS.load(filename_ket2)
print ket1.tobra(labels=ket1.labels)*ket2
pdb.set_trace()
def get1(target_blocki,parityi):
suffix='%s_%s%s'%(suf,target_blocki,parityi)
filename_mps='data/mps_%s.dat'%suffix
filename_eng='data/eng_%s.dat'%suffix
mps=MPS.load(filename_mps)
eng=loadtxt(filename_eng)
return eng,mps
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 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
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
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
def mf_wave(method,append=False,dmu=0.01,**kwargs):
'''
Get the majorana wave functions.
'''
even_block=(0,0)
odd_block=(0,1)
blocks=[even_block,odd_block]
filenames=['data/mps_W1%s_W2%s_U%s_N%s_dmu%s_%s.dat'%(kwargs.get('K1'),kwargs.get('K2'),kwargs.get('U'),kwargs.get('nsite'),dmu,blocks[0]),
'data/mps_W1%s_W2%s_U%s_N%s_dmu%s_%s.dat'%(kwargs.get('K1'),kwargs.get('K2'),kwargs.get('U'),kwargs.get('nsite'),dmu,blocks[1])]
mjfile='data/mf_W1%s_W2%s_U%s_N%s_dmu%s.npy'%(kwargs.get('K1'),kwargs.get('K2'),kwargs.get('U'),kwargs.get('nsite'),dmu)
#filenames2=['data/mps_W1%s_W2%s_U%s_N%s_dmu%s_%s.dat'%(kwargs.get('K1'),kwargs.get('K2'),kwargs.get('U'),kwargs.get('nsite'),-dmu,blocks[0]),
#'data/mps_W1%s_W2%s_U%s_N%s_dmu%s_%s.dat'%(kwargs.get('K1'),kwargs.get('K2'),kwargs.get('U'),kwargs.get('nsite'),-dmu,blocks[1])]
if method=='dmrg':
kets=[]
model,expander=get_solving_system(evolutor_type='masked',perturb={'mu':(0,dmu)},periodic=False,**kwargs)
if not append:
for target_block,filename in zip(blocks,filenames):
EG,ket=solve_dmrg(model,expander,target_block=odd_block,nlevel=1)
ket.save(filename)
kets.append(ket)
ket_even,ket_odd=kets
else:
ket_even=MPS.load(filenames[0])
ket_odd=MPS.load(filenames[1])
#ket_even=MPS.load(filenames[0])+MPS.load(filenames2[0])
#ket_odd=MPS.load(filenames[1])+MPS.load(filenames2[1])
#ket_even.compress()
#ket_odd.compress()
elif method=='direct':
model,expander=get_solving_system(evolutor_type='full',periodic=False,**kwargs)
EGs,EVs=solve_direct(model,k=2)
EG_even,ket_even=EGs[1],state2MPS(EVs[:,1],sitedim=expander.spaceconfig.hndim,l=0)
EG_odd,ket_odd=EGs[0],state2MPS(EVs[:,0],sitedim=expander.spaceconfig.hndim,l=0)
pls=smajorana4mps(spaceconfig=expander.spaceconfig,ket_even=ket_even,ket_odd=ket_odd,theta=0)
if RANK==0:
pls=array(pls)
#pls=majorana4vec(spaceconfig=model.hgen.spaceconfig,ket_even=ket_even.state,ket_odd=ket_odd.state)
#pls=dos4mps(spaceconfig=expander.spaceconfig,ket=ket_even)
#pls=dos4vec(spaceconfig=model.hgen.spaceconfig,ket=EVs[:,0])
save(mjfile,pls)
return pls
def solve1(K1,K2,U,dmu,target_block,nsite,override,C2parity):
'''Get and store the eigen vectors and eigen values for ground state.'''
suffix='W1%s_W2%s_U%s_N%s_dmu%s_%s.dat'%(K1,K2,U,nsite,dmu,target_block)
filename_mps='data/mps_'+suffix
filename_eng='data/eng_'+suffix
if not override and os.path.isfile(filename_mps):
Ei=loadtxt(filename_eng)[0]
return Ei,MPS.load(filename_mps)
model,expander=get_solving_system(evolutor_type='masked',periodic=False,K1=K1,K2=K2,U=U,nsite=nsite)
Ei,mpsi=solve_dmrg(model,expander,target_block=target_block,nlevel=1,call_before=lambda egn:chmu(egn,dmu),C2parity=C2parity)
print 'FIN - CORE:%s'%RANK
mpsi.save(filename_mps)
savetxt(filename_eng,[Ei])
return Ei,mpsi
def _get_mps(hgen_l, hgen_r, phi, direction, labels):
'''Combining hgen_l and hgen_r to get the matrix product state.'''
NL, NR = hgen_l.N, hgen_r.N
phi = tensor.Tensor(phi, labels=['al', 'sl+1', 'al+2', 'sl+2']) #l=NL-1
if direction == '->':
A = hgen_l.evolutor.A(NL - 1, dense=True) #get A[sNL](NL-1,NL)
A = tensor.Tensor(A, labels=['sl+1', 'al', 'al+1\''])
phi = tensor.contract([A, phi])
phi = phi.chorder([0, 2, 1]) #now we get phi(al+1,sl+2,al+2)
#decouple phi into S*B, B is column-wise othorgonal
U, S, V = svd(phi.reshape([phi.shape[0], -1]), full_matrices=False)
U = tensor.Tensor(U, labels=['al+1\'', 'al+1'])
A = (A * U) #get A(al,sl+1,al+1)
B = transpose(
V.reshape([S.shape[0], phi.shape[1], phi.shape[2]]),
axes=(1, 2, 0)
) #al+1,sl+2,al+2 -> sl+2,al+2,al+1, stored in column wise othorgonal format
else:
B = hgen_r.evolutor.A(NR - 1, dense=True) #get B[sNR](NL+1,NL+2)
B = tensor.Tensor(B, labels=['sl+2', 'al+2',
'al+1\'']).conj() #!the conjugate?
phi = tensor.contract([phi, B])
#decouple phi into A*S, A is row-wise othorgonal
U, S, V = svd(phi.reshape([phi.shape[0] * phi.shape[1], -1]),
full_matrices=False)
V = tensor.Tensor(V, labels=['al+1', 'al+1\''])
B = (V * B).chorder([1, 2, 0]).conj(
) #al+1,sl+2,al+2 -> sl+2,al+2,al+1, for B is in transposed order by default.
A = transpose(
U.reshape([phi.shape[0], phi.shape[1], S.shape[0]]),
axes=(1, 0, 2)
) #al,sl+1,al+1 -> sl+1,al,al+1, stored in column wise othorgonal format
AL = hgen_l.evolutor.get_AL(dense=True)[:-1] + [A]
BL = [B] + hgen_r.evolutor.get_AL(dense=True)[::-1][1:]
AL = [transpose(ai, axes=(1, 0, 2)) for ai in AL]
BL = [transpose(bi, axes=(1, 0, 2)).conj() for bi in BL] #transpose
mps = MPS(AL=AL,
BL=BL,
S=S,
labels=labels,
forder=range(NL) + range(NL, NL + NR)[::-1])
return mps
def heisenberg_vmps(J,Jz,h,nsite,append=False):
'''
Run vMPS for Heisenberg model.
'''
filename='mps_heisenberg_%s.dat'%(nsite)
model=HeisenbergModel(J=J,Jz=Jz,h=h,nsite=nsite)
if append:
mps=MPS.load(filename)
else:
#run dmrg to get the initial guess.
hgen=RGHGen(spaceconfig=model.spaceconfig,H=model.H_serial,evolutor_type='masked')
dmrgegn=DMRGEngine(hgen=hgen,tol=0)
EG=dmrgegn.run_finite(endpoint=(1,'<-',0),maxN=10,tol=0)[-1]
#hgen=dmrgegn.query('r',nsite-1)
mps=dmrgegn.get_mps(direction='<-') #right normalized initial state
mps.save(filename)
#run vmps
vegn=VMPSEngine(H=model.H,k0=mps)
vegn.run()
def spin1_vmps(J, Jz, h, nsite, append=False):
"""
Run vMPS for Heisenberg model.
"""
filename = "mps_heisenberg_%s.dat" % (nsite)
model = Spin1Model(J=J, Jz=Jz, h=h, nsite=nsite)
if append:
mps = MPS.load(filename)
else:
# run dmrg to get the initial guess.
hgen = RGHGen(spaceconfig=SpinSpaceConfig([2, 1]), H=model.H_serial, evolutor_type="masked")
dmrgegn = DMRGEngine(hgen=hgen, tol=0)
EG = dmrgegn.run_finite(endpoint=(1, "<-", 0), maxN=10, tol=0)[-1]
# hgen=dmrgegn.query('r',nsite-1)
mps = dmrgegn.get_mps(direction="<-") # right normalized initial state
mps.save(filename)
# run vmps
vegn = VMPSEngine(H=model.H, k0=mps)
vegn.run()
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 solve1(J,target_block,nsite,override=True,C2parity=None,h=0.):
'''Get and store the eigen vectors and eigen values for ground state.'''
model=IsingModel(J=J,h=h,nsite=nsite)
suffix='%s_%s.dat'%(model.get_str(),target_block)
filename_mps='data/mps_'+suffix
filename_eng='data/eng_'+suffix
if not override and os.path.isfile(filename_mps):
Ei=loadtxt(filename_eng)[0]
return Ei,MPS.load(filename_mps)
spaceconfig=SpinSpaceConfig([2,1])
H_serial=model.H_serial
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(model.qnumber,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 show_frac_charge(filename=None,bias=False,usevec=False,theta=0,dmu=0.01,target_block=(0,0),append=False,**kwargs):
'''
Show the fractional charge wave functions.
'''
model,expander=get_solving_system(evolutor_type='masked',periodic=False,**kwargs)
if filename is None:
filename='data/frac_W1%s_W2%s_U%s_N%s'%(kwargs.get('K1'),kwargs.get('K2'),kwargs.get('U'),kwargs.get('nsite'))
if not bias:
ket_even=MPS.load(filename+'-even.dat')
ket_odd=MPS.load(filename+'-odd.dat')
#ket_odd=ket_odd-(ket_even.tobra(labels=ket_even.labels)*ket_odd).item()*ket_even
#combine to left-right edge states.
if usevec:
ket_odd,ket_even=ket_odd.state,ket_even.state
#else:
#ket_odd.recanonicalize(tol=1e-8)
ket_left=ket_even#(ket_even+exp(1j*theta)*ket_odd)/sqrt(2.)
ket_right=ket_odd#(ket_even-exp(1j*theta)*ket_odd)/sqrt(2.)
if not usevec:
ket_left.recanonicalize(tol=1e-8) #we must recanonicalize it, for it is not canonical!!!
ket_right.recanonicalize(tol=1e-8)
print ket_left
print ket_right
pls=[dos4mps(spaceconfig=expander.spaceconfig,ket=ket) for ket in [ket_left,ket_right]]
else:
pls=[dos4vec(spaceconfig=model.hgen.spaceconfig,ket=ket) for ket in [ket_left,ket_right]]
else:
suffix='W1%s_W2%s_U%s_N%s_dmu%s_%s.dat'%(kwargs.get('K1'),kwargs.get('K2'),kwargs.get('U'),kwargs.get('nsite'),dmu,target_block)
filename_mps='data/mps_'+suffix
print filename_mps
fname='data/fracdos_'+suffix
#suffix2='W1%s_W2%s_U%s_N%s_dmu%s_%s.dat'%(kwargs.get('K1'),kwargs.get('K2'),kwargs.get('U'),kwargs.get('nsite'),dmu,(0,-1))
#filename_mps2='data/mps_'+suffix2
if append:
pls=loadtxt(fname)[newaxis,:,:]
else:
ket_bias=MPS.load(filename_mps)
#ket_bias=1./sqrt(2)*(MPS.load(filename_mps2)-1j*ket_bias)
#ket_bias.compress()
pls=[dos4mps(spaceconfig=expander.spaceconfig,ket=ket) for ket in [ket_bias]]
savetxt(fname,pls[0].real)
#pls=sum(pls,axis=1)
pls=array(pls)-0.5
nsite=pls.shape[-1]
pls_left=pls[:,:,:nsite/2]
pls_right=pls[:,:,nsite/2:]
print 'occupation in left block -> %s, right block -> %s.'%(sum(pls_left,axis=(-1,-2)),sum(pls_right,axis=(-1,-2)))
if ONSV: return pls
ion()
lw=2
lc='r'
for n in xrange(len(pls)):
pln=pls[n]
ax=subplot(101+n+10*len(pls))
for s in xrange(2):
color='b' if s==0 else 'r'
lc=LineCollection([[(i,0),(i,pln[s,i].real.item())] for i in xrange(model.nsite)])
lc.set_linewidth(lw)
lc.set_color(color)
lc.set_linestyle('--' if s==1 else '-')
ax.add_collection(lc)
ax.autoscale()
ax.margins(0.1)
xlabel('N')
ylabel(r'$\rho-\bar{\rho}$')
pdb.set_trace()