def test_model2():
J, Jz = -3., 2
N1, N2 = 2, 3
scfg = SpinSpaceConfig([N1 * N2, 2])
config = array([1, 1, 0, 1, 1, 0])
#config=array([1,1,0,0,1,0,1,1,0])
#construct true H
for periodic in [True, False]:
h = HeisenbergH2D(N1, N2, J=J, Jz=Jz, periodic=periodic)
H = FakeVMC(h).get_H()
print 'Testing rmatmul of Hamiltonian(%s)' % ('PBC'
if periodic else 'OBC')
wl, flips = h._rmatmul(1 - 2 * config)
configs = []
for flip in flips:
nc = copy(1 - 2 * config)
nc[asarray(flip)] *= -1
configs.append(nc)
ss = SparseState(wl, configs)
vec = ss.tovec(scfg)
v0 = zeros(scfg.hndim)
v0[scfg.config2ind(config)] = 1
v_true = v0.dot(H)
assert_allclose(vec, v_true)
def get_Ising(self, h, J=1.):
'''Get the hamiltonian.'''
#the hamiltonian for Ising model
Sz = opunit_Sz(spaceconfig=SpinSpaceConfig([1, 2]))
Sx = opunit_Sx(spaceconfig=SpinSpaceConfig([1, 2]))
H = -J * Sz.as_site(0) * Sz.as_site(1) + h * Sx.as_site(0)
return H
def __init__(self, J, Jz, h, nsite, J2=0, J2z=None):
self.spaceconfig = SpinSpaceConfig([1, 2])
I = OpUnitI(hndim=2)
scfg = SpinSpaceConfig([1, 2])
Sx = opunit_Sx(spaceconfig=scfg)
Sy = opunit_Sy(spaceconfig=scfg)
Sz = opunit_Sz(spaceconfig=scfg)
#with second nearest hopping terms.
if J2 == 0:
self.H_serial2 = None
return
elif J2z == None:
J2z = J2
SL = []
for i in xrange(nsite):
Sxi, Syi, Szi = copy.copy(Sx), copy.copy(Sy), copy.copy(Sz)
Sxi.siteindex = i
Syi.siteindex = i
Szi.siteindex = i
SL.append(array([Sxi, Syi, sqrt(J2z / J2) * Szi]))
ops = []
for i in xrange(nsite - 1):
ops.append(J * SL[i].dot(SL[i + 1]))
if i < nsite - 2 and J2z != 0:
ops.append(J2 * SL[i].dot(SL[i + 2]))
mpc = sum(ops)
self.H_serial = mpc
def test_tovec(self):
print 'Test @RBM.tovec'
scfg = SpinSpaceConfig([2, 2])
configs = scfg.ind2config(arange(scfg.hndim))
vec = self.rbm.get_weight(1 - 2 * configs)
assert_allclose(vec, self.vec, atol=1e-8)
print 'Test Translational invariant @RBM.tovec.'
vect = self.rbm_t.tovec(scfg)
assert_allclose(vect, self.vec2, atol=1e-8)
def get_Haldane(self, D, J=1.):
'''Get the hamiltonian.'''
#the hamiltonian for Ising model
Sx = opunit_Sx(spaceconfig=SpinSpaceConfig([1, 3]))
Sy = opunit_Sy(spaceconfig=SpinSpaceConfig([1, 3]))
Sz = opunit_Sz(spaceconfig=SpinSpaceConfig([1, 3]))
H = J * (
Sz.as_site(0) * Sz.as_site(1) + Sx.as_site(0) * Sx.as_site(1) +
Sy.as_site(0) * Sy.as_site(1)) + D * Sz.as_site(0) * Sz.as_site(0)
return H
def __init__(self, J, Jz, h, nsite):
self.spaceconfig = SpinSpaceConfig([1, 2])
I = OpUnitI(hndim=2)
scfg = SpinSpaceConfig([1, 2])
Sz = opunit_Sz(spaceconfig=scfg)
Sp = opunit_Sp(spaceconfig=scfg)
Sm = opunit_Sm(spaceconfig=scfg)
wi = zeros((5, 5), dtype='O')
wi[:, 0], wi[4, 1:] = (I, Sp, Sm, Sz,
-h * Sz), (J / 2. * Sm, J / 2. * Sp, Jz * Sz, I)
WL = [copy.deepcopy(wi) for i in xrange(nsite)]
WL[0] = WL[0][4:]
WL[-1] = WL[-1][:, :1]
self.H_serial = WL2OPC(WL)
def __init__(self,J,Jz,h,nsite):
self.spaceconfig=SpinSpaceConfig([2,1])
I=OpUnitI(hndim=2)
Sx=opunit_Sx(spaceconfig=self.spaceconfig)
Sy=opunit_Sy(spaceconfig=self.spaceconfig)
Sz=opunit_Sz(spaceconfig=self.spaceconfig)
SL,SZ=[],[]
for i in xrange(nsite):
Sxi,Syi,Szi=copy.copy(Sx),copy.copy(Sy),copy.copy(Sz)
Sxi.siteindex=i
Syi.siteindex=i
Szi.siteindex=i
SL.append(array([Sxi,Syi,sqrt(Jz/J)*Szi]))
SZ.append(Szi)
ops=[]
for i in xrange(nsite):
if i!=nsite-1:
ops.append(J*SL[i].dot(SL[i+1]))
ops.append(h[i]*SZ[i])
mpc=sum(ops)
self.H_serial=mpc
mpo=mpc.toMPO(method='direct')
mpo.compress()
self.H=mpo
def __init__(self,J1,J2,K,Jp,nsite,impurity_site=None):
self.spaceconfig=SpinSpaceConfig([2,1])
if impurity_site is None:
impurity_site=nsite/2 #nsite/2 and nsite/2-1
self.impurity_site=impurity_site
self.J1,self.J2,self.K,self.Jp=J1,J2,K,Jp
I=OpUnitI(hndim=self.spaceconfig.hndim)
Sx=opunit_Sx(spaceconfig=self.spaceconfig)
Sy=opunit_Sy(spaceconfig=self.spaceconfig)
Sz=opunit_Sz(spaceconfig=self.spaceconfig)
SL=[]
for i in xrange(nsite):
Sxi,Syi,Szi=copy.deepcopy(Sx),copy.deepcopy(Sy),copy.deepcopy(Sz)
Sxi.siteindex=i
Syi.siteindex=i
Szi.siteindex=i
SL.append(array([Sxi,Syi,Szi]))
ops=[]
for i in xrange(nsite-1):
factor1=J1
if i==impurity_site or i==impurity_site-2:
factor1*=Jp
elif i==impurity_site-1:
factor1*=K
ops.append(factor1*SL[i].dot(SL[i+1]))
if i<nsite-2 and i!=impurity_site-1 and i!=impurity_site-2:
factor2=J2
if i==impurity_site-3 or i==impurity_site:
factor2*=Jp
ops.append(factor2*SL[i].dot(SL[i+2]))
mpc=sum(ops)
self.H_serial=mpc
def solve1(hl,nsite,config,Jz=1.,J=1.,save=True):
'''
Run vMPS for Heisenberg model.
'''
#generate the model
print 'SOLVING %s'%config
model=HeisenbergModel(J=J,Jz=Jz,h=hl,nsite=nsite)
#run vmps
#generate a random mps as initial vector
spaceconfig=SpinSpaceConfig([2,1])
bmg=SimpleBMG(spaceconfig=spaceconfig,qstring='M')
H=model.H.use_bm(bmg)
k0=product_state(config=config,hndim=2,bmg=bmg)
#setting up the engine
vegn=VMPSEngine(H=H,k0=k0.toket(),eigen_solver='JD')
eng,ket=vegn.run(endpoint=(6,'->',0),maxN=20,which='SL',nsite_update=2)
#save to file
if save:
ind=sum(2**arange(nsite-1,-1,-1)*asarray(config))
filename='data/ket%s_h%.2fN%s.dat'%(ind,mean(hl),nsite)
quicksave(filename,(eng,ket))
overlap=abs((k0.tobra()*ket).item())
print 'OVERLAP %s'%overlap
return eng,ket,overlap
def measure_op(which,ket,usempi=False,ofile=None):
'''
Get order parameter from ground states.
Parameters:
:which: str,
* 'Sz', <Sz>
:siteindices: list, the measure points.
Return:
array, the value of order parameter.
'''
nsite=ket.nsite
spaceconfig=SpinSpaceConfig([2,1])
ml=[]
def measure1(siteindex):
if which=='Sz':
op=opunit_S(which='z',spaceconfig=spaceconfig,siteindex=siteindex)
else:
raise NotImplementedError()
m=get_expect(op,ket=ket).item() #,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 arange(nsite):
ml.append(measure1(siteindex))
ml=array(ml)
if RANK==0 and ofile is not None:
savetxt(ofile,ml.real)
return ml
def __init__(self):
nsite = 6 #number of sites
hndim = 2
l = 0
vec = random.random(hndim**nsite) #a random state in form of 1D array.
vec2 = random.random(
hndim**nsite) #a random state in form of 1D array.
mps = state2MPS(vec, sitedim=hndim, l=l,
method='svd') #parse the state into a <MPS> instance.
mps2 = state2MPS(vec2, sitedim=hndim, l=l,
method='svd') #parse the state into a <MPS> instance.
j1, j2 = 0.5, 0.2
scfg = SpinSpaceConfig([1, 2])
I = OpUnitI(hndim=hndim)
Sz = opunit_Sz(spaceconfig=scfg)
Sp = opunit_Sp(spaceconfig=scfg)
Sm = opunit_Sm(spaceconfig=scfg)
wi = zeros((4, 4), dtype='O')
wi[0, 0], wi[1, 0], wi[2, 1], wi[3,
1:] = I, Sz, I, (j1 * Sz, j2 * Sz, I)
WL = [deepcopy(wi) for i in xrange(nsite)]
WL[0] = WL[0][3:4]
WL[-1] = WL[-1][:, :1]
mpo = WL2MPO(WL)
self.mps, self.mps2 = mps, mps2
self.mpo = mpo
self.vec, self.vec2 = vec, vec2
self.spaceconfig = scfg
def test_Haldane(self):
'''Solve model hamiltonians'''
egn = ITEBDEngine(tol=1e-10)
npart = 2
Dlist = arange(0, -0.6, -0.05)
spaceconfig = SpinSpaceConfig([1, 3])
#the initial state
GL = []
for i in xrange(npart):
Gi = (0.5 - random.rand(1, 3, 1)) / 100.
Gi[0, 2 * (i % 2), 0] = 1
GL.append(Gi)
LL = []
for i in xrange(npart):
LL.append(ones([1]))
ivmps0 = IVMPS(GL=GL, LL=LL)
mpsl, HL, EEL = [], [], []
for D in Dlist:
H = self.get_Haldane(J=1., D=D)
mps = egn.run(hs=H,
ivmps=copy.copy(ivmps0),
spaceconfig=spaceconfig,
maxN=20)
mpsl.append(mps)
HL.append(H)
print D, mps.LL[0][:4]
SL, EL, ML1, ML2 = [], [], [], []
for mps, H in zip(mpsl, HL):
mps2 = mps.roll(1)
SL.append(mean(entanglement_entropy(mps)))
print get_expect_ivmps(op=H, ket=mps), get_expect_ivmps(op=H,
ket=mps2)
EL.append(
mean([
get_expect_ivmps(op=H, ket=mps),
get_expect_ivmps(op=H, ket=mps2)
]))
ML1.append(
get_expect_ivmps(
op=2 *
opunit_S(which='z', siteindex=0, spaceconfig=spaceconfig),
ket=mps))
ML2.append(
get_expect_ivmps(
op=2 *
opunit_S(which='z', siteindex=0, spaceconfig=spaceconfig),
ket=mps2))
ion()
subplot(311)
plot(Dlist, SL)
subplot(312)
plot(Dlist, array(EL))
subplot(313)
plot(Dlist, array(ML1))
plot(Dlist, array(ML2))
pdb.set_trace()
def test_lanczos(self):
'''test for directly construct and solve the ground state energy.'''
model = self.get_model(10, 1)
hgen1 = ExpandGenerator(spaceconfig=SpinSpaceConfig([1, 2]),
H=model.H_serial,
evolutor_type='null')
hgen2 = ExpandGenerator(spaceconfig=SpinSpaceConfig([1, 2]),
H=model.H_serial,
evolutor_type='normal')
dmrgegn = DMRGEngine(hgen=hgen1, tol=0, iprint=10)
H = get_H(hgen=hgen1)
H2, bm2 = get_H_bm(hgen=hgen2, bstr='M')
Emin = eigsh(H, k=1)[0]
Emin2 = eigsh(bm2.extract_block(H2, (zeros(1), zeros(1)),
uselabel=True),
k=1)[0]
print 'The Ground State Energy is %s, tolerence %s.' % (Emin,
Emin - Emin2)
assert_almost_equal(Emin, Emin2)
def test_dmrg_finite(self):
'''
Run iDMFT for heisenberg model.
'''
nsite = 10
model = self.get_model(nsite, 1)
hgen1 = ExpandGenerator(spaceconfig=SpinSpaceConfig([1, 2]),
H=model.H_serial,
evolutor_type='null')
hgen2 = ExpandGenerator(spaceconfig=SpinSpaceConfig([1, 2]),
H=model.H_serial,
evolutor_type='masked')
H = get_H(hgen1)
EG1 = eigsh(H, k=1, which='SA')[0]
dmrgegn = DMRGEngine(hgen=hgen2, tol=0, reflect=True)
dmrgegn.use_U1_symmetry('M', target_block=zeros(1))
EG2 = dmrgegn.run_finite(endpoint=(5, '<-', 0),
maxN=[10, 20, 40, 40, 40],
tol=0)[0]
assert_almost_equal(EG1, EG2, decimal=4)
def test_dmrg_infinite(self):
'''test for infinite dmrg.'''
maxiter = 100
model = self.get_model(maxiter + 2, 1)
hgen = ExpandGenerator(spaceconfig=SpinSpaceConfig([1, 2]),
H=model.H_serial,
evolutor_type='masked')
dmrgegn = DMRGEngine(hgen=hgen, tol=0, reflect=True, iprint=10)
dmrgegn.use_U1_symmetry('M', target_block=zeros(1))
EG = dmrgegn.run_infinite(maxiter=maxiter, maxN=20, tol=0)[0]
assert_almost_equal(EG, 0.25 - log(2), decimal=2)
def __init__(self):
J = 1.
nsite = 4
self.scfg = SpinSpaceConfig([nsite, 2])
#construct true H
I2, I4 = eye(2), eye(4)
h2 = J / 4. * (kron(sx, sx) + kron(sz, sz) + kron(sy, sy))
#construct operator H act on config
self.h1 = TFI(nsite=4)
self.h2 = HeisenbergH(nsite=4)
self.toy1, self.toy2 = FakeVMC(self.h1), FakeVMC(self.h2)
self.H1, self.H2 = self.toy1.get_H(), self.toy2.get_H()
self.pW = PartialW()
#generate a random rbm and the corresponding vector v
self.rbm = random_rbm(nin=nsite, nhid=nsite)
self.v = self.rbm.tovec(self.scfg)
self.rbm_g = random_rbm(nin=nsite, nhid=nsite, group=TIGroup(4))
self.v_g = self.rbm_g.tovec(self.scfg)
def solve_ed(hl,nsite,Jz=1.,J=1.):
'''
Run ED for Heisenberg model.
'''
#generate the model
model=HeisenbergModel(J=J,Jz=Jz,h=hl,nsite=nsite)
#run vmps
#generate a random mps as initial vector
spaceconfig=SpinSpaceConfig([2,1])
bmg=SimpleBMG(spaceconfig=spaceconfig,qstring='M')
H=model.H_serial.H().real
E,U=eigh(H)
return E,U
def __init__(self, g, h, nsite, J=1):
self.spaceconfig = SpinSpaceConfig([2, 1])
self.J, self.g, self.h, self.nsite = J, g, h, nsite
scfg = self.spaceconfig
I = OpUnitI(hndim=scfg.hndim)
Sx = opunit_Sx(spaceconfig=scfg) * 2
Sz = opunit_Sz(spaceconfig=scfg) * 2
opc = 0
for i in range(nsite):
hi = h - J if i == 0 or i == nsite - 1 else h
opc = opc + (hi * Sz.as_site(i) + g * Sx.as_site(i))
if i != nsite - 1:
opc = opc + J * Sz.as_site(i) * Sz.as_site(i + 1)
self.opc = opc
def get_H(self):
'''Get the target Hamiltonian Matrix.'''
nsite,periodic=self.h.nsite,self.h.periodic
scfg=SpinSpaceConfig([nsite,2])
if isinstance(self.h,TFI):
Jz,h=self.h.Jz,self.h.h
h2=Jz/4.*kron(sz,sz)
H=0
for i in xrange(nsite):
if i!=nsite-1:
H=H+kron(kron(eye(2**i),h2),eye(2**(nsite-2-i)))
elif periodic: #periodic boundary
H=H+Jz/4.*kron(kron(sz,eye(2**(nsite-2))),sz)
H=H+h/2.*kron(kron(eye(2**i),sx),eye(2**(nsite-i-1)))
return H
elif isinstance(self.h,HeisenbergH):
J,Jz=self.h.J,self.h.Jz
h2=J/4.*(kron(sx,sx)+kron(sy,sy))+Jz/4.*kron(sz,sz)
H=0
for i in xrange(nsite-1):
H=H+kron(kron(eye(2**i),h2),eye(2**(nsite-2-i)))
#impose periodic boundary
if periodic:
H=H+J/4.*(kron(kron(sx,eye(2**(nsite-2))),sx)+kron(kron(sy,eye(2**(nsite-2))),sy))+Jz/4.*(kron(kron(sz,eye(2**(nsite-2))),sz))
return H
elif isinstance(self.h,HeisenbergH2D):
from tba.lattice import Square_Lattice
J,Jz=self.h.J,self.h.Jz
lattice=Square_Lattice(N=(self.h.N1,self.h.N2))
if self.h.periodic: lattice.set_periodic([True,True])
lattice.initbonds(5)
b1s=lattice.getbonds(1)
b1s=[b for b in b1s if b.atom1<b.atom2]
H=0
if False:
sx0=csr_matrix(sx)
sy0=csr_matrix(sy)
sz0=csr_matrix(sz)
sx0,sy0,sz0=sx,sy,sz
for b in b1s:
for ss,Ji in zip([sx0,sy0,sz0],[J,J,Jz]):
H=H+Ji/4.*kron(kron(kron(kron(eye(2**b.atom1),ss),eye(2**(b.atom2-b.atom1-1))),ss),eye(2**(lattice.nsite-b.atom2-1)))
#H=H+Ji/4.*kron(kron(kron(kron(eye(2**(lattice.nsite-b.atom2-1)),ss),eye(2**(b.atom2-b.atom1-1))),ss),eye(2**(b.atom1)))
#e,v=eigsh(H,k=1,which='SA')
#print e/lattice.nsite
return H
def test_ising(self):
'''Solve model hamiltonians'''
npart = 2
hlist = arange(0., 2, 0.1)
spaceconfig = SpinSpaceConfig([1, 2])
#the initial state
GL = []
for i in xrange(npart):
Gi = Tensor(0.5 - 0.01 * ones([spaceconfig.hndim, 1, 1]),
labels=['s%s' % i, 'a%s' % i,
'b%s' % i])
Gi[0, 0, 0] = 1
GL.append(Gi)
GL[1].labels[1:] = GL[1].labels[1:][::-1]
#print GL[0].labels
#print GL[1].labels
LL = [Link(['b0', 'b1'], ones([1])), Link(['a1', 'a0'], ones([1]))]
mpsl, EEL, HL = [], [], []
for h in hlist:
hb = self.get_Ising(h=2 * h, J=4.)
egn = ITEBDEngine(hs=[hb] * 2, tol=1e-10)
ivmps0 = IVMPS(tensors=GL, LL=LL)
mps = egn.run(ivmps=ivmps0, maxN=5)
mpsl.append(mps)
HL.append(hb)
################# Get the exact energies ######################
f = lambda k, h: -2 * sqrt(1 + h**2 - 2 * h * cos(k)) / pi / 2.
E0_exact = integrate.quad(f, 0, pi, args=(h, ))[0]
EEL.append(E0_exact)
SL, EL, ML = [], [], []
for mps, H in zip(mpsl, HL):
SL.append(entanglement_entropy(mps))
#print get_expect_ivmps(op=H,ket=mps),get_expect_ivmps(op=H,ket=mps2)
#EL.append(mean([get_expect_ivmps(op=H,ket=mps),get_expect_ivmps(op=H,ket=mps2)]))
#ML.append(get_expect_ivmps(op=2*opunit_S(which='z',siteindex=0,spaceconfig=spaceconfig),ket=mps))
ion()
subplot(311)
#plot(hlist,abs(array(ML)))
subplot(312)
plot(hlist, SL)
subplot(313)
#plot(hlist,abs(array(EL)-EEL))
pdb.set_trace()
def __init__(self,J,Jz,h,nsite,nspin=3):
self.spaceconfig=SpinSpaceConfig([1,nspin])
scfg=self.spaceconfig
I=OpUnitI(hndim=scfg.hndim)
Sx=opunit_Sx(spaceconfig=scfg)
Sy=opunit_Sy(spaceconfig=scfg)
Sz=opunit_Sz(spaceconfig=scfg)
Sp=opunit_Sp(spaceconfig=scfg)
Sm=opunit_Sm(spaceconfig=scfg)
wi=zeros((5,5),dtype='O')
#wi[:,0],wi[4,1:]=(I,Sp,Sm,Sz,-h*Sz),(J/2.*Sm,J/2.*Sp,Jz*Sz,I)
wi[:,0],wi[4,1:]=(I,Sx,Sy,Sz,-h*Sz),(J*Sx,J*Sy,Jz*Sz,I)
WL=[copy.deepcopy(wi) for i in xrange(nsite)]
WL[0]=WL[0][4:]
WL[-1]=WL[-1][:,:1]
self.H=WL2MPO(WL)
mpc=WL2OPC(WL)
self.H_serial=mpc
def __init__(self,nsite,periodic,model='AFH'):
self.nsite,self.periodic=nsite,periodic
self.model=model
if model=='AFH':
self.h=HeisenbergH(nsite=nsite,J=-1.,Jz=1.,periodic=periodic)
elif model=='AFH2D':
N=int(sqrt(nsite))
self.h=HeisenbergH2D(N,N,J=-1.,Jz=1.,periodic=periodic)
elif model=='TFI':
self.h=TFI(nsite=nsite,Jz=-4.,h=-1.,periodic=periodic)
else:
raise ValueError()
self.scfg=SpinSpaceConfig([nsite,2])
#vmc config
c0=[-1,1]*(nsite/2); random.shuffle(c0)
cgen=RBMConfigGenerator(initial_config=c0,nflip=2 if model[:3]=='AFH' else 1)#repeat([-1,1],(nsite/2)))
self.vmc=VMC(cgen,nbath=500*nsite,nsample=5000*nsite,nmeasure=nsite,sampling_method='metropolis')
def __init__(self,nsite,periodic,model='AFH'):
self.nsite,self.periodic=nsite,periodic
self.model=model
if model=='AFH':
self.h=HeisenbergH(nsite=nsite,J=1.,Jz=1.,periodic=periodic)
elif model=='TFI':
self.h=TFI(nsite=nsite,Jz=-4.,h=-1.,periodic=periodic)
elif model=='AFH2D':
N1=N2=int(sqrt(nsite))
self.h=HeisenbergH2D(N1,N2,J=1.,Jz=1.,periodic=periodic)
else:
raise ValueError()
self.scfg=SpinSpaceConfig([nsite,2])
self.fv=FakeVMC(self.h)
#vmc config
cgen=RBMConfigGenerator(initial_config=[-1,1]*(nsite/2)+[1]*(nsite%2),nflip=2 if model=='AFH' else 1)
self.vmc=VMC(cgen,nbath=500*nsite,nsample=5000*nsite,nmeasure=nsite,sampling_method='metropolis')
def __init__(self,J,Jz,h,N1,N2,nspin=3):
self.spaceconfig=SpinSpaceConfig([1,nspin])
scfg=self.spaceconfig
I=OpUnitI(hndim=scfg.hndim)
Sx=opunit_Sx(spaceconfig=scfg)
Sy=opunit_Sy(spaceconfig=scfg)
Sz=opunit_Sz(spaceconfig=scfg)
Sp=opunit_Sp(spaceconfig=scfg)
Sm=opunit_Sm(spaceconfig=scfg)
opc=OpCollection()
lt=Square_Lattice((N1,N2))
lt.set_periodic([True,True])
lt.initbonds(5)
bonds=[b for b in lt.getbonds(1) if b.atom2>b.atom1]
for b in bonds:
atom1,atom2=b.atom1,b.atom2
opc+=J*(Sx.as_site(atom1)*Sx.as_site(atom2)+Sy.as_site(atom1)*Sy.as_site(atom2))
opc+=Jz*(Sz.as_site(atom1)*Sz.as_site(atom2))
for i in xrange(lt.nsite):
opc=opc+h*Sz.as_site(i)
mpo=opc.toMPO(nsite=lt.nsite,method='direct')
self.H=mpo
4. Get <H> under kA. ''' from numpy import sqrt, Inf from mpslib import random_bmps from opstring import OpCollection from mpo import OPC2MPO from mpolib import opunit_S from tba.hgen import SpinSpaceConfig from contraction import Contractor from pymps.blockmarker import SimpleBMG ########### Generate a random State ###### # the single site Hilbert space(Spin) config, 2 spin, 1 orbital. spaceconfig = SpinSpaceConfig([1, 2]) # the generator of block marker, # using magnetization `M = nup-ndn` as good quantum number. bmg = SimpleBMG(spaceconfig=spaceconfig, qstring='M') # generate a random mps of 10 site and chi = 20, # which is under the supervise of above <BlockMarkerGenerator>. kA = random_bmps(bmg=bmg, nsite=10, maxN=20) # nomalize it kA = kA / sqrt(kA.tobra() * kA).item() ########### Get the Good quantum Number ###### # number of steps, tolerence, maximum bond dimension. kA << kA.nsite, 1e-8, Inf # get the block marker, # the (quantum number)flow direction is left->right, # so the right most bond contains the final good quantum number.
def test_compress():
scfg=SpinSpaceConfig([4,2])
ss=SparseState([0.1j,0.2,0.3],[[1,1,0,1],[1,0,1,0],[1,1,0,1]])
assert_allclose(ss.ws,[0.2,0.3+0.1j])
assert_allclose(ss.configs,[[1,0,1,0],[1,1,0,1]])
def __init__(self):
a = [0.1j, 0.2]
b = [0.1j, 0.2, 0.3]
b2 = [-0.1j, 0.2, -0.3]
W = [[0.1, -0.1, 0.1], [-0.1j, 0.1, 0.1j]]
self.rbm = RBM(a, b, W)
#translational invariant group
tig = TIGroup(ngs=[2])
self.rbm_t = RBM(a, b2, W, group=tig)
#get vec in the brute force way.
self.vec = []
scfg1 = SpinSpaceConfig([2, 2])
scfg2 = SpinSpaceConfig([3, 2])
for i in xrange(scfg1.hndim):
config1 = scfg1.ind2config(i)
s = 1 - config1 * 2
vi = 0j
for j in xrange(scfg2.hndim):
config2 = scfg2.ind2config(j)
h = 1 - 2 * config2
vi += exp((s * a).sum() + (h * b).sum() + s.dot(W).dot(h))
self.vec.append(vi)
self.vec = array(self.vec)
#the second vec
self.vec2 = []
scfg1 = SpinSpaceConfig([2, 2])
scfg2 = SpinSpaceConfig([6, 2])
for i in xrange(scfg1.hndim):
config1 = scfg1.ind2config(i)
s = 1 - config1 * 2
vi = 0j
for j in xrange(scfg2.hndim):
config2 = scfg2.ind2config(j)
h = 1 - 2 * config2
vi += exp((s * a).sum() + (s[::-1] * a).sum() +
(h * concatenate([b2, b2])).sum() +
s.dot(W).dot(h[:3]) + s[::-1].dot(W).dot(h[3:]))
self.vec2.append(vi)
self.vec2 = array(self.vec2)
class TestLinop(object):
def __init__(self):
J = 1.
nsite = 4
self.scfg = SpinSpaceConfig([nsite, 2])
#construct true H
I2, I4 = eye(2), eye(4)
h2 = J / 4. * (kron(sx, sx) + kron(sz, sz) + kron(sy, sy))
#construct operator H act on config
self.h1 = TFI(nsite=4)
self.h2 = HeisenbergH(nsite=4)
self.toy1, self.toy2 = FakeVMC(self.h1), FakeVMC(self.h2)
self.H1, self.H2 = self.toy1.get_H(), self.toy2.get_H()
self.pW = PartialW()
#generate a random rbm and the corresponding vector v
self.rbm = random_rbm(nin=nsite, nhid=nsite)
self.v = self.rbm.tovec(self.scfg)
self.rbm_g = random_rbm(nin=nsite, nhid=nsite, group=TIGroup(4))
self.v_g = self.rbm_g.tovec(self.scfg)
def test_sandwichh(self):
for h, H in [(self.h1, self.H1), (self.h2, self.H2)]:
print 'Testing sandwich %s.' % h.__class__
config = random.randint(0, 2, 4)
ket = zeros(self.scfg.hndim)
ket[self.scfg.config2ind(config)] = 1
H, v, v_g = self.H2, self.v, self.v_g
print 'Testing the non-group version'
O_true = ket.conj().dot(H).dot(v) / sum(ket.conj() * v)
cg = RBMConfigGenerator(nflip=2, initial_config=1 - 2 * config)
cg.set_state(self.rbm)
O_s = c_sandwich(self.h2, cg)
assert_almost_equal(O_s, O_true, decimal=8)
print 'Testing the group version'
cg.set_state(self.rbm_g)
O_sg = c_sandwich(self.h2, cg)
O_trueg = ket.conj().dot(H).dot(v_g) / sum(ket.conj() * v_g)
assert_almost_equal(O_sg, O_trueg, decimal=8)
def test_sandwichpw(self):
print 'Testing sandwich PartialW.'
config = random.randint(0, 2, 4)
ket = zeros(self.scfg.hndim)
ket[self.scfg.config2ind(config)] = 1
H, v, v_g = self.H, self.v, self.v_g
cg = RBMConfigGenerator(nflip=2, initial_config=1 - 2 * config)
cg.set_state(self.rbm)
O_true = ket.conj().dot(Wmat).dot(v) / sum(ket.conj() * v)
O_s = c_sandwich(self.pW, cg)
O_trueg = ket.conj().dot(Wmat).dot(v_g) / sum(ket.conj() * v_g)
cg.set_state(self.rbm_g)
O_sg = c_sandwich(self.pW, cg)
assert_almost_equal(O_s, O_true, decimal=8)
assert_almost_equal(O_sg, O_trueg, decimal=8)
def __init__(self,h):
self.h=h
self.scfg=scfg=SpinSpaceConfig([h.nsite,2])
def test_randomrbm():
nsite = 6
scfg = SpinSpaceConfig([nsite, 2])
rbm = random_rbm(nin=nsite, nhid=2)
print rbm.tovec(scfg)