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([2,1])
I=OpUnitI(hndim=2)
scfg=SpinSpaceConfig([2,1])
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 __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 __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 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 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()
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 __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)
scfg=SpinSpaceConfig([2,1])
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=MPO(WL)
mpc=self.H.serialize()
mpc.compactify()
self.H_serial=mpc
def __init__(self,J,h,nsite):
self.spaceconfig=SpinSpaceConfig([2,1])
self.J,self.h,self.nsite=J,h,nsite
I=OpUnitI(hndim=2)
Sz=opunit_Sz(spaceconfig=self.spaceconfig)
Sx=opunit_Sx(spaceconfig=self.spaceconfig)
wi=zeros((3,3),dtype='O')
wi[:,0],wi[2,1:]=(I,Sx,-h*Sz),(Sx,I)
WL=[copy.deepcopy(wi) for i in xrange(nsite)]
WL[0]=WL[0][2:]
WL[-1]=WL[-1][:,:1]
self.H=MPO(WL)
mpc=self.H.serialize()
mpc.compactify()
if isinstance(mpc,(OpString,OpUnit)):
mpc=OpCollection([mpc])
self.H_serial=mpc
self.qnumber='R'
def __init__(self,J,Jz,D,nsite):
self.spaceconfig=SpinSpaceConfig([3,1])
self.J,self.Jz,self.D,self.nsite=J,Jz,D,nsite
I=OpUnitI(hndim=self.spaceconfig.hndim)
Sz=opunit_Sz(spaceconfig=self.spaceconfig)
Sp=opunit_Sp(spaceconfig=self.spaceconfig)
Sm=opunit_Sm(spaceconfig=self.spaceconfig)
wi=zeros((5,5),dtype='O')
wi[:,0],wi[4,1:]=(I,Sp,Sm,Sz,D*Sz*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=MPO(WL)
mpc=self.H.serialize()
mpc.compactify()
self.H_serial=mpc
ion()
cla()
mpc.show_advanced()
pdb.set_trace()
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 __init__(self,J,Jz,D,nsite,periodic=False):
self.spaceconfig=SpinSpaceConfig([3,1])
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.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]))
ops=[]
for i in xrange(nsite):
if periodic or i!=nsite-1:
ops.append(J*SL[i%nsite].dot(SL[(i+1)%nsite]))
ops.append(D*SL[i][2]*SL[i][2])
mpc=sum(ops)
mpc.compactify()
self.H_serial=mpc