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TNModels.py
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TNModels.py
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import torch
import numpy as np
from opt_einsum import contract
from scipy.special import comb
from HOTRGZ2 import project_Z2
from collections import namedtuple
Models={}
def _register_model(cls):
Models[cls.__name__]=cls
return cls
class TNModel:
def __init__(self,params):
params={k:(params[k] if k in params else v) for k,v in self.get_default_params().items()}
self.params={k:torch.as_tensor(v).type(torch.get_default_dtype()) for k,v in params.items()}
@_register_model
class Ising2D(TNModel):
@staticmethod
def get_default_params():
return {'beta':np.log(1+2**.5)/2,'h':0}#0.44068679350977147
def __init__(self,params={}):
super().__init__(params)
self.spacial_dim=2
def get_T0(self):
beta,h=self.params['beta'],self.params['h']
a=torch.sqrt(torch.cosh(beta))
b=torch.sqrt(torch.sinh(beta))
W=torch.stack([torch.stack([a,b]),torch.stack([a,-b])])
sz=torch.stack([torch.exp(beta*h),torch.exp(-beta*h)])
return contract('Ai,Aj,Ak,Al,A->ijkl',W,W,W,W,sz)#UDLR
def get_dimR(self,Z2=True):
return ((1,1),)*self.spacial_dim if Z2 else ((2,0),)*self.spacial_dim
def get_observables(self):
return {
'magnetization':(self.get_SZT0(),False),
}
def get_SZT0(self):
beta,h=self.params['beta'],self.params['h']
a=torch.sqrt(torch.cosh(beta))
b=torch.sqrt(torch.sinh(beta))
W=torch.stack([torch.stack([a,b]),torch.stack([a,-b])])
sz=torch.stack([torch.exp(beta*h),-torch.exp(-beta*h)])
return contract('Ai,Aj,Ak,Al,A->ijkl',W,W,W,W,sz)#UDLR
def get_PEPS(self):
beta,h=self.params['beta'],self.params['h']
a=torch.sqrt(torch.cosh(beta))
b=torch.sqrt(torch.sinh(beta))
W=torch.stack([torch.stack([a,b]),torch.stack([a,-b])])
sz=torch.stack([
torch.stack([torch.exp(beta*h),torch.exp(-beta*h)]),
torch.stack([torch.exp(beta*h),-torch.exp(-beta*h)]),
])
return contract('Ai,Aj,Ak,Al,AB->ijklB',W,W,W,W,sz)
def get_PEPS_dimR(self,Z2=True):
return ((1,1),)*(self.spacial_dim+1) if Z2 else ((2,0),)*(self.spacial_dim+1)
def get_ET1(self):
beta,h=self.params['beta'],self.params['h']
a=torch.sqrt(torch.cosh(beta))
b=torch.sqrt(torch.sinh(beta))
W=torch.stack([torch.stack([a,b]),torch.stack([a,-b])])
sz=torch.stack([torch.exp(beta*h),torch.exp(-beta*h)])
nBonds=torch.tensor(self.spacial_dim)#each site correspond to one spin and two bonds
Eij=torch.stack([torch.stack([-nBonds-h,nBonds]),torch.stack([nBonds,-nBonds+h])]) # shouldn't x2
w=self.ws[0]
#'ijkl,jmno,kna,lob->(kn)(lo)im'
return contract('Ai,Aj,Ak,Al,A,Bj,Bm,Bn,Bo,B,AB->knloim',W,W,W,W,sz,W,W,W,W,sz,Eij,w,w)
@_register_model
class Ising3D(TNModel):
@staticmethod
def get_default_params():
return {'beta':0.2216544,'h':0}
def __init__(self,params={}):
super().__init__(params)
self.spacial_dim=3
def get_T0(self):
beta,h=self.params['beta'],self.params['h']
a=torch.sqrt(torch.cosh(beta))
b=torch.sqrt(torch.sinh(beta))
W=torch.stack([torch.stack([a,b]),torch.stack([a,-b])])
sz=torch.stack([torch.exp(beta*h),torch.exp(-beta*h)])
return contract('Ai,Aj,Ak,Al,Am,An,A->ijklmn',W,W,W,W,W,W,sz)
def get_dimR(self,Z2=True):
return ((1,1),)*self.spacial_dim if Z2 else ((2,0),)*self.spacial_dim
def get_observables(self):
return {
'magnetization':(self.get_SZT0(),False),
}
def get_SZT0(self):
beta,h=self.params['beta'],self.params['h']
a=torch.sqrt(torch.cosh(beta))
b=torch.sqrt(torch.sinh(beta))
W=torch.stack([torch.stack([a,b]),torch.stack([a,-b])])
sz=torch.stack([torch.exp(beta*h),-torch.exp(-beta*h)])
return contract('Ai,Aj,Ak,Al,Am,An,A->ijklmn',W,W,W,W,W,W,sz)
def get_ET1(self):
beta,h=self.params['beta'],self.params['h']
a=torch.sqrt(torch.cosh(beta))
b=torch.sqrt(torch.sinh(beta))
W=torch.stack([torch.stack([a,b]),torch.stack([a,-b])])
sz=torch.stack([torch.exp(beta*h),torch.exp(-beta*h)])
nBonds=torch.tensor(self.spacial_dim)#each site correspond to one spin and three bonds
Eij=torch.stack([torch.stack([-nBonds-h,nBonds]),torch.stack([nBonds,-nBonds+h])]) # shouldn't x2
#'ijklmn,jopqrs->(kp)(lq)(mr)(ns)io'
return contract('Ai,Aj,Ak,Al,Am,An,A,Bj,Bo,Bp,Bq,Br,Bs,B,AB->kplqmrnsio',W,W,W,W,W,W,sz,W,W,W,W,W,W,sz,Eij)
def get_CG_no_normalization(j):
n=int(2*j)
if n==0:
return torch.eye(1)
CG=torch.zeros((n+1,)+(2,)*n)
for i in range(2**n):
indices=tuple(map(int,bin(i)[2:].zfill(n)))
m=sum(indices)
CG[(m,)+indices]=1
return CG
def get_CG(j):
n=int(2*j)
if n==0:
return torch.eye(1)
CG=torch.zeros((n+1,)+(2,)*n)
for i in range(2**n):
indices=tuple(map(int,bin(i)[2:].zfill(n)))
m=sum(indices)
CG[(m,)+indices]=1/np.sqrt(comb(n,m))
return CG
def get_Singlet():
return torch.tensor([[0,1.],[-1.,0]])
def get_Lxyz(j):
n=int(2*j+1)
Lz=torch.zeros((n,n))
for i in range(n):
m=i-j
Lz[i,i]=m
Lp=torch.zeros((n,n))
for i in range(n-1):
m=i-j
Lp[i+1,i]=np.sqrt(j*(j+1)-m*(m+1))
Lm=Lp.T
Lx=(Lp+Lm)/2
iLy=(Lp-Lm)/2
return Lx,iLy,Lz
def get_Identity(j):
n=int(2*j+1)
return torch.eye(n)
def get_AKLT_Rep_Isometry():
return torch.tensor([[1.,0.,0.,0.],[0.,0.,0.,1.],[0.,np.sqrt(.5),np.sqrt(.5),0.],[0.,np.sqrt(.5),-np.sqrt(.5),0.]]).type(torch.get_default_dtype())
@_register_model
class AKLT2D(TNModel):
@staticmethod
def get_default_params():
return {'a1':np.sqrt(6/4),'a2':np.sqrt(6/1)}
def __init__(self,params={}):
super().__init__(params)
self.spacial_dim=2
def get_dimR(self,Z2=True):
return ((3,1),)*self.spacial_dim if Z2 else ((4,0),)*self.spacial_dim
def get_observables(self):
return {
'magnetizationX':(self.get_ST0(0),False),
'magnetizationY':(self.get_ST0(1),False),
'magnetizationZ':(self.get_ST0(2),True),
}
def get_T(self,op):
projector=get_CG_no_normalization(2)
singlet=get_Singlet()
ac0,ac1,ac2=torch.tensor(1),self.params['a1'],self.params['a2']
deform=torch.stack([ac2,ac1,ac0,ac1,ac2])
node=contract('aIjKl,iI,kK,a->aijkl',projector,singlet,singlet,deform)
T=contract('aijkl,AIJKL,aA->iIjJkKlL',node,node,op).reshape(4,4,4,4)#UDLR
r=get_AKLT_Rep_Isometry()
T=contract('ijkl,Ii,Jj,Kk,Ll->IJKL',T,r,r.conj(),r,r.conj())
return T
def get_T0(self):
return self.get_T(get_Identity(2))
def get_ST0(self,axis):
return self.get_T(get_Lxyz(2)[axis])
@_register_model
class AKLT2DStrange(TNModel):
@staticmethod
def get_default_params():
return {'a1':np.sqrt(6/4),'a2':np.sqrt(6/1)}
def __init__(self,params={}):
super().__init__(params)
self.spacial_dim=2
def get_dimR(self,Z2=True):
# TODO ?????
return ((2,0),)*self.spacial_dim
def get_observables(self):
return {
'magnetizationX':(self.get_ST0(0),False),
'magnetizationY':(self.get_ST0(1),False),
'magnetizationZ':(self.get_ST0(2),True),
}
def get_T(self,op):
projector=get_CG_no_normalization(2)
singlet=get_Singlet()
ac0,ac1,ac2=torch.tensor(1),self.params['a1'],self.params['a2']
deform=torch.stack([ac2,ac1,ac0,ac1,ac2])
AKLTnode=contract('aIjKl,iI,kK,a->aijkl',projector,singlet,singlet,deform)
productStateNode=torch.tensor([0.,0.,1.,0.,0.])
T=contract('aijkl,A,aA->ijkl',AKLTnode,productStateNode,op).reshape(2,2,2,2)#UDLR
return T
def get_T0(self):
return self.get_T(get_Identity(2))
def get_ST0(self,axis):
return self.get_T(get_Lxyz(2)[axis])
@_register_model
class AKLT3D(TNModel):
@staticmethod
def get_default_params():
return {'a1':np.sqrt(20/15),'a2':np.sqrt(20/6),'a3':np.sqrt(20/1)}
def __init__(self,params={}):
super().__init__(params)
self.spacial_dim=3
def get_dimR(self,Z2=True):
return ((3,1),)*self.spacial_dim if Z2 else ((4,0),)*self.spacial_dim
def get_observables(self):
return {
'magnetizationX':(self.get_ST0(0),False),
'magnetizationY':(self.get_ST0(1),False),
'magnetizationZ':(self.get_ST0(2),True),
}
def get_T(self,op):
projector=get_CG_no_normalization(3)
singlet=get_Singlet()
ac0,ac1,ac2,ac3=torch.tensor(1),self.params['a1'],self.params['a2'],self.params['a3']
deform=torch.stack([ac3,ac2,ac1,ac0,ac1,ac2,ac3])
node=contract('aIjKlMn,iI,kK,mM,a->aijklmn',projector,singlet,singlet,singlet,deform)
T=contract('aijklmn,AIJKLMN,aA->iIjJkKlLmMnN',node,node,op).reshape(4,4,4,4,4,4)#UDLRFB
r=get_AKLT_Rep_Isometry()
T=contract('ijklmn,Ii,Jj,Kk,Ll,Mm,Nn->IJKLMN',T,r,r.conj(),r,r.conj(),r,r.conj())
return T
def get_T0(self):
return self.get_T(get_Identity(3))
def get_ST0(self,axis):
return self.get_T(get_Lxyz(3)[axis])
@_register_model
class AKLTHoneycomb(TNModel):
@staticmethod
def get_default_params():
return {'a32':np.sqrt(3/1)}
def __init__(self,params={}):
super().__init__(params)
self.spacial_dim=2
def get_dimR(self,Z2=True):
return ((3,1),)*self.spacial_dim if Z2 else ((4,0),)*self.spacial_dim
def get_observables(self):
return {
'magnetizationX':(self.get_ST0(0),False),
'magnetizationY':(self.get_ST0(1),False),
'magnetizationZ':(self.get_ST0(2),True),
}
def get_T(self,ops):
projector=get_CG_no_normalization(3/2)
singlet=get_Singlet()
ac12,ac32=torch.tensor(1),self.params['a32']
deform=torch.stack([ac32,ac12,ac12,ac32])
node=contract('aIKx,bjlX,iI,kK,xX,a,b->abijkl',projector,projector,singlet,singlet,singlet,deform,deform)
T=contract('abijkl,ABIJKL,aA,bB->iIjJkKlL',node,node,ops[0],ops[1]).reshape(4,4,4,4)#UDLR
r=get_AKLT_Rep_Isometry()
T=contract('ijkl,Ii,Jj,Kk,Ll->IJKL',T,r,r.conj(),r,r.conj())
return T
def get_T0(self):
Id=get_Identity(3/2)
return self.get_T([Id,Id])
def get_ST0(self,axis,weights):
Id=get_Identity(3/2)
op=get_Lxyz(3/2)[axis]
return weights[0]*self.get_T([op,Id])+weights[1]*self.get_T([Id,op])
@_register_model
class AKLTDiamond(TNModel):
@staticmethod
def get_default_params():
return {'a1':np.sqrt(6/4),'a2':np.sqrt(6/1)}
def __init__(self,params={}):
super().__init__(params)
self.spacial_dim=3
#self.observable_checkerboard=False
def get_dimR(self,Z2=True):
return ((3,1),)*self.spacial_dim if Z2 else ((4,0),)*self.spacial_dim
def get_T(self,ops):
projectorA=get_CG_no_normalization(2)
singlet=get_Singlet()
ac0,ac1,ac2=torch.tensor(1),self.params['a1'],self.params['a2']
deformA=torch.stack([ac2,ac1,ac0,ac1,ac2])
node=contract('axIKM,bXjln,iI,kK,mM,xX,a,b->abijklmn',
*([projectorA]*2+[singlet]*4+[deformA]*2))
T=contract('abijklmn,ABIJKLMN,aA,bB->iIjJkKlLmMnN',
*([node,node]+ops)).reshape(4,4,4,4,4,4)#UDLRFB
r=get_AKLT_Rep_Isometry()
T=contract('ijklmn,Ii,Jj,Kk,Ll,Mm,Nn->IJKLMN',T,r,r.conj(),r,r.conj(),r,r.conj())
return T
def get_T0(self):
IdA=get_Identity(2)
return self.get_T([IdA]*2)
def get_ST0(self,axis,weights=[1,0]):
IdA=get_Identity(2)
opA=get_Lxyz(2)[axis]
rtval=0
for i in range(2):
ops=[IdA]*2
mops=[opA]*2
ops[i]=mops[i]
rtval+=weights[i]*self.get_T(ops)
return rtval
@_register_model
class AKLTSinglyDecoratedDiamond(TNModel):
@staticmethod
def get_default_params():
return {'a1':np.sqrt(6/4),'a2':np.sqrt(6/1),'b1':np.sqrt(2/1)}
def __init__(self,params={}):
super().__init__(params)
self.spacial_dim=3
#self.observable_checkerboard=False
def get_dimR(self,Z2=True):
return ((3,1),)*self.spacial_dim if Z2 else ((4,0),)*self.spacial_dim
def get_T(self,ops):
projectorA=get_CG_no_normalization(2)
projectorB=get_CG_no_normalization(1)
singlet=get_Singlet()
ac0,ac1,ac2=torch.tensor(1),self.params['a1'],self.params['a2']
bc0,bc1=torch.tensor(1),self.params['b1']
deformA=torch.stack([ac2,ac1,ac0,ac1,ac2])
deformB=torch.stack([bc1,bc0,bc1])
node=contract('axUVW,bYjln,cXy,dIv,eKu,fMw,iI,kK,mM,uU,vV,wW,xX,yY,a,b,c,d,e,f->abcdefijklmn',
*([projectorA]*2+[projectorB]*4+[singlet]*8+[deformA]*2+[deformB]*4))
T=contract('abcdefijklmn,ABCDEFIJKLMN,aA,bB,cC,dD,eE,fF->iIjJkKlLmMnN',
*([node,node]+ops)).reshape(4,4,4,4,4,4)#UDLRFB
r=get_AKLT_Rep_Isometry()
T=contract('ijklmn,Ii,Jj,Kk,Ll,Mm,Nn->IJKLMN',T,r,r.conj(),r,r.conj(),r,r.conj())
return T
def get_T0(self):
IdA=get_Identity(2)
IdB=get_Identity(1)
return self.get_T([IdA]*2+[IdB]*4)
def get_ST0(self,axis,weights=[1,0,0,0,0,0]):
IdA=get_Identity(2)
IdB=get_Identity(1)
opA=get_Lxyz(2)[axis]
opB=get_Lxyz(1)[axis]
rtval=0
for i in range(6):
ops=[IdA]*2+[IdB]*4
mops=[opA]*2+[opB]*4
ops[i]=mops[i]
rtval+=weights[i]*self.get_T(ops)
return rtval