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GILT_jax.py
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GILT_jax.py
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# Scaling dimensions from linearized tensor renormalization group transformations
# https://arxiv.org/pdf/2102.08136.pdf
# Renormalization of tensor networks using graph independent local truncations
# https://arxiv.org/pdf/1709.07460.pdf
# https://github.com/Gilt-TNR/Gilt-TNR
# https://github.com/Gilt-TNR/Gilt-TNR/blob/master/GiltTNR3D.py
from tqdm.auto import tqdm
import jax.numpy as np
from opt_einsum import contract
import itertools as itt
from dataclasses import dataclass
from jax.numpy import sqrt
from jax.numpy.linalg import svd as _svd
def svd(A):
return _svd(A,full_matrices=False)
# def _toN(t):
# return t.detach().cpu().tolist() if isinstance(t,torch.Tensor) else t
# Basic idea:
# Given a subgraph and a specific leg in that subgraph, the environment tensor E = break the leg, the mapping from the two ends of the broken leg to the external legs of the subgraph
# We can insert arbitrary projector R to that leg if that's in the kernel of E
# We chose R_ab=t_i' U_abi, where E_ab,external=U_ab,i t_i Vh_i,external, and only change t_i which are small: t_i'=t_i**2/(t_i**2+gilt_eps**2), we also do gilt_nIter iterations
# To see how it works
# E factorizes as E(UV and IR entanglement to outside) \otimes I(UV entanglement inside)
# TODO
#svd,sqrt=torch.linalg.svd,torch.sqrt
if np.array([1., 2.]).dtype not in {np.dtype('float64')}:
print(np.array([1., 2.]).dtype)
print('[GILT_jax] Warning! float32 is not precise enough, leads to bad RG behavior')
@dataclass
class GILT_options:
enabled:bool=True
eps:float=8e-7 #too los like 1e-8 will result false fixed topological point
nIter:int=1 #enough
split_insertion:bool=True
TRG_method:str='A'
HOTRG_3D_method:str='square_only'
fix_gauge:bool=True
record_S:bool=False
make_isometric:bool=False
recorded_S=[]
def GILT_getuvh(EEh,options:GILT_options=GILT_options()):
d=EEh.shape[0]
uu,vvh=np.eye(d),np.eye(d)
for _iter in range(options.nIter):
if _iter==0:
U,S,_=svd(EEh.reshape(d**2,d**2))
else:
uvUS=contract('aA,Bb,abc,c->ABc',u,vh,U,S).reshape(d**2,d**2)
U,S,_=svd(uvUS)
U=U.reshape(d,d,d**2)
t=contract('aac->c',U)
Sn=S/np.max(S)
if options.record_S:
recorded_S.append(Sn)
t=t*(Sn**2/(Sn**2+options.eps**2))
Q=contract('abc,c->ab',U,t)
if options.split_insertion:
u,s,vh=svd(Q) # is it necessary to split?
s=np.diag(sqrt(s))
u,vh=u@s,s@vh
else:
# not make sense, introduces numerical error!
u,vh=Q,np.eye(d)
uu,vvh=uu@u,vh@vvh
return uu,vvh
def GILT_getEEh(As,Ais:"list[list[str]]"):
def process(edgeid,legid,tensorid,replicaid):
if edgeid is None:
#contract between corresponding replicas
return 'T'+str(tensorid)+'L'+str(legid)
else:
#internal legs
return 'R'+str(replicaid)+'E'+str(edgeid)
R1Ais=[[process(edgeid,legid,tensorid,0) for legid,edgeid in enumerate(Ai)]for tensorid,Ai in enumerate(Ais)]
R2Ais=[[process(edgeid,legid,tensorid,1) for legid,edgeid in enumerate(Ai)]for tensorid,Ai in enumerate(Ais)]
AAis=[list(filter(lambda x:x[0]=='R',R1Ai+R2Ai)) for R1Ai,R2Ai in zip(R1Ais,R2Ais)]
Ti=['R0Eu','R0Ev','R1Eu','R1Ev']
AAs=[contract(A,R1Ai,A,R2Ai,AAi) for A,R1Ai,R2Ai,AAi in zip(As,R1Ais,R2Ais,AAis)]
#print(AAis)
T=contract(*itt.chain(*zip(AAs,AAis)),Ti)
#print(R1Ais);print(R2Ais);print(AAis);print(Ti)
#for AA,AAi in zip(AAs,AAis):
# print(AA.shape)
# print(AAi)
#print(T.shape)
#print(Ti)
return T
#======================================================
#def GILT_Square_one(As,options:GILT_options=GILT_options()):
# # A1- -A2 A1u vA2 0
# # | O | --> | U | 2A3
# # A3---A4 A3---A4 1
# A1i=[None,'13',None,'u']
# A2i=[None,'24','v',None]
# A3i=['13',None,None,'34']
# A4i=['24',None,'34',None]
# EEh=GILT_getEEh(As,[A1i,A2i,A3i,A4i])
# u,vh=GILT_getuvh(EEh,options=options)
# assert not u.isnan().any() and not vh.isnan().any()
# return u,vh
def replace_leg_with_u_and_v(Ais,leg):
flag=False
for Ai in Ais:
if leg in Ai:
if not flag:
Ai[Ai.index(leg)]='u'
flag=True
else:
Ai[Ai.index(leg)]='v'
return Ais
def GILT_Square_one(As,leg,options:GILT_options=GILT_options()):
# leg: 12 for example
# A1- -A2 A1u vA2 0
# | O | --> | U | 2A3
# A3---A4 A3---A4 1
Ais=[
[None,'13',None,'12'],
[None,'24','12',None],
['13',None,None,'34'],
['24',None,'34',None],
]
if(len(As[0].shape)==5): #it might also works for PEPS I hope
Ais=[Ai+[None] for Ai in Ais]
assert leg in {'12','34','13','24'}
Ais=replace_leg_with_u_and_v(Ais,leg)
EEh=GILT_getEEh(As,Ais)
u,vh=GILT_getuvh(EEh,options=options)
assert not np.any(np.isnan(u)) and not np.any(np.isnan(vh))
return u,vh
def GILT_Cube_one(As,leg,options:GILT_options=GILT_options()):
# leg: 12 for example
# A5+------+A6
# |`. |`. 0
# | A1+-u v-+A2 5`|
# | | | | 2-o-3
# A7+---|--+A8 | |`4
# `. | `. | 1
# A3+------+A4
Ais=[
[None,'13',None,'12',None,'15'],
[None,'24','12',None,None,'26'],
['13',None,None,'34',None,'37'],
['24',None,'34',None,None,'48'],
[None,'57',None,'56','15',None],
[None,'68','56',None,'26',None],
['57',None,None,'78','37',None],
['68',None,'78',None,'48',None],
]
if(len(As[0].shape)==7): #it might also works for PEPS I hope
Ais=[Ai+[None] for Ai in Ais]
assert leg in {'12','34','56','78','13','24','57','68','15','26','37','48'}
Ais=replace_leg_with_u_and_v(Ais,leg)
EEh=GILT_getEEh(As,Ais)
u,vh=GILT_getuvh(EEh,options=options)
assert not u.isnan().any() and not vh.isnan().any()
return u,vh
def GILT_HOTRG2D(T1,T2,options:GILT_options=GILT_options()):
# O | O
# /v1-T1-u1\ 0 2
# -w |\ w- 2T3 -> 0T'1
# \v2-T2-u2/ 14 34
# O |\O
#Y1,Y2=T1,T2
contract_path={4:'ijkl,Kk,Ll->ijKL',5:'ijkla,Kk,Ll->ijKLa'}[len(T1.shape)]
u1,vh1=GILT_Square_one([T2,T2,T1,T1],leg='34',options=options)
T1=contract(contract_path,T1,vh1,u1.T)
u2,vh2=GILT_Square_one([T2,T2,T1,T1],leg='12',options=options)
T2=contract(contract_path,T2,vh2,u2.T)
I=np.eye(T1.shape[0])
gg=[[I,I,vh1,u1.T],[I,I,vh2,u2.T]]
#Y1=contract('ijkl,Ii,Jj,Kk,Ll->IJKL',Y1,*gg[0])
#Y2=contract('ijkl,Ii,Jj,Kk,Ll->IJKL',Y2,*gg[1])
#print((T1-Y1).norm(),(T2-Y2).norm())
return T1,T2,gg
def GILT_HOTRG3D_square_only(T1,T2,options:GILT_options=GILT_options()):
# g4| 5--6
# /g1-T1-g2\ 50 34 |1--2
# -w g8|g3 w- 2T3 -> 0T'1 7| 8|
# \g5-T2-g6/ 14 52 3--4
# |g7
raise NotImplementedError
def GILT_HOTRG3D(T1,T2,options:GILT_options=GILT_options()):
print('not tested!')
# g4| 5--6
# /g1-T1-g2\ 50 34 |1--2
# -w g8|g3 w- 2T3 -> 0T'1 7| 8|
# \g5-T2-g6/ 14 52 3--4
# |g7
Y1,Y2=T1,T2
T21s=[T2,T2,T2,T2,T1,T1,T1,T1]
T12s=[T1,T1,T1,T1,T2,T2,T2,T2]
contract23='ijklmn,Kk,Ll->ijKLmn'
contract45='ijklmn,Mm,Nn->ijklMN'
cube_apply_inner=True
u,vh=GILT_Cube_one(T21s,leg='34',options=options)
T1,g1,g2=contract(contract23,T1,vh,u.T),vh,u.T
u,vh=GILT_Cube_one(T21s,leg='78',options=options)
T1,g1,g2=contract(contract23,T1,vh,u.T),vh@g1,u.T@g2
if cube_apply_inner:
u,vh=GILT_Cube_one(T12s,leg='12',options=options)
T1,g1,g2=contract(contract23,T1,vh,u.T),vh@g1,u.T@g2
u,vh=GILT_Cube_one(T12s,leg='56',options=options)
T1,g1,g2=contract(contract23,T1,vh,u.T),vh@g1,u.T@g2
u,vh=GILT_Cube_one(T21s,leg='37',options=options)
T1,g3,g4=contract(contract45,T1,vh,u.T),vh,u.T
u,vh=GILT_Cube_one(T21s,leg='48',options=options)
T1,g3,g4=contract(contract45,T1,vh,u.T),vh@g3,u.T@g4
if cube_apply_inner:
u,vh=GILT_Cube_one(T12s,leg='15',options=options)
T1,g3,g4=contract(contract45,T1,vh,u.T),vh@g3,u.T@g4
u,vh=GILT_Cube_one(T12s,leg='26',options=options)
T1,g3,g4=contract(contract45,T1,vh,u.T),vh@g3,u.T@g4
u,vh=GILT_Cube_one(T21s,leg='12',options=options)
T2,g5,g6=contract(contract23,T2,vh,u.T),vh,u.T
u,vh=GILT_Cube_one(T21s,leg='56',options=options)
T2,g5,g6=contract(contract23,T2,vh,u.T),vh@g5,u.T@g6
if cube_apply_inner:
u,vh=GILT_Cube_one(T12s,leg='34',options=options)
T2,g5,g6=contract(contract23,T2,vh,u.T),vh@g5,u.T@g6
u,vh=GILT_Cube_one(T12s,leg='78',options=options)
T2,g5,g6=contract(contract23,T2,vh,u.T),vh@g5,u.T@g6
u,vh=GILT_Cube_one(T21s,leg='15',options=options)
T2,g7,g8=contract(contract45,T2,vh,u.T),vh,u.T
u,vh=GILT_Cube_one(T21s,leg='26',options=options)
T2,g7,g8=contract(contract45,T2,vh,u.T),vh@g7,u.T@g8
if cube_apply_inner:
u,vh=GILT_Cube_one(T12s,leg='37',options=options)
T2,g7,g8=contract(contract45,T2,vh,u.T),vh@g7,u.T@g8
u,vh=GILT_Cube_one(T12s,leg='48',options=options)
T2,g7,g8=contract(contract45,T2,vh,u.T),vh@g7,u.T@g8
I=np.eye(T1.shape[0])
gg=[[I,I,g1,g2,g3,g4],[I,I,g5,g6,g7,g8]]
Y1=contract('ijklmn,Ii,Jj,Kk,Ll,Mm,Nn->IJKLMN',Y1,*gg[0])
Y2=contract('ijklmn,Ii,Jj,Kk,Ll,Mm,Nn->IJKLMN',Y2,*gg[1])
print((Y1-T1).norm(),(Y2-T2).norm())
return T1,T2,gg
def GILT_HOTRG(T1,T2,options:GILT_options=GILT_options()):
_GILT_HOTRG={4:GILT_HOTRG2D,5:GILT_HOTRG2D,6:GILT_HOTRG3D}[len(T1.shape)]
T1,T2,gg=_GILT_HOTRG(T1,T2,options=options)
if options.record_S:
import matplotlib.pyplot as plt
plt.hist(recorded_S[0],bins=np.logspace(-9,0,50),log=True)
plt.xscale('log')
plt.show()
recorded_S.clear()
return T1,T2,gg
'''
from HOSVD import HOSVD_layer
from fix_gauge import fix_gauge_2D,minimal_canonical_form,fix_phase
def GILT_HOSVD_layer(T1,T2,max_dim,dimR=None,options:GILT_options=GILT_options()):
if options.enabled:
assert not dimR
T1,T2,gg=GILT_HOTRG(T1,T2,options=options)
Tn,layer=HOSVD_layer(T1,T2,max_dim=max_dim,dimR=dimR)
layer.gg=gg
return Tn,layer
else:
return HOSVD_layer(T1,T2,max_dim=max_dim,dimR=dimR)
'''
#============= GILT On TRG=============
from TRG import TRG_AB
from HOTRGZ2_jax import gauge_invariant_norm
def GILT_SquareA(A,options:GILT_options=GILT_options()):
# Not good precision. Why?
# A- -A vAu vAu
# | O | --> | O |
# A---A vAu-vAu
for i in range(4):
u,vh=GILT_Square_one([A,A,A,A],leg='12',options=options)
A=contract('abcd,Cc,dD->abCD',A,vh,u)
A=contract('abcd->dcab',A)
return A
def GILT_SquareABCD(A,B,C,D,options:GILT_options=GILT_options()):
# A- -B Au vB 0
# | O | --> | O | 2A3
# C---D C---D 1
for i in range(2):
for i in range(4):
u,vh=GILT_Square_one([A,B,C,D],leg='12',options=options)
A,B=contract('abcd,dD->abcD',A,u),contract('abcd,Cc->abCd',B,vh)
CCW='abcd->dcab'
A,B,C,D=contract(CCW,B),contract(CCW,D),contract(CCW,A),contract(CCW,C)#rotate CCW
A,B,C,D=B,A,D,C
return A,B,C,D
def GILT_SquareAB(A,B,options:GILT_options=GILT_options()):
# A---B Au vB 0
# | O | --> | O | 2A3
# B---A vB---Au 1
for i in range(4):
u,vh=GILT_Square_one([A,B,B,A],leg='12',options=options)
A,B=contract('abcd,dD->abcD',A,u),contract('abcd,Cc->abCd',B,vh)
A,B=contract('abcd->dcab',B),contract('abcd->dcab',A)#rotate
return A,B
# def evolve_TRG_GILT_2D(T0,nLayers,max_dim,return_layers=False,options:GILT_options=GILT_options()):
# T,logTotal=T0,0
# if return_layers:
# Ts,logTotals=[T],[logTotal]
# for i in tqdm(range(nLayers),leave=False):
# norm=gauge_invariant_norm(T)
# T=T/norm
# logTotal=2*(logTotal+norm.log())
# if options.TRG_method=='A':
# A=GILT_SquareA(T,options=options)
# T=TRG_AB(A,A,max_dim)
# elif options.TRG_method=='AB':
# A,B=GILT_SquareAB(T,T,options=options)
# T=TRG_AB(A,B,max_dim)
# elif options.TRG_method=='BA':
# A,B=GILT_SquareAB(T,T,options=options)
# T=TRG_AB(B,A,max_dim)
# elif options.TRG_method=='BAAB':
# A,B=GILT_SquareAB(T,T,options=options)
# A,B=GILT_SquareAB(B,A,options=options)
# T=TRG_AB(A,B,max_dim)
# elif options.TRG_method=='BABA':
# A,B=GILT_SquareAB(T,T,options=options)
# A,B=GILT_SquareAB(B,A,options=options)
# T=TRG_AB(B,A,max_dim)
# elif options.TRG_method=='ABCD':
# assert False
# else:
# assert False
# if options.fix_gauge and T.shape==Ts[-1].shape:
# #T=fix_gauge_2D(T,Ts[-1])
# T,_=minimal_canonical_form(T)
# T,_=fix_phase(T,Ts[-1])
# if return_layers:
# Ts.append(T);logTotals.append(logTotal)
# if return_layers:
# return Ts,logTotals
# return T,logTotal