def toEnvOperator(op):
result = bops.unifyLegs(
bops.unifyLegs(
bops.unifyLegs(
bops.unifyLegs(bops.permute(op, [0, 4, 1, 5, 2, 6, 3, 7]), 6,
7), 4, 5), 2, 3), 0, 1)
tn.remove_node(op)
return result
def getBMPS(hs, steps):
for h in hs:
h = np.round(h, 1)
if int(h) == h:
h = int(h)
with open('ising/origTensors/ising_field_' + str(h) + '_A', 'rb') as f:
ATensor = pickle.load(f)
with open('ising/origTensors/ising_field_' + str(h) + '_B', 'rb') as f:
BTensor = pickle.load(f)
A = tn.Node(ATensor)
A = bops.permute(A, [1, 2, 3, 0, 4])
B = tn.Node(BTensor)
B = bops.permute(B, [1, 2, 3, 0, 4])
def toEnvOperator(op):
result = bops.unifyLegs(
bops.unifyLegs(
bops.unifyLegs(
bops.unifyLegs(
bops.permute(op, [0, 4, 1, 5, 2, 6, 3, 7]), 6, 7),
4, 5), 2, 3), 0, 1)
tn.remove_node(op)
return result
AEnv = toEnvOperator(bops.multiContraction(A, A, '4', '4*'))
BEnv = toEnvOperator(bops.multiContraction(B, B, '4', '4*'))
envOpAB = bops.permute(bops.multiContraction(AEnv, BEnv, '1', '3'),
[0, 3, 2, 4, 1, 5])
envOpBA = bops.permute(bops.multiContraction(BEnv, AEnv, '1', '3'),
[0, 3, 2, 4, 1, 5])
curr = bops.permute(
bops.multiContraction(envOpBA, envOpAB, '45', '01'),
[0, 2, 4, 6, 1, 3, 5, 7])
for i in range(2):
[C, D, te] = bops.svdTruncation(curr, [0, 1, 2, 3], [4, 5, 6, 7],
'>>',
normalize=True)
curr = bops.permute(bops.multiContraction(D, C, '23', '12'),
[1, 3, 0, 5, 2, 4])
curr = bops.permute(
bops.multiContraction(curr, envOpAB, '45', '01'),
[0, 2, 4, 6, 1, 3, 5, 7])
b = 1
currAB = curr
rowTensor = np.zeros((11, 4, 4, 11), dtype=complex)
rowTensor[0, 3, 3, 0] = 1
rowTensor[1, 3, 3, 2] = 1
rowTensor[2, 3, 3, 3] = 1
rowTensor[3, 3, 0, 4] = 1
rowTensor[4, 0, 3, 1] = 1
rowTensor[5, 3, 3, 6] = 1
rowTensor[6, 3, 0, 7] = 1
rowTensor[7, 0, 3, 8] = 1
rowTensor[8, 3, 3, 5] = 1
row = tn.Node(rowTensor)
print('60')
upRow = bops.unifyLegs(
bops.unifyLegs(
bops.unifyLegs(
bops.unifyLegs(
bops.permute(
bops.multiContraction(row, tn.Node(currAB.tensor),
'12', '04'),
[0, 2, 3, 4, 7, 1, 5, 6]), 5, 6), 5, 6), 0, 1), 0,
1)
[C, D, te] = bops.svdTruncation(upRow, [0, 1], [2, 3],
'>>',
normalize=True)
upRow = bops.multiContraction(D, C, '2', '0')
[cUp, dUp, te] = bops.svdTruncation(upRow, [0, 1], [2, 3],
'>>',
normalize=True)
GammaC, LambdaC, GammaD, LambdaD = peps.getBMPSRowOps(
cUp, tn.Node(np.ones(cUp[2].dimension)), dUp,
tn.Node(np.ones(dUp[2].dimension)), AEnv, BEnv, steps)
cUp = bops.multiContraction(GammaC, LambdaC, '2', '0', isDiag2=True)
dUp = bops.multiContraction(GammaD, LambdaD, '2', '0', isDiag2=True)
upRow = bops.multiContraction(cUp, dUp, '2', '0')
downRow = bops.copyState([upRow])[0]
rightRow = peps.bmpsCols(upRow,
downRow,
AEnv,
BEnv,
steps,
option='right',
X=upRow)
leftRow = peps.bmpsCols(upRow,
downRow,
AEnv,
BEnv,
steps,
option='left',
X=upRow)
circle = bops.multiContraction(
bops.multiContraction(
bops.multiContraction(upRow, rightRow, '3', '0'), upRow, '5',
'0'), leftRow, '70', '03')
openA = tn.Node(
np.transpose(
np.reshape(np.kron(A.tensor, np.conj(A.tensor)),
[d**2, d**2, d**2, d**2, d, d]),
[4, 0, 1, 2, 3, 5]))
openB = tn.Node(
np.transpose(
np.reshape(np.kron(B.tensor, np.conj(B.tensor)),
[d**2, d**2, d**2, d**2, d, d]),
[4, 0, 1, 2, 3, 5]))
ABNet = bops.permute(
bops.multiContraction(
bops.multiContraction(openB, openA, '2', '4'),
bops.multiContraction(openA, openB, '2', '4'),
'28',
'16',
cleanOr1=True,
cleanOr2=True),
[1, 5, 6, 13, 14, 9, 10, 2, 0, 4, 8, 12, 3, 7, 11, 15])
dm = bops.multiContraction(circle, ABNet, '01234567', '01234567')
ordered = np.round(np.reshape(dm.tensor, [16, 16]), 14)
ordered /= np.trace(ordered)
print(h, getM(ordered))
with open('ising/bmpsResults_' + str(h), 'wb') as f:
pickle.dump(
[upRow, downRow, leftRow, rightRow, openA, openB, A, B], f)
rowTensor[0, 0, 0, 0] = 1
rowTensor[1, 0, 0, 2] = 1
rowTensor[2, 0, 0, 3] = 1
rowTensor[3, 0, 3, 4] = 1
rowTensor[4, 3, 0, 1] = 1
rowTensor[5, 0, 0, 6] = 1
rowTensor[6, 0, 3, 7] = 1
rowTensor[7, 3, 0, 8] = 1
rowTensor[8, 0, 0, 5] = 1
row = tn.Node(rowTensor)
upRow = bops.unifyLegs(
bops.unifyLegs(
bops.unifyLegs(
bops.unifyLegs(
bops.permute(
bops.multiContraction(row, tn.Node(currAB.tensor),
'12', '04'),
[0, 2, 3, 4, 7, 1, 5, 6]), 5, 6), 5, 6), 0, 1), 0,
1)
[C, D, te] = bops.svdTruncation(upRow, [0, 1], [2, 3],
'>>',
normalize=True)
upRow = bops.multiContraction(D, C, '2', '0')
[cUp, dUp, te] = bops.svdTruncation(upRow, [0, 1], [2, 3],
'>>',
normalize=True)
GammaC, LambdaC, GammaD, LambdaD = peps.getBMPSRowOps(
cUp, tn.Node(np.ones(cUp[2].dimension)), dUp,
tn.Node(np.ones(dUp[2].dimension)), AEnv, BEnv, 50)
cUp = bops.multiContraction(GammaC, LambdaC, '2', '0', isDiag2=True)
def bmpsRowStep(gammaL, lambdaMid, gammaR, lambdaSide, envOp):
row = bops.multiContraction(bops.multiContraction(bops.multiContraction(
bops.multiContraction(lambdaSide, gammaL, '1', '0', isDiag1=True),
lambdaMid,
'2',
'0',
cleanOr1=True,
cleanOr2=True,
isDiag2=True),
gammaR,
'2',
'0',
cleanOr1=True,
cleanOr2=True),
lambdaSide,
'3',
'0',
cleanOr1=True,
isDiag2=True)
opRow = bops.permute(
bops.multiContraction(row, envOp, '12', '01', cleanOr1=True),
[0, 2, 4, 5, 1, 3])
[U, S, V, truncErr] = bops.svdTruncation(opRow, [0, 1, 2], [3, 4, 5],
dir='>*<',
maxBondDim=chi)
newLambdaMid = bops.multNode(S, 1 / np.sqrt(sum(S.tensor**2)))
lambdaSideInv = tn.Node(
np.array([1 / val if val > 1e-15 else 0 for val in lambdaSide.tensor],
dtype=complex))
newGammaL = bops.multiContraction(lambdaSideInv,
U,
'1',
'0',
cleanOr2=True,
isDiag1=True)
splitter = tn.Node(
bops.getLegsSplitterTensor(newGammaL[0].dimension,
newGammaL[1].dimension))
newGammaL = bops.unifyLegs(newGammaL, 0, 1)
newGammaR = bops.multiContraction(V,
lambdaSideInv,
'2',
'0',
cleanOr1=True,
cleanOr2=True,
isDiag2=True)
newGammaR = bops.unifyLegs(newGammaR, 2, 3)
newLambdaSide = bops.multiContraction(bops.multiContraction(lambdaSide,
splitter,
'1',
'0',
cleanOr1=True,
isDiag1=True),
splitter,
'01',
'01',
cleanOr1=True,
cleanOr2=True)
temp = newLambdaSide
newLambdaSide = tn.Node(np.diag(newLambdaSide.tensor))
tn.remove_node(temp)
return newGammaL, newLambdaMid, newGammaR, newLambdaSide