def matvec(self, v):
v_ = v.clone(
) # if don't clone, vectordot Tr in Lanczos_ER will not be rank-1
psi_u = cytnx.UniTensor(v_, 0) ## share memory, no copy
psi_u.reshape_(*self.shapes)
self.anet.PutUniTensor("psi", psi_u, False)
out = self.anet.Launch(
optimal=True).get_block_() # get_block_ without copy
out.flatten_() # only change meta, without copy.
return out
def matvec(self, psi):
psi_p = cytnx.UniTensor(psi.clone(), 0) ## clone here
psi_p.reshape_(*self.psi_shape)
self.anet.PutUniTensor("psi", psi_p,
False) ## no- redundant clone here
H_psi = self.anet.Launch(
optimal=True).get_block_() # get_block_ without copy
H_psi.flatten_()
return H_psi
def Projector(psi, L, M1, M2, R):
''' psi is Tensor, while L,M1,M2,R are UniTensor.
Return: h|psi> (Tensor)'''
psi_p = cytnx.UniTensor(psi, 0) ## share memory, no copy
psi_p.reshape_(L.shape()[1], M1.shape()[2], M2.shape()[2], R.shape()[1])
anet = cytnx.Network("projector.net")
anet.PutUniTensor("M2", M2)
anet.PutUniTensors(["psi", "L", "M1", "R"], [psi_p, L, M1, R], False)
H_psi = anet.Launch(optimal=True).get_block_() # get_block_ without copy
H_psi.flatten_() # only change meta, without copy.
psi.flatten_() ## this just in case psi is something shared.
return H_psi
#print(Sz,Sx) ## Build Evolution Operator TFterm = cytnx.linalg.Kron(Sx,I) + cytnx.linalg.Kron(I,Sx) ZZterm = cytnx.linalg.Kron(Sz,Sz) H = Hx*TFterm + J*ZZterm del TFterm, ZZterm eH = cytnx.linalg.ExpH(H,-dt) ## or equivantly ExpH(-dt*H) eH.reshape_(2,2,2,2) print(eH) H.reshape_(2,2,2,2) eH = cytnx.UniTensor(eH,2) eH.print_diagram() print(eH) H = cytnx.UniTensor(H,2) H.print_diagram() ## Create MPS: # # | | # --A-la-B-lb-- # A = cytnx.UniTensor([cytnx.Bond(chi),cytnx.Bond(2),cytnx.Bond(chi)],rowrank=1,labels=[-1,0,-2]); B = cytnx.UniTensor(A.bonds(),rowrank=1,labels=[-3,1,-4]);
# -------
# ^ ^
# 0 1
#
TFterm = cytnx.linalg.Kron(Sx, I) + cytnx.linalg.Kron(I, Sx)
ZZterm = cytnx.linalg.Kron(Sz, Sz)
H = Hx * TFterm + J * ZZterm
del TFterm, ZZterm
eH = cytnx.linalg.ExpH(H, -dt) ## or equivantly ExpH(-dt*H)
eH.reshape_(2, 2, 2, 2)
print(eH)
H.reshape_(2, 2, 2, 2)
eH = cytnx.UniTensor(eH, 2)
eH.tag() # this will tag with in/out(ket/bra) on each bond.
eH.print_diagram()
H = cytnx.UniTensor(H, 2)
H.tag()
H.print_diagram()
## Create MPS, with bond tagged with direction in/out(ket/bra):
# ^ ^
# | |
# ->-A-> ->la-> ->B-> ->lb->
#
A = cytnx.UniTensor([
cytnx.Bond(chi, cytnx.BD_KET),
cytnx.Bond(2, cytnx.BD_BRA),
## Initialiaze MPO ##>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> d = 2 s = 0.5 sx = cytnx.physics.spin(0.5, 'x') sy = cytnx.physics.spin(0.5, 'y') sp = sx + 1j * sy sm = sx - 1j * sy eye = cytnx.eye(d) M = cytnx.zeros([4, 4, d, d]) M[0, 0] = M[3, 3] = eye M[0, 1] = M[2, 3] = 2**0.5 * sp.real() M[0, 2] = M[1, 3] = 2**0.5 * sm.real() M = cytnx.UniTensor(M, 0) L0 = cytnx.UniTensor(cytnx.zeros([4, 1, 1]), 0) #Left boundary R0 = cytnx.UniTensor(cytnx.zeros([4, 1, 1]), 0) #Right boundary L0.get_block_()[0, 0, 0] = 1. R0.get_block_()[3, 0, 0] = 1. ## Init MPS train # # 0-A[0]-2 2-A[1]-4 4-A[2]-6 ... 2k-A[k]-2k+2 # | | | | # 1 3 5 2k+1 # ##>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> A = [None for i in range(Nsites)] A[0] = cytnx.UniTensor(cytnx.random.normal([1, d, min(chi, d)], 0., 1.), 2)
H = cy.linalg.Kron(H, I)
H.reshape_(2, 2, 2, 2, 2, 2)
H = H + H.permute(0, 2, 1, 3, 5, 4) + H.permute(2, 0, 1, 5, 3, 4)
###################
tau = 1.0
D = 3
maxit = 1000
# Here, we explicitly seperate up/down
# which is the same in this model, but in general they could be different
Hup = H
Hdown = Hup.clone()
## Hamiltonain
Hu = cy.UniTensor(Hup, 3)
Hd = cy.UniTensor(Hdown, 3)
## create 3PESS:
s1 = cy.UniTensor(cy.random.normal([D, D, D], 0, 0.5), 0)
s2 = s1.clone()
A = cy.UniTensor(cy.random.normal([D, 2, D], 0, 0.5), 2)
B = cy.UniTensor(cy.random.normal([D, 2, D], 0, 0.5), 2)
C = cy.UniTensor(cy.random.normal([D, 2, D], 0, 0.5), 2)
Ls1 = [
cy.UniTensor([cy.Bond(D), cy.Bond(D)], rowrank=1, is_diag=True)
for i in range(3)
]
for i in Ls1:
i.put_block(cy.ones(D))
Ls2 = [i.clone() for i in Ls1]
W[1,1] = -np.sqrt(np.sinh(beta))
## Method-1 (faster):
T = cLA.Kron(cLA.Kron(W[0],W[0]),cLA.Kron(W[0],W[0]))+\
cLA.Kron(cLA.Kron(W[1],W[1]),cLA.Kron(W[1],W[1]))
T.reshape_(2,2,2,2)
## Method-2 (slower in python):
#Tchk = cytnx.zeros([2,2,2,2])
#for i in range(2):
# for j in range(2):
# for k in range(2):
# for l in range(2):
# for a in range(2):
# Tchk[i,j,k,l] += W[a,i]*W[a,j]*W[a,k]*W[a,l]
cT = cytnx.UniTensor(T,2)
## Let's start by normalize the block with it's local partition function
## to avoid the blow-up of partition function:
#
# 1
# |
# 0--cT--2
# |
# 3
#
Nrm = cT.get_block().Trace(0,2).Trace(0,1).item()
cT/=Nrm
print(Tn2a)
print(Tn3a)
##=============================
## Bond
##=============================
bd_in = cytnx.Bond(10, cytnx.bondType.BD_BRA)
print(bd_in)
bd_sym = cytnx.Bond(3,cytnx.bondType.BD_KET,\
[[0,2],[1,2],[1,3]],\
[cytnx.Symmetry.Zn(2),\
cytnx.Symmetry.U1()])
print(bd_sym)
print(bd_sym == bd_sym)
bd_1 = cytnx.Bond(3)
bd_2 = cytnx.Bond(2)
bd_3 = cytnx.Bond(4)
U = cytnx.UniTensor([bd_1, bd_2, bd_3], Rowrank=2, dtype=cytnx.Type.Double)
U.print_diagram()
U.permute_(0, 2, 1, Rowrank=1)
U.print_diagram()
print(U)
X = U[0, :, :]
X.print_diagram()
U.reshape_(6, -1)
U.print_diagram()
#
# [J]*SzSz + 2[Hx]*Sx
#
#
J = 1.0
Hx = 1.0
d = 2
sx = cytnx.physics.pauli('x').real()
sz = cytnx.physics.pauli('z').real()
eye = cytnx.eye(d)
M = cytnx.zeros([3, 3, d, d])
M[0, 0] = M[2, 2] = eye
M[0, 1] = M[1, 2] = sz
M[0, 2] = 2 * Hx * sx
M = cytnx.UniTensor(M, 0)
L0 = cytnx.UniTensor(cytnx.zeros([3, 1, 1]), 0) #Left boundary
R0 = cytnx.UniTensor(cytnx.zeros([3, 1, 1]), 0) #Right boundary
L0.get_block_()[0, 0, 0] = 1.
R0.get_block_()[2, 0, 0] = 1.
## Local Measurement Operator:
## Here, we consider a local measurement of energy.
H = J * cytnx.linalg.Kron(
sz, sz) + Hx * (cytnx.linalg.Kron(sx, eye) + cytnx.linalg.Kron(eye, sx))
H = cytnx.UniTensor(H.reshape(2, 2, 2, 2), 2)
## Init the left and right enviroment
#
# L[0]: R[0]:
## #Example of 1D Heisenberg model ## iTEBD ##------------------------------------- chi = 40 J = 1.0 CvgCrit = 1.0e-12 dt = 0.1 ## Create Si Sj local H with symmetry: ## SzSz + S+S- + h.c. bdi = cytnx.Bond(2, cytnx.BD_KET, [[1], [-1]]) bdo = bdi.clone().set_type(cytnx.BD_BRA) H = cytnx.UniTensor([bdi, bdi, bdo, bdo], labels=[2, 3, 0, 1], rowrank=2) ## assign: # Q = 2 # Q = 0: # Q = -2: # [1] [[ -1, 1] [1] # [ 1,-1]] H.get_block_([2])[0] = 1 T0 = H.get_block_([0]) T0[0, 0] = T0[1, 1] = -1 T0[0, 1] = T0[1, 0] = 1 H.get_block_([-2])[0] = 1 ## create gate: eH = cytnx.linalg.ExpH(H, -dt) ## Create MPS: