def Get_spin_operators(spin):
#Returns tuple of 3 spin operators and a unit matrix for given value of spin.
s = int(spin.split('/')[0]) / int(spin.split('/')[1]) if (
'/' in spin) else int(spin)
d = int(2 * s + 1)
return cytnx.physics.spin(s, 'x'), cytnx.physics.spin(
s, 'y'), cytnx.physics.spin(s, 'z'), cytnx.eye(d).astype(
cytnx.Type.ComplexDouble)
def Create_loop_gas_operator(spin):
"""Returns loop gas (LG) operator Q_LG for spin=1/2 or spin=1 Kitaev model."""
tau_tensor = cytnx.zeros(
(2, 2, 2), dtype=cytnx.Type.ComplexDouble) # tau_tensor_{i j k}
if '/' in spin:
tau_tensor[0, 0, 0] = -1j
else:
tau_tensor[0, 0, 0] = 1
tau_tensor[0, 1, 1] = tau_tensor[1, 0, 1] = tau_tensor[1, 1, 0] = 1
sx, sy, sz, one = Get_spin_operators(spin)
d = one.shape()[0]
Q_LG = cytnx.zeros((d, d, 2, 2, 2),
dtype=cytnx.Type.ComplexDouble) # Q_LG_{s s' i j k}
u_gamma = None
if '/' in spin:
u_gamma = list(
map(lambda x: -1j * cytnx.linalg.ExpM(1j * np.pi * x),
(sx, sy, sz)))
else:
u_gamma = list(
map(lambda x: cytnx.linalg.ExpM(1j * np.pi * x), (sx, sy, sz)))
for i in range(2):
for j in range(2):
for k in range(2):
temp = cytnx.eye(d)
if i == 0:
temp = cytnx.linalg.Matmul(temp, u_gamma[0])
if j == 0:
temp = cytnx.linalg.Matmul(temp, u_gamma[1])
if k == 0:
temp = cytnx.linalg.Matmul(temp, u_gamma[2])
for s in range(d):
for sp in range(d):
Q_LG[s, sp, i, j,
k] = tau_tensor[i, j, k] * temp[s, sp]
return Q_LG
chi = 32 Nsites = 20 numsweeps = 4 # number of DMRG sweeps maxit = 2 # iterations of Lanczos method krydim = 4 # dimension of Krylov subspace ## 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 # | | | |
OPTS_numsweeps = 6 # number of DMRG sweeps
OPTS_dispon = 1 # level of output display
OPTS_updateon = True # level of output display
OPTS_maxit = 2 # iterations of Lanczos method
OPTS_krydim = 4 # dimension of Krylov subspace
'''
########## Initialiaze MPO (quantum XX model) and random MPS ##########
'''
d = 2
s = 0.5
sx = cytnx.physics.spin(0.5, 'x')
sy = cytnx.physics.spin(0.5, 'y')
sz = cytnx.physics.spin(0.5, 'y')
sp = sx + 1j * sy
sm = sx - 1j * sy
eye = cytnx.eye(d).astype(cytnx.Type.ComplexDouble)
if model == 'XX':
W = cytnx.zeros([4, 4, d, d]).astype(cytnx.Type.ComplexDouble)
W[0, 0, :, :] = W[3, 3, :, :] = eye
W[0, 1, :, :] = W[2, 3, :, :] = 2**0.5 * sp
W[0, 2, :, :] = W[1, 3, :, :] = 2**0.5 * sm
WL = cytnx.zeros([4, 1, 1]).astype(cytnx.Type.ComplexDouble)
WR = cytnx.zeros([4, 1, 1]).astype(cytnx.Type.ComplexDouble)
WL[0, 0, 0] = 1.
WR[3, 0, 0] = 1.
if model == 'Ising':
W = cytnx.zeros([3, 3, d, d]).astype(cytnx.Type.ComplexDouble)
W[0, 0, :, :] = W[2, 2, :, :] = eye
W[0, 1, :, :] = sx * 2
W[0, 2, :, :] = -1.0 * (sz * 2) ## g
W[1, 2, :, :] = sx * 2
out = A.clone()
b = out.get_block_()
for i in range(b.shape()[0]):
if (b[i].item() < clip):
b[i] = 0
else:
b[i] = 1. / b[i]
return out
## create opeartor:
Sz = cy.physics.spin(0.5, 'z')
Sx = cy.physics.spin(0.5, 'x')
Sy = cy.physics.spin(0.5, 'y')
I = cy.eye(2)
H = cy.linalg.Kron(Sz, Sz) + cy.linalg.Kron(Sx, Sx) + cy.linalg.Kron(Sy, Sy)
H = H.real() # since it's real ,let's truncate imag part.
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