def OptT(Mpo, HL, HR, T): # 所有T
Ns = len(T)
Eng0 = np.zeros(Ns)
Eng1 = np.zeros(Ns)
for r in range(100):
#print (r)
for i in range(Ns - 1):
T[i], Eng1[i] = OptTSite(Mpo, HL[i], HR[i], T[i], Method=1)
# print i,Eng1[i]
T[i], U = Sub.Mps_QR0P(T[i])
HL[i + 1] = Sub.NCon(
[HL[i], np.conj(T[i]), Mpo, T[i]],
[[1, 3, 5], [1, 2, -1], [3, 4, -2, 2], [5, 4, -3]])
T[i + 1] = np.tensordot(U, T[i + 1], (1, 0))
for i in range(Ns - 1, 0, -1):
T[i], Eng1[i] = OptTSite(Mpo, HL[i], HR[i], T[i], Method=1)
# print i,Eng1[i]
U, T[i] = Sub.Mps_LQ0P(T[i])
HR[i - 1] = Sub.NCon(
[HR[i], T[i], Mpo, np.conj(T[i])],
[[1, 3, 5], [-1, 2, 1], [-2, 2, 3, 4], [-3, 4, 5]])
T[i - 1] = np.tensordot(T[i - 1], U, (2, 0))
#print (Eng1)
if abs(Eng1[1] - Eng0[1]) < 1.0e-7: # Eng1[1]是第一个非边界点
break
Eng0 = copy.copy(Eng1) # Eng0 = Eng1会导致0随1一起改变
print(Eng1 / float(Ns))
return T, Eng1[0] / float(Ns)
def OptTSite(Mpo, HL, HR, T, Method=0): # 一个T
DT = np.shape(T)
Dl = np.prod(DT)
if Method == 0:
A = Sub.NCon([HL, Mpo, HR], [[-1, 1, -4], [1, -5, 2, -2], [-6, 2, -3]])
A = Sub.Group(A, [[0, 1, 2], [3, 4, 5]])
Eig, V = LAs.eigsh(A, k=1, which='SA') # 本征值从小到大排列，对应能量，为负数
T = np.reshape(V, DT)
if Method == 1:
def UpdateV(V):
V = np.reshape(V, DT)
V = Sub.NCon([HL, V, Mpo, HR],
[[-1, 3, 1], [1, 2, 4], [3, 2, 5, -2], [4, 5, -3]])
V = np.reshape(V, [Dl])
return V
V0 = np.reshape(T, [Dl])
MV = LAs.LinearOperator((Dl, Dl), matvec=UpdateV)
Eig, V = LAs.eigsh(MV, k=1, which='SA', v0=V0) # 等价于直接求MV*v，而不知道MV具体多少
# print Eig
T = np.reshape(V, DT)
Eig = np.real(Eig)
return T, Eig
def Operator_Identity(Mpo, T):
Ns = len(T)
Dmpo = np.shape(Mpo)[0]
Dp = np.shape(Mpo)[1]
opL = [None] * Ns
opR = [None] * Ns
opL[0] = np.zeros((1, Dmpo, 1))
opL[0][0, 0, 0] = 1.0
opR[-1] = np.zeros((1, Dmpo, 1))
opR[-1][0, -1, 0] = 1.0
I_mpo = GetMpo_Identity(Dp)
for i in range(Ns - 1, 0, -1):
opR[i - 1] = Sub.NCon(
[opR[i], T[i], I_mpo, np.conj(T[i])],
[[1, 3, 5], [-1, 2, 1], [-2, 2, 3, 4], [-3, 4, 5]])
for i in range(0, Ns - 1):
opL[i +
1] = Sub.NCon([opL[i], np.conj(T[i]), I_mpo, T[i]],
[[1, 3, 5], [1, 2, -1], [3, 4, -2, 2], [5, 4, -3]])
return opL, opR
def OptT_TwoSite(Mpo, HL, HR, T1, T2, Method=1):
Dl = T1.shape[0]
Dm = T1.shape[2]
Dr = T2.shape[2]
Dp = Mpo.shape[1]
T = Sub.NCon([T1, T2], [[-1, -2, 1], [1, -3, -4]])
DT = np.shape(T)
DT_V = np.prod(DT)
if Method == 1:
def UpdateV(V):
V = np.reshape(V, DT)
V = Sub.NCon([HL, V, Mpo, Mpo, HR],
[[-1, 3, 1], [1, 2, 6, 5], [3, 2, 4, -2],
[4, 6, 7, -3], [5, 7, -4]])
V = np.reshape(V, [DT_V])
return V
V0 = np.reshape(T, [DT_V])
MV = LAs.LinearOperator((DT_V, DT_V), matvec=UpdateV)
Eig, V = LAs.eigsh(MV, k=1, which='SA', v0=V0)
T_mix = np.reshape(V, [Dl * Dp, Dp * Dr])
T1, s, T2, Dm = Sub.SplitSvd_Lapack(T_mix, Dm, 0)
T1 = T1.reshape(Dl, Dp, -1)
T2 = T2.reshape(-1, Dp, Dr)
return T1, T2, s, Eig
def UpdateV(V):
V = np.reshape(V, DT)
V = Sub.NCon([HL, V, Mpo, Mpo, HR],
[[-1, 3, 1], [1, 2, 6, 5], [3, 2, 4, -2],
[4, 6, 7, -3], [5, 7, -4]])
V = np.reshape(V, [DT_V])
return V
def Get_Value(op, T, Dp):
Ns = len(T)
Mpo = GetMpo_OneSite(op, Dp)
opL, opR = Operator_Identity(Mpo, T)
value = [None] * Ns
for site in range(Ns):
value[site] = Sub.NCon(
[opL[site], Mpo, opR[site], T[site],
np.conj(T[site])],
[[5, 3, 1], [3, 2, 7, 4], [8, 7, 6], [1, 2, 8], [5, 4, 6]])
return value
def InitH(Mpo, T):
Ns = len(T)
Dmpo = np.shape(Mpo)[0]
HL = [None] * Ns
HR = [None] * Ns
HL[0] = np.zeros((1, Dmpo, 1))
HL[0][0, 0, 0] = 1.0
HR[-1] = np.zeros((1, Dmpo, 1))
HR[-1][0, -1, 0] = 1.0
for i in range(Ns - 1, 0, -1):
HR[i -
1] = Sub.NCon([HR[i], T[i], Mpo, np.conj(T[i])],
[[1, 3, 5], [-1, 2, 1], [-2, 2, 3, 4], [-3, 4, 5]])
for i in range(0, Ns - 1):
HL[i +
1] = Sub.NCon([HL[i], np.conj(T[i]), Mpo, T[i]],
[[1, 3, 5], [1, 2, -1], [3, 4, -2, 2], [5, 4, -3]])
return HL, HR
def InitMps(Ns, Dp, Ds):
T = [None] * Ns
# Refer to page 17 on 20191021 slides
# Bond dimension of T varies along the chain
for i in range(Ns):
Dl = min(Dp**i, Dp**(Ns - i), Ds)
Dr = min(Dp**(i + 1), Dp**(Ns - 1 - i), Ds)
T[i] = np.random.rand(Dl, Dp, Dr)
U = np.eye(np.shape(T[-1])[-1])
for i in range(Ns - 1, 0, -1):
U, T[i] = Sub.Mps_LQP(T[i], U)
return T
def OptT(Mpo, HL, HR, T):
Ns = len(T)
Eng0 = np.zeros(Ns)
Eng1 = np.zeros(Ns)
File_Entopy = open('Entropy.txt', 'w')
for r in range(100):
Entropy = [None] * Ns
for i in range(Ns - 1):
T[i], T[i + 1], s, Eng1[i] = OptT_TwoSite(Mpo, HL[i], HR[i + 1],
T[i], T[i + 1])
T[i], U = Sub.Mps_QR0P(T[i])
HL[i + 1] = Sub.NCon(
[HL[i], np.conj(T[i]), Mpo, T[i]],
[[1, 3, 5], [1, 2, -1], [3, 4, -2, 2], [5, 4, -3]])
T[i + 1] = Sub.NCon([U, np.diag(s), T[i + 1]],
[[-1, 1], [1, 2], [2, -2, -3]])
Entropy[i] = Get_Entropy(s)
File_Entopy.write(str(Entropy)[1:-1] + '\n')
Entropy = [None] * Ns
for i in range(Ns - 1, 0, -1):
T[i - 1], T[i], s, Eng1[i] = OptT_TwoSite(Mpo, HL[i - 1], HR[i],
T[i - 1], T[i])
U, T[i] = Sub.Mps_LQ0P(T[i])
HR[i - 1] = Sub.NCon(
[HR[i], T[i], Mpo, np.conj(T[i])],
[[1, 3, 5], [-1, 2, 1], [-2, 2, 3, 4], [-3, 4, 5]])
T[i - 1] = Sub.NCon([U, np.diag(s), T[i - 1]],
[[2, -3], [1, 2], [-1, -2, 1]])
Entropy[i] = Get_Entropy(s)
File_Entopy.write(str(Entropy)[1:-1] + '\n')
if abs(Eng1[1] - Eng0[1]) < 1.0e-7:
break
Eng0 = copy.copy(Eng1)
File_Entopy.close()
print(Eng1 / float(Ns))
return T, Eng1[0] / float(Ns)
def UpdateV(V):
V = np.reshape(V, DT)
V = Sub.NCon([HL, V, Mpo, HR],
[[-1, 3, 1], [1, 2, 4], [3, 2, 5, -2], [4, 5, -3]])
V = np.reshape(V, [Dl])
return V