def test_u2p():
umat = uni10.Matrix(4,4,[0.,0.,0.9,0.,0.,0.,0.,0.1,0.9,0.,0.,0.,0.,0.1,0.,0.])
umat = uni10.Matrix(4,4,[-1., -0., -0., -1.,-0., -0., -1., -0., -0., -1., -0., -0.,-1.,-0.,-0.,1.])
U = uni10.UniTensor([bdi,bdi,bdo,bdo],'U')
U.putBlock(umat)
pstr, _ = pauli2body()
coef = []
for i in range(len(pstr)):
c = unitary2pauli(U,pstr[i],2)
coef.append(c)
print coef
def test_energy_lr(N_uni, l, l_d, r, r_d, q,qq,U,E1, E2, E3, E4, E5,E6,a_u,b_u): U.setLabel([-20,-40,20,40]) Iden=uni10.UniTensor(U.bond()) Bond_val=U.bond()[0].dim()*U.bond()[1].dim() matrix_Iden=uni10.Matrix(Bond_val, Bond_val) matrix_Iden.identity() Iden.putBlock(matrix_Iden) Iden.setLabel([-20,-40,20,40]) a_u.setLabel([20,13,1,2,3]) a_d=copy.copy(a_u) a_d.setLabel([-20,-13,-1,-2,-3]) b_u.setLabel([40,2,4,5,6]) b_d=copy.copy(b_u) b_d.setLabel([-40,-2,-4,-5,-6]) B=(((r*r_d)*U)*(l*l_d))*(N_uni) A=(((r*r_d)*Iden)*(l*l_d))*(N_uni) print 'E=', B[0]/A[0] a_ut=q*r a_ut.permute([20,4,5,3,2],3) print a_ut.similar(a_u),distance_two(a_u.getBlock(),a_ut.getBlock()) b_ut=qq*l b_ut.permute([40,3,4,5,6],3) print b_ut.similar(b_u), distance_two(b_u.getBlock(),b_ut.getBlock())
def intialize_unitary_list(L, L_lay, d, delta):
U_list = []
bdi_spin = uni10.Bond(uni10.BD_IN, d)
bdo_spin = uni10.Bond(uni10.BD_OUT, d)
Svd = []
matrix_random = uni10.Matrix(d * d, d * d)
for i in xrange(d * d):
for j in xrange(d * d):
if (i == j):
matrix_random[i * d * d + j] = 1.0
else:
matrix_random[i * d * d + j] = 0.0
#matrix_random.setIdentity()
for i in xrange(L / 2):
U_list.append([])
for i in xrange(L / 2):
for j in xrange(len(L_lay)):
U_uni10 = uni10.UniTensor([bdi_spin, bdi_spin, bdo_spin, bdo_spin],
"Unitary_uni10")
matrix_random1 = copy.copy(matrix_random)
matrix_random1.randomize()
matrix_random1 = matrix_random + (delta) * matrix_random1
Svd = matrix_random1.svd()
U_uni10.putBlock(Svd[0] * Svd[2])
U_list[i].append(U_uni10)
return U_list
def Mat_np_to_Uni(Mat_np):
d0 = np.size(Mat_np, 0)
d1 = np.size(Mat_np, 1)
Mat_uni = uni10.Matrix(d0, d1)
for i in xrange(d0):
for j in xrange(d1):
Mat_uni[i * d1 + j] = Mat_np[i, j]
return Mat_uni
def Initialize_function(Gamma, Landa):
for i in xrange(len(Gamma)):
Gamma[i].randomize()
D = Gamma[0].bond(1).dim()
matrix_Iden = uni10.Matrix(D, D)
matrix_Iden.identity()
for i in xrange(len(Landa)):
Landa[i].putBlock(matrix_Iden)
def final_test_distance(ap_u, bp_u, a_u, b_u,E1, E2, E3, E4, E5,E6,U,N_uni): U.setLabel([-20,-40,20,40]) H1=copy.copy(U) H1.transpose() H1.setLabel([-20,-40,30,50]) U.setLabel([30,50,20,40]) H=U*H1 H.permute([-20,-40,20,40],2) #H.setLabel([-20,-40,20,40]) H1.setLabel([-20,-40,20,40]) U.setLabel([-20,-40,20,40]) Iden=uni10.UniTensor(U.bond()) matrix_Iden=uni10.Matrix(U.bond()[0].dim()*U.bond()[1].dim(), U.bond()[2].dim()*U.bond()[3].dim()) matrix_Iden.identity() Iden.putBlock(matrix_Iden) Iden.setLabel([-20,-40,20,40]) a_u.setLabel([20,13,1,2,3]) a_d=copy.copy(a_u) a_d.setLabel([-20,-13,-1,-2,-3]) b_u.setLabel([40,2,4,5,6]) b_d=copy.copy(b_u) b_d.setLabel([-40,-2,-4,-5,-6]) ap_u.setLabel([20,13,1,2,3]) ap_d=copy.copy(ap_u) ap_d.setLabel([-20,-13,-1,-2,-3]) bp_u.setLabel([40,2,4,5,6]) bp_d=copy.copy(bp_u) bp_d.setLabel([-40,-2,-4,-5,-6]) #N=(((((E2*)*E1)*E3)*Iden)*((((E5)*E6)*E4))) # a_u=q*r # a_u.permute([20,4,5,3,2],3) # a_u.setLabel([0,1,2,3,4]) # #print a_ut.similar(a_u)#,a_ut.printDiagram() # # b_u=qq*l # b_u.permute([40,3,4,5,6],3) # b_u.setLabel([0,1,2,3,4]) # #print b_ut.similar(b_u) A1=(((((E2*(a_u*a_d))*E1)*E3)*H)*(((((b_u*b_d)*E5)*E6)*E4))) A2=((((E2*(ap_u*ap_d))*E1)*E3)*Iden)*(((((bp_u*bp_d)*E5)*E6)*E4)) A3=((((E2*(a_u*ap_d))*E1)*E3)*U)*(((((b_u*bp_d)*E5)*E6)*E4)) A4=((((E2*(ap_u*a_d))*E1)*E3)*H1)*(((((bp_u*b_d)*E5)*E6)*E4)) A=A1+A2+(-1.00)*A3+(-1.00)*A4 return A
def sqt(Landa2):
invLanda2 = uni10.UniTensor(Landa2.bond())
invL2 = uni10.Matrix(Landa2.bond()[0].dim(), Landa2.bond()[1].dim())
D = Landa2.bond()[0].dim()
for i in xrange(Landa2.bond()[0].dim()):
for j in xrange(Landa2.bond()[0].dim()):
invL2[i * D + j] = ((Landa2[i * D + j])**(1.00 / 2.00))
invLanda2.putBlock(invL2)
return invLanda2
def vec2uni(v, L):
bond_dim = 2
vl = list(v)
vl10 = uni10.Matrix(2**L, 1, vl)
bdi = uni10.Bond(uni10.BD_IN, bond_dim)
bdo = uni10.Bond(uni10.BD_OUT, bond_dim)
vtensor = uni10.UniTensor([bdi] * L, 'GS')
vtensor.putBlock(vl10)
return vtensor
def inverse(Landa2):
invLanda2 = uni10.UniTensor(Landa2.bond())
invL2 = uni10.Matrix(Landa2.bond()[0].dim(), Landa2.bond()[1].dim())
D = Landa2.bond()[0].dim()
for i in xrange(Landa2.bond()[0].dim()):
for j in xrange(Landa2.bond()[0].dim()):
invL2[i * D + j] = 0 if ((Landa2[i * D + j].real) < 1.0e-12) else (
1.00 / (Landa2[i * D + j].real))
invLanda2.putBlock(invL2)
return invLanda2
def Reduction_lastbond(U_up_1, n, Letter):
Mat=U_up_1.getBlock()
dim0=U_up_1.bond(0).dim()
dim1=U_up_1.bond(1).dim()
dim2=U_up_1.bond(2).dim()
dim3=U_up_1.bond(3).dim()
if Letter is 'up':
Mat1=uni10.Matrix(dim0*dim1, dim2)
Mat1.set_zero()
for i in xrange(dim0):
for j in xrange(dim1):
for m in xrange(dim2):
Mat1[i*dim1*dim2+j*dim2+m]=U_up_1[i*dim1*dim2*dim3+j*dim2*dim3+m*dim3+n]
bond_list=list(U_up_1.bond())
#print list(bond_list)
bond_list=list(bond_list)
bond_list.pop()
#print bond_list
Uni_tensor=uni10.UniTensor(bond_list,U_up_1.getName())
Uni_tensor.putBlock(Mat1)
#print Uni_tensor.printDiagram(), n
return Uni_tensor
elif Letter is 'down':
Mat1=uni10.Matrix(dim0, dim2*dim3)
Mat1.set_zero()
for i in xrange(dim0):
for j in xrange(dim3):
for m in xrange(dim2):
Mat1[i*dim3*dim2+m*dim3+j]=U_up_1[i*dim1*dim2*dim3+n*dim2*dim3+m*dim3+j]
bond_list=list(U_up_1.bond())
#print list(bond_list)
bond_list=list(bond_list)
A=bond_list.pop()
B=bond_list.pop()
C=bond_list.pop()
bond_list.append(B)
bond_list.append(A)
#print bond_list
Uni_tensor=uni10.UniTensor(bond_list,U_up_1.getName())
Uni_tensor.putBlock(Mat1)
#print Uni_tensor.printDiagram(), n
return Uni_tensor
def l_optimum_full(l, r, l_d, r_d, lp, rp, lp_d, rp_d ,N_uni,U): U.setLabel([-20,-40,20,40]) H1=copy.copy(U) H1.transpose() H1.setLabel([-20,-40,20,40]) Iden=uni10.UniTensor(U.bond()) Bond_val=U.bond()[0].dim()*U.bond()[1].dim() matrix_Iden=uni10.Matrix(Bond_val, Bond_val) matrix_Iden.identity() Iden.putBlock(matrix_Iden) Iden.setLabel([-20,-40,20,40]) A2=(((rp*rp_d)*N_uni)*Iden) A2.permute([2,40,3,-2,-40,-3],3) A2_trans=copy.copy(A2) A2_trans.transpose() A2=A2+A2_trans A3=((l)*U*(r*rp_d))*N_uni A3.permute([-2,-40,-3],0) A3p=((l_d)*U*(rp*r_d))*N_uni A3p.permute([2,40,3],0) A3=A3+A3p svd=A2.getBlock().svd() Landa=inv(svd[1]) #print Landa.getBlock()*svd[1] v=copy.copy(svd[2]) v.transpose() u=svd[0] u.transpose() s=Landa.getBlock() A2_inv=v*s*u A2_mat=A2.getBlock() #distance_iden_val=distance_iden(A2_mat,A2_inv) #print 'distance=', distance_iden_val A=A3.getBlock() A=A*A2_inv A3.putBlock(A) A3.setLabel([2,40,3]) A3.permute([2,40,3],2) lf=copy.copy(A3) lf_d=copy.copy(lf) lf_d.setLabel([-2,-40,-3]) return lf, lf_d
def r_optimum_full(l, r, l_d, r_d, lp, rp, lp_d, rp_d ,N_uni,U): U.setLabel([-20,-40,20,40]) H1=copy.copy(U) H1.transpose() H1.setLabel([-20,-40,30,50]) #print H1, U Iden=uni10.UniTensor(U.bond()) d=U.bond()[0].dim()*U.bond()[1].dim() matrix_Iden=uni10.Matrix(d, d) matrix_Iden.identity() Iden.putBlock(matrix_Iden) Iden.setLabel([-20,-40,20,40]) A2=(((lp*lp_d)*N_uni)*Iden) A2.permute([3,20,1,-3,-20,-1],3) A2_trans=copy.copy(A2) A2_trans.transpose() A2=A2+A2_trans A3=((r)*U*(l*lp_d))*N_uni A3.permute([-3,-20,-1],0) A3p=((r_d)*U*(l_d*lp))*N_uni A3p.permute([3,20,1],0) A3=A3+A3p svd=A2.getBlock().svd() Landa=inv(svd[1]) #print Landa.getBlock()*svd[1] v=copy.copy(svd[2]) v.transpose() u=svd[0] u.transpose() s=Landa.getBlock() A2_inv=v*s*u A2_mat=A2.getBlock() #distance_iden_val=distance_iden(A2_mat,A2_inv) #print 'distance1=', distance_iden_val #print A2.getBlock()*A2_inv A=A3.getBlock() A=A*A2_inv A3.putBlock(A) A3.setLabel([3,20,1]) A3.permute([3,20,1],2) rf=copy.copy(A3) rf_d=copy.copy(rf) rf_d.setLabel([-3,-20,-1]) return rf, rf_d
def transverseIsing(h):
spin = 0.5
sx = 0.5 * (matSp() + matSm())
sz = matSz()
iden = uni10.Matrix(2, 2, [1, 0, 0, 1])
ham =uni10.otimes(2*sz,2*sz)*(-1) \
+0.25*float(h)*(uni10.otimes(iden,2*sx)+uni10.otimes(2*sx,iden))
dim = int(spin * 2 + 1)
bdi = uni10.Bond(uni10.BD_IN, dim)
bdo = uni10.Bond(uni10.BD_OUT, dim)
H = uni10.UniTensor([bdi, bdi, bdo, bdo], "TFIM")
H.putBlock(ham)
return H
def Ham(h):
spin = 0.5
sx = (matSp() + matSm())
sz = matSz()
iden = uni10.Matrix(2, 2, [1, 0, 0, 1])
ham = uni10.otimes(sz, sz) * (-2.00) + (-0.500) * float(h) * (
uni10.otimes(iden, sx) + uni10.otimes(sx, iden))
dim = int(spin * 2 + 1)
bdi = uni10.Bond(uni10.BD_IN, dim)
bdo = uni10.Bond(uni10.BD_OUT, dim)
H = uni10.UniTensor([bdi, bdi, bdo, bdo], "TFIM")
H.putBlock(ham)
return H
def Iden_uni10(d):
bdi=uni10.Bond(uni10.BD_IN, d)
bdo=uni10.Bond(uni10.BD_OUT, d)
Iden_Matrix=uni10.Matrix(d*d,d)
for i in xrange(d):
for j in xrange(d):
for m in xrange(d):
if i is j and j is m:
Iden_Matrix[i*d+j,m]=1
else:
Iden_Matrix[i*d+j,m]=0
Iden_uni10=uni10.UniTensor([bdi,bdi,bdo], 'Iden_uni10')
Iden_uni10.putBlock(Iden_Matrix)
return Iden_uni10
def transverseIsing(h):
spin = 0.5
sx = matSx()
sy = matSy()
sz = matSz()
iden = uni10.Matrix(2, 2, [1, 0, 0, 1])
ham = uni10.otimes(sz, sz) * (-1) + (-0.2500) * float(h) * (
uni10.otimes(iden, sx) + uni10.otimes(sx, iden))
dim = int(spin * 2 + 1)
bdi = uni10.Bond(uni10.BD_IN, dim)
bdo = uni10.Bond(uni10.BD_OUT, dim)
H = uni10.UniTensor([bdi, bdi, bdo, bdo], "TFIM")
H.putBlock(ham)
return H
def Heisenberg(h):
spin = 0.5
sx = matSx()
sy = matSy()
sz = matSz()
iden = uni10.Matrix(2, 2, [1, 0, 0, 1])
ham = (float(h) * uni10.otimes(sz, sz) * (1.00 / 4.00) +
(1.00 / 4.00) * uni10.otimes(sx, sx) +
(-1.00 / 4.00) * uni10.otimes(sy, sy))
dim = int(spin * 2 + 1)
bdi = uni10.Bond(uni10.BD_IN, dim)
bdo = uni10.Bond(uni10.BD_OUT, dim)
H = uni10.UniTensor([bdi, bdi, bdo, bdo], "Heisenberg")
H.putBlock(ham)
return H
def distance_iden(A2,A2_inv):
A=A2*A2_inv
d=int(A.row())
matrixI=uni10.Matrix(d, d)
for i in xrange(d):
for j in xrange(d):
if(i==j):
matrixI[i*d+j]=1.0
else:
matrixI[i*d+j]=0.0
sum=0
for i in xrange(d):
for j in xrange(d):
sum=abs(A[i*d+j]+(-1.00)*matrixI[i*d+j])
return sum
def Obtain_grad(l, r, l_d, r_d, lp, rp, lp_d, rp_d ,N_uni,U): U.setLabel([-20,-40,20,40]) Iden=uni10.UniTensor(U.bond()) d=U.bond()[0].dim()*U.bond()[1].dim() matrix_Iden=uni10.Matrix(d, d) matrix_Iden.identity() Iden.putBlock(matrix_Iden) Iden.setLabel([-20,-40,20,40]) A2=(((lp*lp_d*rp)*N_uni)*Iden) A2.permute([-3,-20,-1],0) D_r=copy.copy(A2) A2=(((lp*lp_d*rp_d)*N_uni)*Iden) A2.permute([3,20,1],0) D_r=D_r+A2 A3=((r)*U*(l*lp_d))*N_uni A3.permute([-3,-20,-1],0) D_r=D_r+(-1.00)*A3 A3p=((r_d)*U*(l_d*lp))*N_uni A3p.permute([3,20,1],0) D_r=D_r+(-1.00)*A3p D_r.setLabel([3,20,1]) D_r.permute([3,20,1],2) A2=(((rp*rp_d*lp)*N_uni)*Iden) A2.permute([-2,-40,-3],0) D_l=copy.copy(A2) A2=(((rp*rp_d*lp_d)*N_uni)*Iden) A2.permute([2,40,3],0) D_l=A2+D_l A3=((l)*U*(r*rp_d))*N_uni A3.permute([-2,-40,-3],0) D_l=D_l+(-1.00)*A3 A3p=((l_d)*U*(rp*r_d))*N_uni A3p.permute([2,40,3],0) D_l=D_l+(-1.00)*A3p D_l.setLabel([2,40,3]) D_l.permute([2,40,3],2) return D_r, D_l
def exp_matrix(H_direct, Gamma, U_update):
dim0 = int(H_direct.row())
dim1 = int(H_direct.col())
M0 = np.zeros((dim0, dim1))
M_return1 = uni10.Matrix(dim0, dim1)
#t0 = time.time()
for i in xrange(dim0):
for j in xrange(dim1):
M0[i, j] = H_direct[i * dim1 + j]
#print time.time() - t0, "replacing"
M0 = expm(+Gamma * M0)
for i in xrange(dim0):
for j in xrange(dim1):
M_return1[i * dim1 + j] = M0[i, j]
M_return1 = M_return1 * U_update
return M_return1
def Distance(l, r, lp, rp ,N_uni, U): U.setLabel([-20,-40,20,40]) H1=copy.copy(U) H1.transpose() H1.setLabel([-20,-40,30,50]) U.setLabel([30,50,20,40]) H=U*H1 H.permute([-20,-40,20,40],2) #H.setLabel([-20,-40,20,40]) H1.setLabel([-20,-40,20,40]) U.setLabel([-20,-40,20,40]) Iden=uni10.UniTensor(U.bond()) matrix_Iden=uni10.Matrix(U.bond()[0].dim()*U.bond()[1].dim(), U.bond()[2].dim()*U.bond()[3].dim()) matrix_Iden.identity() Iden.putBlock(matrix_Iden) Iden.setLabel([-20,-40,20,40]) lp_d=copy.copy(lp) rp_d=copy.copy(rp) rp_d.setLabel([-3,-20,-1]) lp_d.setLabel([-2,-40,-3]) l_d=copy.copy(l) r_d=copy.copy(r) r_d.setLabel([-3,-20,-1]) l_d.setLabel([-2,-40,-3]) A1=((((r*r_d)*H)*(N_uni))*l*l_d) A2=((((rp*rp_d)*Iden)*(N_uni))*lp*lp_d) A3=((((r*rp_d)*U)*(N_uni))*l*lp_d) A4=((((rp*r_d)*H1)*(N_uni))*lp*l_d) A=A1+A2+(-1.00)*A3+(-1.00)*A4 return A
def matSy():
spin = 0.5
dim = int(spin * 2 + 1)
Mat = (1.0) * uni10.Matrix(dim, dim, [0.0, -1.00, 1.00, 0.00])
return Mat
def matSz():
spin = 0.5
dim = int(spin * 2 + 1)
Mat = (1.0) * uni10.Matrix(dim, dim, [1.0, 0, 0, -1.0])
return Mat
def mat2uni(mat, lmat):
mat = mat.reshape(lmat**2)
mat = list(mat)
unimat = uni10.Matrix(lmat, lmat, mat)
return unimat
def matSm(): spin = 1.0 dim = int(spin * 2 + 1) return np.sqrt(2)*uni10.Matrix(dim, dim, [0, 0, 0, 1, 0, 0, 0, 1, 0])
def matSx():
spin = 0.5
dim = int(spin * 2 + 1)
return uni10.Matrix(dim, dim, [0.0, 1.0, 1.00, 0.0])
def bondrm(T, L, bidx):
invL = uni10.Matrix(L.row(), L.col(), True)
for i in xrange(L.elemNum()):
invL[i] = 0 if L[i] == 0 else 1.0 / L[i]
bondcat(T, invL, bidx)
def matIden():
spin_t = 0.5
dimT = int(2 * spin_t + 1)
Mat = uni10.Matrix(dimT, dimT, [1, 0, 0, 1])
return Mat
import sys
import pyUni10 as uni10
import copy
# Spin 1/2 Heisenberg hamiltonian
elem = [1.0/4, 0, 0, 0,\
0, -1.0/4, 1.0/2, 0,\
0, 1.0/2, -1.0/4, 0,\
0, 0, 0, 1.0/4]
H = uni10.Matrix(4, 4, elem)
# Diagonlize H
print H
results = H.eigh()
print "The eigen values:\n\n", results[0]
print "The eigen vectors:\n\n", results[1]
# Access element in a diagonal matrix
D = results[0]
print "D[2] =", D[2]
# Assign element
print "\nAssign D[3] = 7\n"
D[3] = 7
print D
# Access element
print "H[5] =", H[5]
#Make a pure density matrix from ground state
sys.path.append("/Users/sunchong/CodingDir/TNMBL")
from qsampl import *
from pauli2body import *
import pyUni10 as uni10
from scipy import linalg as sla
import copy
L=6
# ### bond construction
sx = np.array([0.,1.,1.,0.]).reshape(2,2)
sy = np.array([0.,-1,1,0.]).reshape(2,2)
sz = np.array([1.,0.,0.,-1.]).reshape(2,2)
si = np.eye(2)
Sx = uni10.Matrix(2,2,[0.,1.,1.,0.])
Sy = uni10.Matrix(2,2,[0.,-1,1,0.])
Sz = uni10.Matrix(2,2,[1.,0.,0.,-1.])
Si = uni10.Matrix(2,2,[1.,0.,0.,1.])
hm = -1.* np.kron(sx,sx)-0.5*(np.kron(sz,si)+np.kron(si,sz))
hl = -1.* np.kron(sx,sx)-0.5*np.kron(si,sz)-np.kron(sz,si)
hr = -1.* np.kron(sx,sx)-np.kron(si,sz)-0.5*np.kron(sz,si)
bdi = uni10.Bond(uni10.BD_IN,2)
bdo = uni10.Bond(uni10.BD_OUT,2)
u11 = np.einsum('ij,kl->ikjl',sx,sz)
u12 = np.einsum('ij,kl->ikjl',si,sx)
u13 = np.einsum('ij,kl->ikjl',sz,sz)
