def pauli4body():
'''
Tensors for 4-body Pauli strings.
'''
bond_dim = 2
iden = matIden()
sx = matSx()
sy = matSy()
sz = matSz()
bdi = uni10.Bond(uni10.BD_IN, bond_dim)
bdo = uni10.Bond(uni10.BD_OUT, bond_dim)
pauli1b = [iden, sx, sy, sz]
pauli4b = []
pauli2b = []
l2b = 16
for i in xrange(4):
for j in xrange(4):
mat = uni10.otimes(pauli1b[i], pauli1b[j])
pauli2b.append(mat)
for i in xrange(l2b):
for j in xrange(l2b):
mat = uni10.otimes(pauli2b[i], pauli2b[j])
P = uni10.UniTensor([bdi, bdi, bdi, bdi, bdo, bdo, bdo, bdo])
P.putBlock(mat)
pauli4b.append(P)
return pauli4b
def pauli6body():
'''
Tensors for 6-body Pauli strings.
'''
bond_dim = 2
iden = matIden()
sx = matSx()
sy = matSy()
sz = matSz()
bdi = uni10.Bond(uni10.BD_IN, bond_dim)
bdo = uni10.Bond(uni10.BD_OUT, bond_dim)
pauli1b = [iden, sx, sy, sz]
pauli6b = []
bonds = [bdi] * 6 + [bdo] * 6
pauli3b = []
for i in xrange(4):
for j in xrange(4):
for k in xrange(4):
mat = uni10.otimes(uni10.otimes(pauli1b[i], pauli1b[j]),
pauli1b[k])
pauli3b.append(mat)
l3b = 64
for i in xrange(l3b):
for j in xrange(l3b):
mat = uni10.otimes(pauli3b[i], pauli3b[j])
P = uni10.UniTensor(bonds)
P.putBlock(mat)
pauli6b.append(P)
return pauli6b
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 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 Heisenberg(D, Delta, h, J):
iden = matId()
sm = matSm()
sp = matSp()
sz = matSz()
sz2 = matSz2()
ham = float(J)*(0.5*(uni10.otimes(sm,sp)+uni10.otimes(sp,sm))+float(Delta)*uni10.otimes(sz,sz))
ham += 0.5*float(h)*(uni10.otimes(iden,sz)+uni10.otimes(sz,iden))
ham += 0.5*float(D)*(uni10.otimes(iden,sz2)+uni10.otimes(sz2,iden))
spin = 1.0
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 get_Hbond_tensor(model,bond_idx,L,J=1.0,Fieldz=1.0,hzlist=[],bond_dim=2,\
avebond=True):
#TODO put Z terms only into the even bonds
'''
_________________________________________________________________
Ising Model: | Heisenberg Model
-J XX - h Z (h=Fieldz) | J(XX + ZZ - YY) + h Z (h=hzlist)
____________________________|____________________________________
Result in a tensor:
_____
0 __| |__ 2
1 __| H |__ 3
|_____|
_________________________________________________________________
'''
# make matrix
sx = utils.matSx()
sy = utils.matSy()
sz = utils.matSz()
s0 = utils.matIden()
if (model == 'Ising'):
Hbond_mat = (-1.*J)*uni10.otimes(sx,sx)
if avebond:
if (bond_idx == 0):
Hbond_mat += (-1.0*Fieldz)*uni10.otimes(sz,s0)
Hbond_mat += (-0.5*Fieldz)*uni10.otimes(s0,sz)
elif (bond_idx == L-2):
Hbond_mat += (-0.5*Fieldz)*uni10.otimes(sz,s0)
Hbond_mat += (-1.0*Fieldz)*uni10.otimes(s0,sz)
else:
Hbond_mat += (-0.5*Fieldz)*uni10.otimes(sz,s0)
Hbond_mat += (-0.5*Fieldz)*uni10.otimes(s0,sz)
else:
if (bond_idx%2 == 0):
Hbond_mat += (-1.0*Fieldz)*uni10.otimes(sz,s0)
Hbond_mat += (-1.0*Fieldz)*uni10.otimes(s0,sz)
elif (model == 'Heisenberg'):
#TODO try evenly distributed bond
Hbond_mat = (1.*J)*uni10.otimes(sx,sx)
Hbond_mat += (-1.*J)*uni10.otimes(sy,sy)
Hbond_mat += (1.*J)*uni10.otimes(sz,sz)
if avebond:
if (bond_idx == 0):
Hbond_mat += (1. *hzlist[0])*uni10.otimes(sz,s0)
Hbond_mat += (0.5*hzlist[1])*uni10.otimes(s0,sz)
elif (bond_idx == L-2):
Hbond_mat += (0.5*hzlist[L-2])*uni10.otimes(sz,s0)
Hbond_mat += (1. *hzlist[L-1])*uni10.otimes(s0,sz)
else:
Hbond_mat += (0.5*hzlist[bond_idx])*uni10.otimes(sz,s0)
Hbond_mat += (0.5*hzlist[bond_idx+1])*uni10.otimes(s0,sz)
else:
if (bond_idx%2 == 0):
Hbond_mat += (1.*hzlist[bond_idx])*uni10.otimes(sz,s0)
Hbond_mat += (1.*hzlist[bond_idx+1])*uni10.otimes(s0,sz)
else:
raise Exception("The model can only be Ising or Heisenberg!")
# construct tensor
bdi = uni10.Bond(uni10.BD_IN, bond_dim)
bdo = uni10.Bond(uni10.BD_OUT, bond_dim)
Hbond = uni10.UniTensor([bdi,bdi,bdo,bdo],'Hbond')
Hbond.putBlock(Hbond_mat)
Hbond.setLabel([0,1,2,3])
return Hbond
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)
u21 = np.einsum('ij,kl->ikjl',sz,sx)
u22 = np.einsum('ij,kl->ikjl',sz,si)
u23 = np.einsum('ij,kl->ikjl',sx,sx)
U11 = uni10.UniTensor([bdi,bdi,bdo,bdo])
U11.putBlock(uni10.otimes(Sx,Sz))
U12 = uni10.UniTensor([bdi,bdi,bdo,bdo])
U12.putBlock(uni10.otimes(Si,Sx))
U13 = uni10.UniTensor([bdi,bdi,bdo,bdo])
U13.putBlock(uni10.otimes(Sz,Sz))
U21 = uni10.UniTensor([bdi,bdi,bdo,bdo])
U21.putBlock(uni10.otimes(Sz,Sx))
U22 = uni10.UniTensor([bdi,bdi,bdo,bdo])
U22.putBlock(uni10.otimes(Sz,Si))
U23 = uni10.UniTensor([bdi,bdi,bdo,bdo])
U23.putBlock(uni10.otimes(Sx,Sx))
Ulist = [[U11,U21],[U12,U22],[U13,U23]]
def test_Umpo(ind, dag=False):
u11 = np.einsum('ij,kl->ikjl', sx, sz)
u12 = np.einsum('ij,kl->ikjl', si, sx)
u13 = np.einsum('ij,kl->ikjl', sz, sz)
u21 = np.einsum('ij,kl->ikjl', sz, sx)
u22 = np.einsum('ij,kl->ikjl', sz, si)
u23 = np.einsum('ij,kl->ikjl', sx, sx)
U11 = uni10.UniTensor([bdi, bdi, bdo, bdo])
U11.putBlock(uni10.otimes(Sx, Sz))
U12 = uni10.UniTensor([bdi, bdi, bdo, bdo])
U12.putBlock(uni10.otimes(Si, Sx))
U13 = uni10.UniTensor([bdi, bdi, bdo, bdo])
U13.putBlock(uni10.otimes(Sz, Sz))
U21 = uni10.UniTensor([bdi, bdi, bdo, bdo])
U21.putBlock(uni10.otimes(Sz, Sx))
U22 = uni10.UniTensor([bdi, bdi, bdo, bdo])
U22.putBlock(uni10.otimes(Sz, Si))
U23 = uni10.UniTensor([bdi, bdi, bdo, bdo])
U23.putBlock(uni10.otimes(Sx, Sx))
Ulist = [[U11, U21], [U12, U22], [U13, U23]]
if ind == 0:
print "Bond ID: Left Bond"
U = get_unitary4bond_up(Ulist, L, 0)
u = np.einsum('ijkl,lmnp->ijmknp', u11, u21).reshape(8, 8)
if dag is False:
print "Numpy result: "
print u
print "My result: "
print U.getBlock()
else:
U.permute([5, 6, 7, 2, 3, 4], 3)
U.setLabel([8, 9, 10, 0, 1, 4])
print u.T
print U.getBlock()
if ind == 1:
print "Bond ID: Right Bond"
U = get_unitary4bond_up(Ulist, L, L - 2)
u = np.einsum('ijkl,mknp->mijnpl', u13, u22).reshape(8, 8)
#print u13.reshape(4,4)
#print u22.reshape(4,4)
if dag is False:
print "Numpy result: "
print u
print "My result: "
print U.getBlock()
print U
else:
U.permute([5, 6, 7, 4, 2, 3], 3)
U.setLabel([8, 9, 10, 4, 0, 1])
print u.T
print U.getBlock()
if ind == 2:
print "Bond ID: Odd Bond"
U = get_unitary4bond_up(Ulist, L, 1)
u = np.einsum('ijkl,lmnp,qrms -> ijqrknps', u11, u21,
u12).reshape(16, 16)
#print u11.reshape(4,4)
#print u12.reshape(4,4)
#print u21.reshape(4,4)
if dag is False:
print u
print U.getBlock()
else:
U.permute([5, 6, 7, 8, 4, 2, 3, -4], 4)
U.setLabel([9, 10, 11, 12, 4, 0, 1, -4])
print u.T
print U.getBlock()
if ind == 3:
print "Bond ID: Even Bond"
U = get_unitary4bond_up(Ulist, L, 2)
u = np.einsum('ijkl,nkmp,lqrs -> nijqmprs', u12, u21,
u22).reshape(16, 16)
#print u12.reshape(4,4)
#print u21.reshape(4,4)
#print u22.reshape(4,4)
if dag is False:
print u
print U.getBlock()
else:
U.permute([5, 6, 7, 8, 4, 2, 3, -4], 4)
U.setLabel([9, 10, 11, 12, 4, 0, 1, -4])
print u.T
print U.getBlock()
def test_UHU(ind):
u11 = np.einsum('ij,kl->ikjl', sx, sz)
u12 = np.einsum('ij,kl->ikjl', si, sx)
u13 = np.einsum('ij,kl->ikjl', sz, sz)
u21 = np.einsum('ij,kl->ikjl', sz, sx)
u22 = np.einsum('ij,kl->ikjl', sz, si)
u23 = np.einsum('ij,kl->ikjl', sx, sx)
U11 = uni10.UniTensor([bdi, bdi, bdo, bdo])
U11.putBlock(uni10.otimes(Sx, Sz))
U12 = uni10.UniTensor([bdi, bdi, bdo, bdo])
U12.putBlock(uni10.otimes(Si, Sx))
U13 = uni10.UniTensor([bdi, bdi, bdo, bdo])
U13.putBlock(uni10.otimes(Sz, Sz))
U21 = uni10.UniTensor([bdi, bdi, bdo, bdo])
U21.putBlock(uni10.otimes(Sz, Sx))
U22 = uni10.UniTensor([bdi, bdi, bdo, bdo])
U22.putBlock(uni10.otimes(Sz, Si))
U23 = uni10.UniTensor([bdi, bdi, bdo, bdo])
U23.putBlock(uni10.otimes(Sx, Sx))
Ulist = [[U11, U21], [U12, U22], [U13, U23]]
#Hm = get_Hbond_tensor(edge=False)
#Hl = get_Hbond_tensor(edge=True, edgeside='L')
#Hr = get_Hbond_tensor(edge=True, edgeside='R')
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)
UHU = contract_UHU(6, Ulist)
#print UHU[0]
if ind == 0: # LEFT EDGE
u11_ = u11.reshape(4, 4)
uhu1 = np.dot(u11_.T, np.dot(hl, u11_))
uhu1 = uhu1.reshape(2, 2, 2, 2)
u21T = (u21.reshape(4, 4).T).reshape(2, 2, 2, 2)
uhu = np.einsum('ijkl,mknp,plrs->mijnrs', u21T, uhu1,
u21).reshape(8, 8)
print uhu
print UHU[0].getBlock()
elif ind == 1: # Interior Odd Bonds
hm_ = hm.reshape(2, 2, 2, 2)
u11T = (u11.reshape(4, 4).T).reshape(2, 2, 2, 2)
u12T = (u12.reshape(4, 4).T).reshape(2, 2, 2, 2)
u21T = (u21.reshape(4, 4).T).reshape(2, 2, 2, 2)
uhu1 = np.einsum('ijkl,mnpq,lprs,kruv,sqwx->ijmnuvwx', u11T, u12T, hm_,
u11, u12)
uhu = np.einsum('ijkl,mklnpqrs,qruv->mijnpuvs', u21T, uhu1,
u21).reshape(16, 16)
print uhu
print UHU[1].getBlock()
elif ind == 2:
u12_ = u12.reshape(4, 4)
uhu1 = np.dot(u12_.T, np.dot(hm, u12_)).reshape(2, 2, 2, 2)
u21T = (u21.reshape(4, 4).T).reshape(2, 2, 2, 2)
u22T = (u22.reshape(4, 4).T).reshape(2, 2, 2, 2)
uhu = np.einsum('ijkl,mnpq,lpxy,kxrs,yquv->ijmnrsuv', u21T, u22T, uhu1,
u21, u22).reshape(16, 16)
print uhu
print UHU[2].getBlock()
else:
u13_ = u13.reshape(4, 4)
uhu1 = np.dot(u13_.T, np.dot(hr, u13_)).reshape(2, 2, 2, 2)
u22T = (u22.reshape(4, 4).T).reshape(2, 2, 2, 2)
uhu = np.einsum('ijkl,lmqn,kqrs->ijmrsn', u22T, uhu1,
u22).reshape(8, 8)
print uhu
print UHU[-1].getBlock()
