def nAverage_fpeps2by2(peps0):
debug = False
nr, nc = peps0.shape
# <P|P>
tmp = peps0[0, 1].copy()
p23 = tmp.ptys[0]
d23 = tmp.dims[0]
p1 = tmp.ptys[2]
d1 = tmp.dims[2]
swap = fpeps_util.genSwap(p23, d23, p1, d1)
peps1 = peps.copy(peps0)
peps1[0, 1] = einsum('pludr,pUuP->PlUdr', peps1[0, 1], swap)
ovlp = peps.dot(peps1, peps1)
if debug:
print
print "Ovlp=", peps.dot(peps0, peps0)
print "Ovlp=", ovlp
nloc = fpeps_util.genNloc()
# \hat{N} is a sum of local terms
nav = 0.0
for i in range(nr):
for j in range(nc):
peps2 = peps.copy(peps1)
peps2[i, j] = einsum('Pp,pludr->Pludr', nloc, peps1[i, j])
nav += peps.dot(peps1, peps2)
return ovlp, nav
def localRotation(peps0,theta):
rmat = fpeps_util.genRmat(theta)
nr,nc = peps0.shape
peps1 = peps.copy(peps0)
for i in range(nr):
for j in range(nc):
peps1[i,j] = einsum('qp,pludr->qludr',rmat,peps1[i,j])
return peps1
def nAverage_fpeps3by3(peps0):
nr, nc = peps0.shape
# <P|P>
peps0b = reflection(peps0)
peps1b = peps.copy(peps0b)
for i in range(nr):
for j in range(nc):
tmp = peps1b[i, j].copy()
p0 = tmp.ptys[1]
d0 = tmp.dims[1]
p1 = tmp.ptys[2]
d1 = tmp.dims[2]
swapLU = fpeps_util.genSwap(p0, d0, p1, d1)
tmp = einsum('luUL,pLUdr->pludr', swapLU, tmp)
p0 = tmp.ptys[4]
d0 = tmp.dims[4]
p1 = tmp.ptys[3]
d1 = tmp.dims[3]
swapRD = fpeps_util.genSwap(p0, d0, p1, d1)
tmp = einsum('RDdr,pluDR->pludr', swapRD, tmp)
peps1b[i, j] = tmp.copy()
ovlp = fpeps_util.fdot(peps0b, peps1b)
if debug:
print
print "Ovlp=", peps.dot(peps0, peps0)
print "Ovlp=", ovlp
nloc = fpeps_util.genNloc()
# \hat{N} is a sum of local terms
nav = 0.0
for j in range(nc):
for i in range(nr):
# Measure each local occupation <Ni>
peps2b = peps.copy(peps1b)
peps2b[i, j] = einsum('Pp,pludr->Pludr', nloc, peps1b[i, j])
nii = fpeps_util.fdot(peps0b, peps2b)
nav += nii
print '(i,j)=', (i, j), '<Nloc>=', nii, nii / ovlp
print 'nav=', ovlp, nav, nav / ovlp
return ovlp, nav
def energy_fpeps3by3(peps0):
nr, nc = peps0.shape
# <P|P>
peps0b = reflection(peps0)
peps1b = peps.copy(peps0b)
for i in range(nr):
for j in range(nc):
tmp = peps1b[i, j].copy()
p0 = tmp.ptys[1]
d0 = tmp.dims[1]
p1 = tmp.ptys[2]
d1 = tmp.dims[2]
swapLU = fpeps_util.genSwap(p0, d0, p1, d1)
tmp = einsum('luUL,pLUdr->pludr', swapLU, tmp)
p0 = tmp.ptys[4]
d0 = tmp.dims[4]
p1 = tmp.ptys[3]
d1 = tmp.dims[3]
swapRD = fpeps_util.genSwap(p0, d0, p1, d1)
tmp = einsum('RDdr,pluDR->pludr', swapRD, tmp)
peps1b[i, j] = tmp.copy()
ovlp = fpeps_util.fdot(peps0b, peps1b)
if debug:
print
print "Ovlp=", peps.dot(peps0, peps0)
print "Ovlp=", ovlp
etot = 0.0
# <P|U[i]|P>
if debug: print "\nU-terms:"
uterm = fpeps_util.genUterm(U)
for j in range(nc):
for i in range(nr):
peps2 = peps.copy(peps0)
peps2[i, j] = einsum('Pp,pludr->Pludr', uterm, peps0[i, j])
peps2b = reflection(peps2)
eloc = fpeps_util.fdot(peps2b, peps1b)
if debug: print '(i,j)=', (i, j), ' <U>=', eloc
etot += eloc
#
# T-term
#
tC_aa, tA_aa = fpeps_util.genTaa()
tC_bb, tA_bb = fpeps_util.genTbb()
# Jordan-Wigner sign factor for i\=j
parity = fpeps_util.genParitySgn([0, 1], [2, 2])
tC_aa = einsum('xqp,pr->xqr', tC_aa, parity)
tC_bb = einsum('xqp,pr->xqr', tC_bb, parity)
# Vertical bond => Simple is the chosen embedding
if debug: print "\nVbonds:"
for j in range(nc):
for i in range(nr - 1):
eloc = [0, 0]
for idx, thops in enumerate([[tC_aa, tA_aa], [tC_bb, tA_bb]]):
tC, tA = thops
peps2 = peps.copy(peps0)
peps2[i, j] = einsum('xqp,pludr->qlxudr', tC,
peps2[i, j]).merge_adjpair(2, 3)
peps2[i + 1, j] = einsum('xqp,pludr->qluxdr', tA,
peps2[i + 1, j]).merge_adjpair(3, 4)
sgn = fpeps_util.genParitySgn(peps2[i + 1, j].ptys[1],
peps2[i + 1, j].dims[1])
peps2[i + 1, j] = einsum('lL,qLudr->qludr', sgn, peps2[i + 1,
j])
peps2b = reflection(peps2)
eloc[idx] = 2.0 * fpeps_util.fdot(peps2b, peps1b)
if debug: print 't<i,j>=', (i, j), 'eloc=', sum(eloc), eloc
etot += sum(eloc)
# horizontal bond
# |/ |/
# --A----B--
# /| /|
# *----*
# | |
if debug: print "\nHbonds:"
for i in range(nr):
for j in range(nc - 1):
for idx, thops in enumerate([[tC_aa, tA_aa], [tC_bb, tA_bb]]):
tC, tA = thops
peps2 = peps.copy(peps0)
peps2[i, j] = einsum('xqp,pludr->qludxr', tC,
peps2[i, j]).merge_adjpair(4, 5)
peps2[i, j + 1] = einsum('xqp,pludr->qxludr', tA,
peps2[i, j + 1]).merge_adjpair(1, 2)
sgn = fpeps_util.genParitySgn(peps2[i, j].ptys[2],
peps2[i, j].dims[2])
peps2[i, j] = einsum('uU,qlUdr->qludr', sgn, peps2[i, j])
#??? WHY??? => ABSORBED.
#for k in range(i):
# sgn = fpeps_util.genParitySgn(peps2[k,j+1].ptys[0],peps2[k,j+1].dims[0])
# peps2[k,j+1] = einsum('qQ,Qludr->qludr',sgn,peps2[k,j+1])
peps2b = reflection(peps2)
eloc[idx] = 2.0 * fpeps_util.fdot(peps2b, peps1b)
if debug: print 't<i,j>=', (i, j), 'eloc=', sum(eloc), eloc
etot += sum(eloc)
return ovlp, etot
def energy_fpeps2by2(peps0):
debug = True
nr, nc = peps0.shape
# <P|P>
tmp = peps0[0, 1].copy()
p23 = tmp.ptys[0]
d23 = tmp.dims[0]
p1 = tmp.ptys[1]
d1 = tmp.dims[1]
swap1 = fpeps_util.genSwap(p23, d23, p1, d1)
# In fact, for 'uniform' distribution swap1=swap2
tmp = peps0[0, 2].copy()
p23 = tmp.ptys[0]
d23 = tmp.dims[0]
p1 = tmp.ptys[2]
d1 = tmp.dims[2]
swap2 = fpeps_util.genSwap(p23, d23, p1, d1)
# 'Bosonic peps'
peps1 = peps.copy(peps0)
peps1[0, 1] = einsum('pludr,pLlP->PLudr', peps1[0, 1], swap1)
peps1[0, 2] = einsum('pludr,pUuP->PlUdr', peps1[0, 2], swap2)
ovlp = peps.dot(peps1, peps1)
if debug:
print
print "Ovlp(bare)=", peps.dot(peps0, peps0)
print "Ovlp(swap)=", ovlp
etot = 0.0
# <P|U[i]|P>
if debug: print "\nU-terms:"
U = 1.5
uterm = fpeps_util.genUterm(U)
for j in range(nc):
for i in range(nr):
peps2 = peps.copy(peps1)
peps2[i, j] = einsum('Pp,pludr->Pludr', uterm, peps1[i, j])
eloc = peps.dot(peps1, peps2)
if debug: print '(i,j)=', (i, j), ' <U>=', eloc
etot = etot + eloc
exit()
# #
# # a b c d
# # | | | |
# # | 2--*-3
# # |/ |/
# # 0----1
# #
# tC_aa,tA_aa = fpeps_util.genTaa()
# tC_bb,tA_bb = fpeps_util.genTbb()
#
# # H02 = vertical bond
# peps2 = peps1.copy()
# peps2[0,0] = einsum('xqp,pludr->qlxudr',tC_aa,peps1[0,0]).merge_adjpair(2,3)
# peps2[1,0] = einsum('xqp,pludr->qluxdr',tA_aa,peps1[1,0]).merge_adjpair(3,4)
# elocA = peps.dot(peps1,peps2)
# peps2 = peps1.copy()
# peps2[0,0] = einsum('xqp,pludr->qlxudr',tC_bb,peps1[0,0]).merge_adjpair(2,3)
# peps2[1,0] = einsum('xqp,pludr->qluxdr',tA_bb,peps1[1,0]).merge_adjpair(3,4)
# elocB = peps.dot(peps1,peps2)
# etot = etot + 2.0*(elocA+elocB)
# if debug:
# print
# print 't02aa=',elocA
# print 't02bb=',elocB
#
# # H23 = horizontal bond
# # | |
# # *----*
# # |/ |/
# # --2----3--
# # / /
# peps2 = peps1.copy()
# peps2[1,0] = einsum('xqp,pludr->qludxr',tC_aa,peps1[1,0]).merge_adjpair(4,5)
# peps2[1,1] = einsum('xqp,pludr->qxludr',tA_aa,peps1[1,1]).merge_adjpair(1,2)
# elocA = peps.dot(peps1,peps2)
# peps2 = peps1.copy()
# peps2[1,0] = einsum('xqp,pludr->qludxr',tC_bb,peps1[1,0]).merge_adjpair(4,5)
# peps2[1,1] = einsum('xqp,pludr->qxludr',tA_bb,peps1[1,1]).merge_adjpair(1,2)
# elocB = peps.dot(peps1,peps2)
# etot = etot + 2.0*(elocA+elocB)
# if debug:
# print
# print 't23aa=',elocA
# print 't23bb=',elocB
#
# # parity along physical index
# parity = fpeps_util.genParitySgn([0,1],[2,2])
#
# # H01 - hbond
# peps2 = peps1.copy()
# peps2[0,0] = einsum('xqp,pludr->qludxr',tC_aa,peps1[0,0]).merge_adjpair(4,5)
# peps2[0,1] = einsum('xqp,pludr->qxludr',tA_aa,peps1[0,1]).merge_adjpair(1,2)
# peps2[1,0] = einsum( 'qp,pludr->qludr',parity,peps1[1,0])
# peps2[1,1] = einsum( 'qp,pludr->qludr',parity,peps1[1,1])
# elocA = peps.dot(peps1,peps2)
# peps2 = peps1.copy()
# peps2[0,0] = einsum('xqp,pludr->qludxr',tC_bb,peps1[0,0]).merge_adjpair(4,5)
# peps2[0,1] = einsum('xqp,pludr->qxludr',tA_bb,peps1[0,1]).merge_adjpair(1,2)
# peps2[1,0] = einsum( 'qp,pludr->qludr',parity,peps1[1,0])
# peps2[1,1] = einsum( 'qp,pludr->qludr',parity,peps1[1,1])
# elocB = peps.dot(peps1,peps2)
# etot = etot + 2.0*(elocA+elocB)
# if debug:
# print
# print 't01aa=',elocA
# print 't01bb=',elocB
#
# # H13 - vbond
# peps2 = peps1.copy()
# peps2[0,1] = einsum( 'qp,pludr->qludr',parity,peps1[0,1])
# peps2[0,1] = einsum('xqp,pludr->qlxudr',tC_aa,peps2[0,1]).merge_adjpair(2,3)
# peps2[1,1] = einsum('xqp,pludr->qluxdr',tA_aa,peps1[1,1]).merge_adjpair(3,4)
# peps2[1,1] = einsum( 'qp,pludr->qludr',parity,peps2[1,1])
# elocA = peps.dot(peps1,peps2)
# peps2 = peps1.copy()
# peps2[0,1] = einsum( 'qp,pludr->qludr',parity,peps1[0,1])
# peps2[0,1] = einsum('xqp,pludr->qlxudr',tC_bb,peps2[0,1]).merge_adjpair(2,3)
# peps2[1,1] = einsum('xqp,pludr->qluxdr',tA_bb,peps1[1,1]).merge_adjpair(3,4)
# peps2[1,1] = einsum( 'qp,pludr->qludr',parity,peps2[1,1])
# elocB = peps.dot(peps1,peps2)
# etot = etot + 2.0*(elocA+elocB)
# if debug:
# print
# print 't13aa=',elocA
# print 't13bb=',elocB
return ovlp, etot
def energy_fpeps2by2(peps0):
nr, nc = peps0.shape
# <P|P>
tmp = peps0[0, 1].copy()
p23 = tmp.ptys[0]
d23 = tmp.dims[0]
p1 = tmp.ptys[2]
d1 = tmp.dims[2]
swap = fpeps_util.genSwap(p23, d23, p1, d1)
peps1 = peps.copy(peps0)
peps1[0, 1] = einsum('pludr,pUuP->PlUdr', peps1[0, 1], swap)
ovlp = peps.dot(peps1, peps1)
if debug:
print
print "Ovlp=", peps.dot(peps0, peps0)
print "Ovlp=", ovlp
etot = 0.0
# <P|U[i]|P>
if debug: print "\nU-terms:"
uterm = fpeps_util.genUterm(U)
for i in range(nr):
for j in range(nc):
peps2 = peps.copy(peps1)
peps2[i, j] = einsum('Pp,pludr->Pludr', uterm, peps1[i, j])
eloc = peps.dot(peps1, peps2)
if debug: print '(i,j)=', (i, j), ' <U>=', eloc
etot = etot + eloc
#
# a b c d
# | | | |
# | 1--*-3
# |/ |/
# 0----2
#
tC_aa, tA_aa = fpeps_util.genTaa()
tC_bb, tA_bb = fpeps_util.genTbb()
# Test local terms:
if debug:
tCA_aa = einsum('xqr,xrp->qp', tC_aa, tA_aa)
tCA_bb = einsum('xqr,xrp->qp', tC_bb, tA_bb)
for i in [0, 1]:
peps2 = peps.copy(peps1)
peps2[i, 0] = einsum('qp,pludr->qludr', tCA_aa, peps1[i, 0])
elocA = 2.0 * peps.dot(peps1, peps2)
print 't[' + str(i) + ']aa=', elocA
peps2 = peps.copy(peps1)
peps2[i, 0] = einsum('qp,pludr->qludr', tCA_bb, peps1[i, 0])
elocA = 2.0 * peps.dot(peps1, peps2)
print 't[' + str(i) + ']bb=', elocA
# Jordan-Wigner sign factor for i\=j
parity = fpeps_util.genParitySgn([0, 1], [2, 2])
tC_aa = einsum('xqp,pr->xqr', tC_aa, parity)
tC_bb = einsum('xqp,pr->xqr', tC_bb, parity)
# H01 = vertical bond
peps2 = peps.copy(peps1)
peps2[0, 0] = einsum('xqp,pludr->qlxudr', tC_aa,
peps1[0, 0]).merge_adjpair(2, 3)
peps2[1, 0] = einsum('xqp,pludr->qluxdr', tA_aa,
peps1[1, 0]).merge_adjpair(3, 4)
elocA = 2.0 * peps.dot(peps1, peps2)
peps2 = peps.copy(peps1)
peps2[0, 0] = einsum('xqp,pludr->qlxudr', tC_bb,
peps1[0, 0]).merge_adjpair(2, 3)
peps2[1, 0] = einsum('xqp,pludr->qluxdr', tA_bb,
peps1[1, 0]).merge_adjpair(3, 4)
elocB = 2.0 * peps.dot(peps1, peps2)
etot = etot + (elocA + elocB)
if debug:
print
print 't01aa=', elocA
print 't01bb=', elocB
# H13 = horizontal bond
# | |
# *----*
# |/ |/
# --1----3--
# / /
peps2 = peps.copy(peps1)
peps2[1, 0] = einsum('xqp,pludr->qludxr', tC_aa,
peps1[1, 0]).merge_adjpair(4, 5)
peps2[1, 1] = einsum('xqp,pludr->qxludr', tA_aa,
peps1[1, 1]).merge_adjpair(1, 2)
elocA = 2.0 * peps.dot(peps1, peps2)
peps2 = peps.copy(peps1)
peps2[1, 0] = einsum('xqp,pludr->qludxr', tC_bb,
peps1[1, 0]).merge_adjpair(4, 5)
peps2[1, 1] = einsum('xqp,pludr->qxludr', tA_bb,
peps1[1, 1]).merge_adjpair(1, 2)
elocB = 2.0 * peps.dot(peps1, peps2)
etot = etot + (elocA + elocB)
if debug:
print
print 't13aa=', elocA
print 't13bb=', elocB
# H02 - hbond
peps2 = peps.copy(peps1)
peps2[0, 0] = einsum('xqp,pludr->qludxr', tC_aa,
peps1[0, 0]).merge_adjpair(4, 5)
peps2[0, 1] = einsum('xqp,pludr->qxludr', tA_aa,
peps1[0, 1]).merge_adjpair(1, 2)
peps2[1, 0] = einsum('qp,pludr->qludr', parity, peps1[1, 0])
peps2[1, 1] = einsum('qp,pludr->qludr', parity, peps1[1, 1])
elocA = 2.0 * peps.dot(peps1, peps2)
peps2 = peps.copy(peps1)
peps2[0, 0] = einsum('xqp,pludr->qludxr', tC_bb,
peps1[0, 0]).merge_adjpair(4, 5)
peps2[0, 1] = einsum('xqp,pludr->qxludr', tA_bb,
peps1[0, 1]).merge_adjpair(1, 2)
peps2[1, 0] = einsum('qp,pludr->qludr', parity, peps1[1, 0])
peps2[1, 1] = einsum('qp,pludr->qludr', parity, peps1[1, 1])
elocB = 2.0 * peps.dot(peps1, peps2)
etot = etot + (elocA + elocB)
if debug:
print
print 't02aa=', elocA
print 't02bb=', elocB
# H23 - vbond
peps2 = peps.copy(peps1)
peps2[0, 1] = einsum('qp,pludr->qludr', parity, peps1[0, 1])
peps2[0, 1] = einsum('xqp,pludr->qlxudr', tC_aa,
peps2[0, 1]).merge_adjpair(2, 3)
peps2[1, 1] = einsum('xqp,pludr->qluxdr', tA_aa,
peps1[1, 1]).merge_adjpair(3, 4)
peps2[1, 1] = einsum('qp,pludr->qludr', parity, peps2[1, 1])
elocA = 2.0 * peps.dot(peps1, peps2)
peps2 = peps.copy(peps1)
peps2[0, 1] = einsum('qp,pludr->qludr', parity, peps1[0, 1])
peps2[0, 1] = einsum('xqp,pludr->qlxudr', tC_bb,
peps2[0, 1]).merge_adjpair(2, 3)
peps2[1, 1] = einsum('xqp,pludr->qluxdr', tA_bb,
peps1[1, 1]).merge_adjpair(3, 4)
peps2[1, 1] = einsum('qp,pludr->qludr', parity, peps2[1, 1])
elocB = 2.0 * peps.dot(peps1, peps2)
etot = etot + (elocA + elocB)
if debug:
print
print 't23aa=', elocA
print 't23bb=', elocB
print
print 'ovlp,etot=', ovlp, etot
return ovlp, etot