def genHubbardSpatial(dmrg, isite):
iden = mpo_dmrg_spinopers.genIpMat()
nanb = mpo_dmrg_spinopers.genNaNbMat()
creA = mpo_dmrg_opers.genElemSpatialMat(2 * isite, isite, 1)
creB = mpo_dmrg_opers.genElemSpatialMat(2 * isite + 1, isite, 1)
annA = mpo_dmrg_opers.genElemSpatialMat(2 * isite, isite, 0)
annB = mpo_dmrg_opers.genElemSpatialMat(2 * isite + 1, isite, 0)
# ai^+[alpha]*aj[alpha] = creA*sgnA*sgnB * annA
# -ai[alpha]*aj^+[alpha] = -annA*sgnA*sgnB * creA
# ai^+[beta]*aj[beta] = sgnA*creB*sgnB * annB
# -ai[beta]*aj^+[beta] = -sgnA*annB*sgnB * creB
sa = genSaSpatialMat()
sb = genSbSpatialMat()
sasb = genSaSbSpatialMat()
creAs = numpy.dot(creA, sasb)
annAs = numpy.dot(annA, sasb)
# Note that creB already contains a sign factor sgnA, so
# an additional sgnA is needed to cancel it.
creBs = numpy.dot(sa, numpy.dot(creB, sb))
annBs = numpy.dot(sa, numpy.dot(annB, sb))
# Set up elements
if isite == 0:
# [I C D] = [ I (-t)au^+ (-t)ad^+ (-t)au (-t)ad U*niA*niB ]
cop = numpy.zeros((1, 6, 4, 4))
cop[0, 0] = iden
cop[0, 1] = -dmrg.model_t * creAs
cop[0, 2] = -dmrg.model_t * creBs
cop[0, 3] = -dmrg.model_t * annAs
cop[0, 4] = -dmrg.model_t * annBs
cop[0, 5] = dmrg.model_u * nanb
elif isite == dmrg.nsite - 1:
# [D B I]^T
cop = numpy.zeros((6, 1, 4, 4))
cop[0, 0] = dmrg.model_u * nanb
cop[1, 0] = annA
cop[2, 0] = annB
cop[3, 0] = -creA
cop[4, 0] = -creB
cop[5, 0] = iden
else:
# [ I -t*a^+ -t*a D ]
# [ 0 0 0 a ]
# [ 0 0 0 -a^+]
# [ 0 0 0 I ]
cop = numpy.zeros((6, 6, 4, 4))
cop[0, 0] = iden
cop[0, 1] = -dmrg.model_t * creAs
cop[0, 2] = -dmrg.model_t * creBs
cop[0, 3] = -dmrg.model_t * annAs
cop[0, 4] = -dmrg.model_t * annBs
cop[0, 5] = dmrg.model_u * nanb
cop[1, 5] = annA
cop[2, 5] = annB
cop[3, 5] = -creA
cop[4, 5] = -creB
cop[5, 5] = iden
return cop
def test_creann():
# LOAD MPS
fname = './mps.h5'
mps, qnum = mps_io.loadMPS(fname)
lmps = [mps, qnum]
bdim = [len(x) for x in qnum]
print(' bdim = ', bdim)
nsite = len(mps)
qphys = mpo_dmrg_qphys.initSpatialOrb(nsite, 2)
ta = 0.
tb = 0.
for isite in range(nsite):
ql = qnum[isite]
qn = qphys[isite]
qr = qnum[isite + 1]
cl = qtensor_util.classification(ql)
cn = qtensor_util.classification(qn)
cr = qtensor_util.classification(qr)
print('isite/nsite=', isite, nsite)
site = mps[isite]
tmps = qtensor.qtensor([False, False, True])
tmps.fromDenseTensor(site, [ql, qn, qr])
tmps.prt()
for iop in [1, 0]:
for p in range(2 * nsite):
t0 = time.time()
op = mpo_dmrg_opers.genElemSpatialMat(p, isite, iop)
#csite = numpy.einsum('ij,ajb->aib',op,site)
csite = numpy.tensordot(op, site, axes=([1], [1])) # iab
csite = csite.transpose(1, 0, 2)
t1 = time.time()
qop = qtensor_opers.genElemSpatialQt(p, isite, iop)
# ijab,xby-> ijaxy -> ix,a,jy
tmps2 = qtensor.tensordot(qop, tmps, axes=([3], [1]))
tmps2 = tmps2.transpose(0, 3, 2, 1, 4)
tmps2 = tmps2.merge([[0, 1], [2], [3, 4]])
tsite = tmps2.toDenseTensor()
t2 = time.time()
assert csite.shape == tsite.shape
diff = numpy.linalg.norm(tsite - csite)
print('iop,p,diff=', iop, p, csite.shape, diff, ' t0=',
t1 - t0, ' t1=', t2 - t1)
assert diff < 1.e-10
ta += t1 - t0
tb += t2 - t1
# In case of large bond dimension, e.g.,
# D=2000, t0/t1~0.21/0.09 due to sparsity!
print()
print('ta=', ta) # ta= 20.7766697407
print('tb=', tb) # tb= 18.2862818241
print()
return 0
def genCAopsNQt(norder, dmrg, fbmps, fkmps, fname, status, debug=False):
if dmrg.comm.rank == 0:
print '[mpo_dmrg_block.genCAopsNQt] status=', status
print ' fname = ', fname
t0 = time.time()
bnsite = fbmps['nsite'].value
knsite = fkmps['nsite'].value
assert bnsite == knsite
nsite = bnsite
sbas = 2 * nsite
prefix = fname + '_site_'
#
# On-site operators
#
sgnn = numpy.array([1., -1., -1., 1.])
cre = [0] * 2
cre[0] = mpo_dmrg_opers.genElemSpatialMat(0, 0, 1)
cre[1] = mpo_dmrg_opers.genElemSpatialMat(1, 0, 1)
ann = [0] * 2
ann[0] = mpo_dmrg_opers.genElemSpatialMat(0, 0, 0)
ann[1] = mpo_dmrg_opers.genElemSpatialMat(1, 0, 0)
cc2 = cre[0].dot(cre[1])
aa2 = ann[0].dot(ann[1])
ca2 = [cre[i].dot(ann[j]) for i in range(2) for j in range(2)]
ac2 = [ann[i].dot(cre[j]) for i in range(2) for j in range(2)]
#
# L->R sweeps
#
if status == 'L':
mpo_dmrg_init.genBmat(dmrg, fname, -1)
for isite in range(0, nsite):
if debug: print ' isite=', isite, ' of nsite=', nsite
ti = time.time()
f0 = h5py.File(prefix + str(isite - 1), "r")
f1name = prefix + str(isite)
f1 = h5py.File(f1name, "w")
bsite = mpo_dmrg_io.loadSite(fbmps, isite, dmrg.ifQt)
ksite = mpo_dmrg_io.loadSite(fkmps, isite, dmrg.ifQt)
# 0. Qnums
porbs = 2 * isite
nqum = fkmps['qnum' + str(isite)].value[:, 0]
sgnl = numpy.power(-1.0, nqum)
ksite2 = numpy.einsum('l,lnr->lnr', sgnl, ksite)
# 1. Similar to mpo_dmrg_init.genSopsNQt: <li[A]|lj[B]>
oplst = ['mat']
renorm_l1(bsite, ksite, f0, f1, oplst)
# 2. Part-1: <l'n'|op|ln> = <l'|op|l>*<n'|n> if p < 2k
oplst = ['op_C_'+str(p) for p in range(porbs)]\
+ ['op_A_'+str(p) for p in range(porbs)]
renorm_l1(bsite, ksite, f0, f1, oplst)
# Part-2: <l'n'|op|ln> = <l'|l>(-1)^l*<n'|op|n> if p = 2k,2k+1
# <L'|op|L> = A[l'n',L']*<l'|l><n'|op|n>*A[ln,L]
tmp0 = renorm_l2_absorb_lop(bsite, f0['mat'])
for ispin in range(2):
tmp = renorm_l2_transform_nop(tmp0, cre[ispin], ksite2)
f1['op_C_' + str(2 * isite + ispin)] = tmp
tmp = renorm_l2_transform_nop(tmp0, ann[ispin], ksite2)
f1['op_A_' + str(2 * isite + ispin)] = tmp
# 3. Part-1: <l'n'|aa(p<q)|ln> = <l'|apq|l><n'|n> if p,q < 2k
oplst = ['op_CC_'+str(p)+'_'+str(q) for p in range(porbs) for q in range(p+1,porbs)]\
+ ['op_AA_'+str(p)+'_'+str(q) for p in range(porbs) for q in range(p+1,porbs)]
renorm_l1(bsite, ksite, f0, f1, oplst)
# Part-2: <l'|ap|l>*<n'|aq|n> if p < 2k and q in 2k,2k+1
for p in range(porbs):
# CC
tmp0 = renorm_l2_absorb_lop(bsite, f0['op_C_' + str(p)])
for ispin in range(2):
tmp = renorm_l2_transform_nop(tmp0, cre[ispin], ksite2)
f1['op_CC_' + str(p) + '_' + str(2 * isite + ispin)] = tmp
# AA
tmp0 = renorm_l2_absorb_lop(bsite, f0['op_A_' + str(p)])
for ispin in range(2):
tmp = renorm_l2_transform_nop(tmp0, ann[ispin], ksite2)
f1['op_AA_' + str(p) + '_' + str(2 * isite + ispin)] = tmp
# Part-3: <l'|l>*<n'|apq|n> if p,q in 2k,2k+1
# <L'|opq|L> = A[l'n',L']*<l'|l><n'|op|n>*A[ln,L]
tmp0 = renorm_l2_absorb_lop(bsite, f0['mat'])
tmp = renorm_l2_transform_nop(tmp0, cc2, ksite)
f1['op_CC_' + str(2 * isite + 0) + '_' + str(2 * isite + 1)] = tmp
tmp = renorm_l2_transform_nop(tmp0, aa2, ksite)
f1['op_AA_' + str(2 * isite + 0) + '_' + str(2 * isite + 1)] = tmp
# 4. Part-1: <l'n'|cp*aq|ln> = <l'|cp*aq|l><n'|n> if p,q < 2k
oplst = ['op_CA_'+str(p)+'_'+str(q) for p in range(porbs) for q in range(porbs)]\
+ ['op_AC_'+str(p)+'_'+str(q) for p in range(porbs) for q in range(porbs)]
renorm_l1(bsite, ksite, f0, f1, oplst)
# Part-2: cp[l]*aq[n] or cq[n]*ap[l]=-ap[l]*cq[n]
# ap[l]*cq[n] or aq[n]*cp[l]=-cp[l]*aq[n]
# for p < 2*k and q in 2k,2k+1
for p in range(porbs):
# CA
tmp0 = renorm_l2_absorb_lop(bsite, f0['op_C_' + str(p)])
for ispin in range(2):
tmp = renorm_l2_transform_nop(tmp0, ann[ispin], ksite2)
f1['op_CA_' + str(p) + '_' + str(2 * isite + ispin)] = tmp
f1['op_AC_' + str(2 * isite + ispin) + '_' + str(p)] = -tmp
# AC
tmp0 = renorm_l2_absorb_lop(bsite, f0['op_A_' + str(p)])
for ispin in range(2):
tmp = renorm_l2_transform_nop(tmp0, cre[ispin], ksite2)
f1['op_AC_' + str(p) + '_' + str(2 * isite + ispin)] = tmp
f1['op_CA_' + str(2 * isite + ispin) + '_' + str(p)] = -tmp
# Part-3: <l'|l>*<n'|cp*aq|n> if p,q in 2k,2k+1
tmp0 = renorm_l2_absorb_lop(bsite, f0['mat'])
for ispin in range(2):
for jspin in range(2):
tmp = renorm_l2_transform_nop(tmp0, ca2[ispin * 2 + jspin],
ksite)
f1['op_CA_' + str(2 * isite + ispin) + '_' +
str(2 * isite + jspin)] = tmp
tmp = renorm_l2_transform_nop(tmp0, ac2[ispin * 2 + jspin],
ksite)
f1['op_AC_' + str(2 * isite + ispin) + '_' +
str(2 * isite + jspin)] = tmp
# final isite
f0.close()
f1.close()
tf = time.time()
if dmrg.comm.rank == 0:
print ' isite =', os.path.split(
f1name)[-1], ' t = %.2f s' % (tf - ti)
#
# L<-R sweeps: For properties, left canonical form is assumed even for R sweeps!
#
elif status == 'R':
mpo_dmrg_init.genBmat(dmrg, fname, nsite)
for isite in range(nsite - 1, -1, -1):
if debug: print ' isite=', isite, ' of nsite=', nsite
ti = time.time()
f0 = h5py.File(prefix + str(isite + 1), "r")
f1name = prefix + str(isite)
f1 = h5py.File(f1name, "w")
bsite = mpo_dmrg_io.loadSite(fbmps, isite, dmrg.ifQt)
ksite = mpo_dmrg_io.loadSite(fkmps, isite, dmrg.ifQt)
# 0. Qnums
porbs = 2 * (isite + 1)
ksite2 = numpy.einsum('n,lnr->lnr', sgnn, ksite)
# 1. <ri[A]|rj[B]>
oplst = ['mat']
renorm_r1(bsite, ksite, f0, f1, oplst)
# 2. Part-1: <n'r'|op|nr> = <n'|n>(-1)^n*<r'|op|r> if p > 2k
# A[l',n',r']<n'|n>(-1)^n*<r'|op|r>*A[l,n,r]
oplst = ['op_C_'+str(p) for p in range(porbs,sbas)]\
+ ['op_A_'+str(p) for p in range(porbs,sbas)]
renorm_r1(bsite, ksite2, f0, f1, oplst)
# Part-2: <n'r'|op|nr> = <n'|op|n>*<r'|r> if p = 2k,2k+1
# <l'|op|l> = A[l',n'r']*<n'|op|n>*<r'|r>*A[l,nr]
tmp0 = renorm_r2_absorb_rop(ksite, f0['mat'])
for ispin in range(2):
tmp = renorm_r2_transform_nop(tmp0, cre[ispin], bsite)
f1['op_C_' + str(2 * isite + ispin)] = tmp
tmp = renorm_r2_transform_nop(tmp0, ann[ispin], bsite)
f1['op_A_' + str(2 * isite + ispin)] = tmp
# 3. Part-1: <n'r'|aa(p<q)|n'r'> = <n'|n><r'|apq|r> if p,q > 2k
# <l'|aa(p<q)|l> = A[l',n',r']<n'|n><r'|apq|r>A[l,n,r]
oplst = ['op_CC_'+str(p)+'_'+str(q) for p in range(porbs,sbas) for q in range(p+1,porbs)]\
+ ['op_AA_'+str(p)+'_'+str(q) for p in range(porbs,sbas) for q in range(p+1,porbs)]
renorm_r1(bsite, ksite, f0, f1, oplst)
# Part-2: <n'r'|aa(p<q)|n'r'> = <n'|ap|n>*S*<r'|aq|r> if p in 2k,2k+1 and q > 2k
# <l'|aa(p<q)|l> = A[l',n',r']*<n'|ap|n>S*<r'|aq|r>*A[l,n,r]
for p in range(porbs, sbas):
# CC
tmp0 = renorm_r2_absorb_rop(ksite2, f0['op_C_' + str(p)])
for ispin in range(2):
tmp = renorm_r2_transform_nop(tmp0, cre[ispin], bsite)
f1['op_CC_' + str(2 * isite + ispin) + '_' + str(p)] = tmp
# AA
tmp0 = renorm_r2_absorb_rop(ksite2, f0['op_A_' + str(p)])
for ispin in range(2):
tmp = renorm_r2_transform_nop(tmp0, ann[ispin], bsite)
f1['op_AA_' + str(2 * isite + ispin) + '_' + str(p)] = tmp
# Part-3: <n'r'|aa(p<q)|n'r'> = <n'|apq|n>*<r'|r> if p,q in 2k,2k+1
# <l'|aa(p<q)|l> = A[l',n',r]*<n'|apq|n>*<r'|r>*A[l,n,r]
tmp0 = renorm_r2_absorb_rop(ksite, f0['mat'])
tmp = renorm_r2_transform_nop(tmp0, cc2, bsite)
f1['op_CC_' + str(2 * isite + 0) + '_' + str(2 * isite + 1)] = tmp
tmp = renorm_r2_transform_nop(tmp0, aa2, bsite)
f1['op_AA_' + str(2 * isite + 0) + '_' + str(2 * isite + 1)] = tmp
# 4. Part-1: <n'r'|cp*aq|nr> = <n'|n><r'|cp*aq|r> if p,q > 2k
# <l'|cp*aq|l> = A[l',nr']*<r'|cp*aq|r>*A[l,nr]
oplst = ['op_CA_'+str(p)+'_'+str(q) for p in range(porbs,sbas) for q in range(porbs,sbas)]\
+ ['op_AC_'+str(p)+'_'+str(q) for p in range(porbs,sbas) for q in range(porbs,sbas)]
renorm_r1(bsite, ksite, f0, f1, oplst)
# Part-2: <n'r'|cp*aq|nr> = <n'|cp|n>S*<r'|aq|r>
for p in range(porbs, sbas):
# CA
tmp0 = renorm_r2_absorb_rop(ksite2, f0['op_A_' + str(p)])
for ispin in range(2):
tmp = renorm_r2_transform_nop(tmp0, cre[ispin], bsite)
f1['op_CA_' + str(2 * isite + ispin) + '_' + str(p)] = tmp
f1['op_AC_' + str(p) + '_' + str(2 * isite + ispin)] = -tmp
# AA
tmp0 = renorm_r2_absorb_rop(ksite2, f0['op_C_' + str(p)])
for ispin in range(2):
tmp = renorm_r2_transform_nop(tmp0, ann[ispin], bsite)
f1['op_AC_' + str(2 * isite + ispin) + '_' + str(p)] = tmp
f1['op_CA_' + str(p) + '_' + str(2 * isite + ispin)] = -tmp
# Part-3: <n'r'|cp*aq|n'r'> = <n'|cp*aq|n>*<r'|r> if p,q in 2k,2k+1
tmp0 = renorm_r2_absorb_rop(ksite, f0['mat'])
for ispin in range(2):
for jspin in range(2):
tmp = renorm_r2_transform_nop(tmp0, ca2[ispin * 2 + jspin],
bsite)
f1['op_CA_' + str(2 * isite + ispin) + '_' +
str(2 * isite + jspin)] = tmp
tmp = renorm_r2_transform_nop(tmp0, ac2[ispin * 2 + jspin],
bsite)
f1['op_AC_' + str(2 * isite + ispin) + '_' +
str(2 * isite + jspin)] = tmp
# final isite
f0.close()
f1.close()
tf = time.time()
if dmrg.comm.rank == 0:
print ' isite =', os.path.split(
f1name)[-1], ' t = %.2f s' % (tf - ti)
# CHECK
f = h5py.File(f1name, 'r')
rdm1 = numpy.zeros((sbas, sbas))
hdm1 = numpy.zeros((sbas, sbas))
for i in range(sbas):
for j in range(sbas):
rdm1[i, j] = f['op_CA_' + str(i) + '_' + str(j)].value
hdm1[j, i] = f['op_AC_' + str(i) + '_' + str(j)].value
sab = f['mat'].value[0, 0]
#print rdm1+hdm1
print ' ovlap=', sab
print ' P+H-I=', numpy.linalg.norm(rdm1 + hdm1 -
numpy.identity(sbas) * sab)
print ' skewP=', numpy.linalg.norm(rdm1 - rdm1.T)
print ' skewH=', numpy.linalg.norm(hdm1 - hdm1.T)
print ' trace=', numpy.trace(rdm1)
f.close()
t1 = time.time()
dmrg.comm.Barrier()
print ' time for genHops = %.2f s' % (t1 - t0), ' rank =', dmrg.comm.rank
return rdm1
mps_i1 = mps_i1.add(k1)
mps_i1 = mps_i1.add(k2)
mps_i1 = mps_i1.add(k3)
mps_i1 = mps_i1.add(k4)
norm = compress(mps_i1, maxM)
return mps_i1, norm
for isite in slst:
# create complex MPS
mpsi = None
mpsi = [mps[i] + 0.j for i in range(nsite)]
# MPSi = ai*|psi0>
annA = mpo_dmrg_opers.genElemSpatialMat(2 * isite, isite, 0)
tmp = numpy.tensordot(annA, mpsi[isite], axes=([1], [1]))
mpsi[isite] = tmp.transpose(1, 0, 2)
# sign change
for jsite in range(isite):
sgn = mpo_dmrg_model.genSaSbSpatialMat()
tmp = numpy.tensordot(sgn, mpsi[jsite], axes=([1], [1]))
mpsi[jsite] = tmp.transpose(1, 0, 2)
# MPS class
mps_i0 = mps_class.class_mps(nsite, sites=mpsi, iop=1)
mps_i = mps_class.class_mps(nsite, sites=mpsi, iop=1)
# DM[i,i]
norm0 = mps_i.norm()