def FT_DM(mol,
J,
nexciton,
T,
nsteps,
particle="hardcore boson",
prop_method="unitary"):
'''
finite temperature thermal equilibrium density matrix by imaginary time TDH
'''
DM = []
fe = 1
fv = 0
# initial state infinite T density matrix
H_el_indep, H_el_dep = Ham_elec(mol, J, nexciton, particle=particle)
dim = H_el_indep.shape[0]
DM.append(np.diag([1.0] * dim, k=0))
nmols = len(mol)
for imol in xrange(nmols):
for iph in xrange(mol[imol].nphs):
dim = mol[imol].ph[iph].H_vib_indep.shape[0]
DM.append(np.diag([1.0] * dim, k=0))
fv += 1
# the coefficent a
DM.append(1.0)
# normalize the dm (physical \otimes ancilla)
mflib.normalize(DM)
beta = constant.T2beta(T) / 2.0
dbeta = beta / float(nsteps)
for istep in xrange(nsteps):
DM = TDH(mol,
J,
nexciton,
DM,
dbeta / 1.0j,
fe,
fv,
prop_method=prop_method,
particle=particle)
mflib.normalize(DM)
Z = DM[-1]**2
print "partition function Z=", Z
# divide by np.sqrt(partition function)
DM[-1] = 1.0
return DM
def test_FT_dynamics_TDH(self):
mol, J = parameter_PBI.construct_mol(4, nphs=10)
TDH.construct_Ham_vib(mol, hybrid=False)
nexciton = 0
T = 2000
insteps = 1
DM = TDH.FT_DM(mol, J, nexciton, T, insteps)
Os = []
for imol in xrange(len(mol)):
dipoleO = TDH.construct_onsiteO(mol,
"a^\dagger a",
dipole=False,
sitelist=[imol])
Os.append(dipoleO)
dipoleO = TDH.construct_onsiteO(mol,
"a^\dagger",
dipole=True,
sitelist=[0])
DM[0] = dipoleO.dot(DM[0])
mflib.normalize(DM)
nsteps = 300
dt = 10.0
fe, fv = 1, 40
data = TDH.dynamics_TDH(mol,
J,
1,
DM,
dt,
nsteps,
fe,
fv,
property_Os=Os)
with open("std_data/TDH/FT_occ10.npy", 'rb') as f:
std = np.load(f)
self.assertTrue(np.allclose(data, std))
def linear_spectra(spectratype, mol, J, nexciton, WFN, dt, nsteps, fe, fv,\
E_offset=0.0, prop_method="unitary", particle="hardcore boson", T=0):
'''
ZT/FT linear spectra by TDH
'''
assert spectratype in ["abs", "emi"]
assert particle in ["hardcore boson", "fermion"]
assert (fe + fv) == (len(WFN) - 1)
nmols = len(mol)
if spectratype == "abs":
dipolemat = construct_onsiteO(mol, "a^\dagger", dipole=True)
nexciton += 1
elif spectratype == "emi":
dipolemat = construct_onsiteO(mol, "a", dipole=True)
nexciton -= 1
WFNket = copy.deepcopy(WFN)
WFNket[0] = dipolemat.dot(WFNket[0])
# normalize ket
mflib.normalize(WFNket)
if T == 0:
WFNbra = copy.deepcopy(WFNket)
else:
WFNbra = copy.deepcopy(WFN)
# normalize bra
mflib.normalize(WFNbra)
# check whether the energy is conserved
def check_conserveE():
if T == 0:
Nouse, Etot_bra = construct_H_Ham(mol, J, nexciton, WFNbra, fe, fv)
else:
Nouse, Etot_bra = construct_H_Ham(mol, J, 1 - nexciton, WFNbra, fe,
fv)
Nouse, Etot_ket = construct_H_Ham(mol, J, nexciton, WFNket, fe, fv)
return Etot_bra, Etot_ket
Etot_bra0, Etot_ket0 = check_conserveE()
autocorr = []
t = 0.0
for istep in xrange(nsteps):
if istep != 0:
t += dt
if T == 0:
if istep % 2 == 1:
WFNket = TDH(mol,
J,
nexciton,
WFNket,
dt,
fe,
fv,
prop_method=prop_method,
particle=particle)
else:
WFNbra = TDH(mol,
J,
nexciton,
WFNbra,
-dt,
fe,
fv,
prop_method=prop_method,
particle=particle)
else:
# FT
WFNket = TDH(mol,
J,
nexciton,
WFNket,
dt,
fe,
fv,
prop_method=prop_method,
particle=particle)
WFNbra = TDH(mol,
J,
1 - nexciton,
WFNbra,
dt,
fe,
fv,
prop_method=prop_method,
particle=particle)
# E_offset to add a prefactor
ft = np.conj(WFNbra[-1]) * WFNket[-1] * np.exp(-1.0j * E_offset * t)
for iwfn in xrange(fe + fv):
if T == 0:
ft *= np.vdot(WFNbra[iwfn], WFNket[iwfn])
else:
# FT
if iwfn == 0:
ft *= mflib.exp_value(WFNbra[iwfn], dipolemat.T,
WFNket[iwfn])
else:
ft *= np.vdot(WFNbra[iwfn], WFNket[iwfn])
autocorr.append(ft)
autocorr_store(autocorr, istep)
Etot_bra1, Etot_ket1 = check_conserveE()
return autocorr, [Etot_bra0, Etot_bra1, Etot_ket0, Etot_ket1]
def FT_DM_hybrid_TDDMRG_TDH(mol, J, nexciton, T, nsteps, pbond, ephtable, \
thresh=0., TDDMRG_prop_method="C_RK4", cleanexciton=None, QNargs=None, space=None):
'''
construct the finite temperature density matrix by hybrid TDDMRG/TDH method
'''
# initial state infinite T density matrix
# TDDMRG
if nexciton == 0:
DMMPS, DMMPSdim = tMPS.Max_Entangled_GS_MPS(mol,
pbond,
norm=True,
QNargs=QNargs)
DMMPO = tMPS.hilbert_to_liouville(DMMPS, QNargs=QNargs)
elif nexciton == 1:
DMMPO, DMMPOdim = tMPS.Max_Entangled_EX_MPO(mol,
pbond,
norm=True,
QNargs=QNargs)
DMMPO = mpslib.MPSdtype_convert(DMMPO, QNargs=QNargs)
# TDH
DMH = []
nmols = len(mol)
for imol in xrange(nmols):
for iph in xrange(mol[imol].nphs_hybrid):
dim = mol[imol].ph_hybrid[iph].H_vib_indep.shape[0]
DMH.append(np.diag([1.0] * dim, k=0))
# the coefficent a
DMH.append(1.0)
mflib.normalize(DMH)
beta = constant.T2beta(T) / 2.0
dbeta = beta / float(nsteps)
for istep in xrange(nsteps):
if space is None:
DMMPO, DMH = hybrid_TDDMRG_TDH(mol, J, DMMPO, DMH, dbeta/1.0j, ephtable, \
thresh=thresh, cleanexciton=cleanexciton, QNargs=QNargs, \
TDDMRG_prop_method=TDDMRG_prop_method, normalize=1.0)
else:
MPOprop, HAM, Etot = ExactPropagator_hybrid_TDDMRG_TDH(mol, J, \
DMMPO, DMH, -1.0*dbeta, space=space, QNargs=QNargs)
DMH[-1] *= np.exp(-1.0 * Etot * dbeta)
TDH.unitary_propagation(HAM, DMH, dbeta / 1.0j)
DMMPO = mpslib.mapply(MPOprop, DMMPO, QNargs=QNargs)
# DMMPO is not normalize in the imaginary time domain
MPOnorm = mpslib.norm(DMMPO, QNargs=QNargs)
DMMPO = mpslib.scale(DMMPO, 1. / MPOnorm, QNargs=QNargs)
DMH[-1] *= MPOnorm
# normlize the dm (physical \otimes ancilla)
mflib.normalize(DMH)
# divided by np.sqrt(partition function)
DMH[-1] = 1.0
return DMMPO, DMH