def Exact_Spectra_hybrid_TDDMRG_TDH(spectratype, mol, J, MPS, dipoleMPO, WFN, \
nsteps, dt, E_offset=0.):
'''
exact spectra by hybrid TDDMRG/TDH approach for ZT abs and emi
'''
assert spectratype in ["emi", "abs"]
if spectratype == "emi":
space = "GS"
else:
space = "EX"
AketMPS = mpslib.mapply(dipoleMPO, MPS)
factor = mpslib.norm(AketMPS)
AketMPS = mpslib.scale(AketMPS, 1. / factor)
AbraMPS = mpslib.add(AketMPS, None)
WFN[-1] *= factor
WFNbra = copy.deepcopy(WFN)
MPOprop, HAM, Etot = ExactPropagator_hybrid_TDDMRG_TDH(mol,
J,
AketMPS,
WFN,
-1.0j * dt,
space=space)
print "TD Etot", Etot
autocorr = []
t = 0.
for istep in xrange(nsteps):
if istep != 0:
t += dt
WFN[-1] *= np.exp(-1.0j * Etot * dt)
AketMPS = mpslib.mapply(MPOprop, AketMPS)
TDH.unitary_propagation(HAM, WFN, dt)
ft = mpslib.dot(mpslib.conj(AbraMPS), AketMPS)
ft *= np.conj(WFNbra[-1]) * WFN[-1] * np.exp(-1.0j * E_offset * t)
for iwfn in xrange(len(WFN) - 1):
ft *= np.vdot(WFNbra[iwfn], WFN[iwfn])
autocorr.append(ft)
autocorr_store(autocorr, istep)
return autocorr
def test_FT_dynamics_hybrid_TDDMRG_TDH(self, value):
mol, J = parameter_PBI.construct_mol(4, nphs=value[0])
TDH.construct_Ham_vib(mol, hybrid=True)
nexciton = 0
dmrg_procedure = [[20, 0.5], [20, 0.3], [10, 0.2], [5, 0], [1, 0]]
MPS, MPSdim, MPSQN, MPO, MPOdim, MPOQN, MPOQNidx, MPOQNtot, ephtable, pbond = \
MPSsolver.construct_MPS_MPO_2(mol, J, dmrg_procedure[0][0], nexciton)
QNargs = [ephtable, False]
T = 2000.
insteps = 1
iMPS, WFN = hybrid_TDDMRG_TDH.FT_DM_hybrid_TDDMRG_TDH(mol, J, nexciton, T, \
insteps, pbond, ephtable, thresh=1e-3, cleanexciton=nexciton,\
QNargs=QNargs, space="GS")
dipoleMPO, dipoleMPOdim = MPSsolver.construct_onsiteMPO(mol, pbond, "a^\dagger",\
QNargs=QNargs, sitelist=[0])
iMPS = mpslib.mapply(dipoleMPO, iMPS, QNargs=QNargs)
norm = mpslib.norm(iMPS, QNargs=QNargs)
WFN[-1] *= norm
iMPS = mpslib.scale(iMPS, 1. / norm, QNargs=QNargs)
iMPS = mpslib.MPSdtype_convert(iMPS, QNargs=QNargs)
WFN = [wfn.astype(np.complex128) for wfn in WFN[:-1]] + [WFN[-1]]
nsteps = 90
dt = 10.0
MPOs = []
for imol in xrange(len(mol)):
dipoleMPO, dipoleMPOdim = MPSsolver.construct_onsiteMPO(mol, pbond, "a^\dagger a",\
QNargs=QNargs, sitelist=[imol])
MPOs.append(dipoleMPO)
data = hybrid_TDDMRG_TDH.dynamics_hybrid_TDDMRG_TDH(mol, J, iMPS, \
WFN, nsteps, dt, ephtable,thresh=1e-3, \
TDDMRG_prop_method="C_RK4", QNargs=QNargs, property_MPOs=MPOs)
with open("std_data/hybrid_TDDMRG_TDH/FT_occ" + str(value[0]) + ".npy",
'rb') as f:
std = np.load(f)
self.assertTrue(np.allclose(data, std))
def ZeroTcorr_hybrid_TDDMRG_TDH(mol, J, iMPS, dipoleMPO, WFN0, nsteps, dt, ephtable,\
thresh=0., TDDMRG_prop_method="C_RK4", E_offset=0., cleanexciton=None, QNargs=None):
'''
ZT linear spectra
'''
AketMPS = mpslib.mapply(dipoleMPO, iMPS, QNargs=QNargs)
factor = mpslib.norm(AketMPS, QNargs=QNargs)
AketMPS = mpslib.scale(AketMPS, 1. / factor, QNargs=QNargs)
AbraMPS = mpslib.add(AketMPS, None, QNargs=QNargs)
WFN0[-1] *= factor
WFNket = copy.deepcopy(WFN0)
WFNbra = copy.deepcopy(WFN0)
autocorr = []
t = 0.0
for istep in xrange(nsteps):
if istep != 0:
t += dt
if istep % 2 == 1:
AketMPS, WFNket = hybrid_TDDMRG_TDH(mol, J, AketMPS, WFNket,\
dt, ephtable, thresh=thresh, cleanexciton=cleanexciton, QNargs=QNargs, \
TDDMRG_prop_method=TDDMRG_prop_method, TDH_prop_method="unitary")
else:
AbraMPS, WFNbra = hybrid_TDDMRG_TDH(mol, J, AbraMPS, WFNbra,\
-dt, ephtable, thresh=thresh, cleanexciton=cleanexciton, QNargs=QNargs, \
TDDMRG_prop_method=TDDMRG_prop_method, TDH_prop_method="unitary")
ft = mpslib.dot(mpslib.conj(AbraMPS, QNargs=QNargs),
AketMPS,
QNargs=QNargs)
ft *= np.conj(WFNbra[-1]) * WFNket[-1] * np.exp(-1.0j * E_offset * t)
for iwfn in xrange(len(WFN0) - 1):
ft *= np.vdot(WFNbra[iwfn], WFNket[iwfn])
autocorr.append(ft)
autocorr_store(autocorr, istep)
return autocorr
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
def FiniteT_spectra_TDDMRG_TDH(spectratype, T, mol, J, nsteps, dt, insteps, pbond, ephtable,\
thresh=0., ithresh=1e-4, TDDMRG_prop_method="C_RK4", E_offset=0., QNargs=None):
'''
FT linear spectra
'''
assert spectratype in ["abs", "emi"]
dipoleMPO, dipoleMPOdim = MPSsolver.construct_onsiteMPO(mol,
pbond,
"a^\dagger",
dipole=True,
QNargs=QNargs)
# construct initial thermal equilibrium density matrix and apply dipole matrix
if spectratype == "abs":
nexciton = 0
DMMPO, DMH = FT_DM_hybrid_TDDMRG_TDH(mol, J, nexciton, T, insteps, pbond, ephtable, \
thresh=ithresh, TDDMRG_prop_method=TDDMRG_prop_method, QNargs=QNargs, space="GS")
DMMPOket = mpslib.mapply(dipoleMPO, DMMPO, QNargs=QNargs)
else:
nexciton = 1
DMMPO, DMH = FT_DM_hybrid_TDDMRG_TDH(mol, J, nexciton, T, insteps, pbond, ephtable, \
thresh=ithresh, TDDMRG_prop_method=TDDMRG_prop_method, QNargs=QNargs, space=None)
if QNargs is not None:
dipoleMPO[1] = [[0] * len(impsdim) for impsdim in dipoleMPO[1]]
dipoleMPO[3] = 0
DMMPOket = mpslib.mapply(DMMPO, dipoleMPO, QNargs=QNargs)
factor = mpslib.norm(DMMPOket, QNargs=QNargs)
DMMPOket = mpslib.scale(DMMPOket, 1. / factor, QNargs=QNargs)
DMMPObra = mpslib.add(DMMPOket, None, QNargs=QNargs)
DMH[-1] *= factor
DMHket = copy.deepcopy(DMH)
DMHbra = copy.deepcopy(DMH)
autocorr = []
t = 0.0
def prop(DMMPO, DMH, dt):
MPOprop, HAM, Etot = ExactPropagator_hybrid_TDDMRG_TDH(mol, J, \
DMMPO, DMH, -1.0j*dt, space="GS", QNargs=QNargs)
DMMPO = mpslib.mapply(DMMPO, MPOprop, QNargs=QNargs)
DMH[-1] *= np.exp(-1.0j * Etot * dt)
for iham, hamprop in enumerate(HAM):
w, v = scipy.linalg.eigh(hamprop)
DMH[iham] = DMH[iham].dot(v).dot(np.diag(np.exp(-1.0j * dt *
w))).dot(v.T)
DMMPO, DMH = hybrid_TDDMRG_TDH(mol, J, DMMPO, DMH, \
-dt, ephtable, thresh=thresh, QNargs=QNargs, TDDMRG_prop_method=TDDMRG_prop_method, normalize=1.0)
return DMMPO, DMH
print("Real time dynamics starts!")
for istep in xrange(nsteps):
print("istep=", istep)
if istep != 0:
t += dt
if istep % 2 == 0:
DMMPObra, DMHbra = prop(DMMPObra, DMHbra, dt)
else:
DMMPOket, DMHket = prop(DMMPOket, DMHket, -dt)
ft = mpslib.dot(mpslib.conj(DMMPObra, QNargs=QNargs),
DMMPOket,
QNargs=QNargs)
ft *= np.conj(DMHbra[-1]) * DMHket[-1]
for idm in xrange(len(DMH) - 1):
ft *= np.vdot(DMHbra[idm], DMHket[idm])
if spectratype == "emi":
ft = np.conj(ft)
# for emi bra and ket is conjugated
ft *= np.exp(-1.0j * E_offset * t)
autocorr.append(ft)
autocorr_store(autocorr, istep)
return autocorr