class SpectraFtCV(SpectraCv):
''' Finite temperature CV-DMRG for absorption/emission
Parameters:
mol_list : MolList
provide the molecular information
spectratype : string
"abs" or "emi"
temperature : Quantity
"a.u."
freq_reg : list
frequency window to be calculated (/ a.u.)
m_max : int
maximal bond dimension of correction vector MPO
eta : float
Lorentzian broadening width
icompress_config : CopressConfig
for imaginary time evolution in emission
insteps : int
evolve steps for imaginary time
method : string
"1site"
procedure_cv : list
percent used for each sweep
cores : int
cores used for parallel
Example::
>>> from renormalizer.cv.finitet import SpectraFtCV
>>> from renormalizer.tests.parameter import mol_list
>>> import numpy as np
>>> from renormalizer.utils import Quantity
>>> def run():
... freq_reg = np.arange(0.08, 0.10, 5.e-4).tolist()
... T = Quantity(298, unit='K')
... spectra = SpectraFtCV(mol_list, "abs", T, test_freq,
... 10, 1.e-3, cores=1)
... spectra.init_oper()
... spectra.init_mps()
... result = spectra.run()
>>> if __name__ == "__main__":
... run()
'''
def __init__(self,
mol_list,
spectratype,
temperature,
freq_reg,
m_max,
eta,
icompress_config=None,
ievolve_config=None,
insteps=None,
method='1site',
procedure_cv=None,
dump_dir: str = None,
job_name=None,
cores=1):
super().__init__(mol_list, spectratype, freq_reg, m_max, eta, method,
procedure_cv, cores)
self.temperature = temperature
self.evolve_config = ievolve_config
self.compress_config = icompress_config
if self.evolve_config is None:
self.evolve_config = \
EvolveConfig()
if self.compress_config is None:
self.compress_config = \
CompressConfig(CompressCriteria.fixed,
max_bonddim=m_max)
self.compress_config.set_bonddim(len(mol_list.pbond_list))
self.insteps = insteps
self.job_name = job_name
self.dump_dir = dump_dir
def init_mps(self):
beta = self.temperature.to_beta()
self.h_mpo = Mpo(self.mol_list)
if self.spectratype == "abs":
dipole_mpo = Mpo.onsite(self.mol_list, r"a^\dagger", dipole=True)
i_mpo = MpDm.max_entangled_gs(self.mol_list)
tp = ThermalProp(i_mpo, self.h_mpo, exact=True, space='GS')
tp.evolve(None, 1, beta / 2j)
ket_mpo = tp.latest_mps
else:
impo = MpDm.max_entangled_ex(self.mol_list)
dipole_mpo = Mpo.onsite(self.mol_list, "a", dipole=True)
if self.job_name is None:
job_name = None
else:
job_name = self.job_name + "_thermal_prop"
impo.compress_config = self.compress_config
tp = ThermalProp(impo,
self.h_mpo,
evolve_config=self.evolve_config,
dump_dir=self.dump_dir,
job_name=job_name)
self._defined_output_path = tp._defined_output_path
if tp._defined_output_path:
try:
logger.info(
f"load density matrix from {self._thermal_dump_path}")
ket_mpo = MpDm.load(self.mol_list, self._thermal_dump_path)
logger.info(f"density matrix loaded: {ket_mpo}")
except FileNotFoundError:
logger.debug(f"no file found in {self._thermal_dump_path}")
tp.evolve(None, self.insteps, beta / 2j)
ket_mpo = tp.latest_mps
ket_mpo.dump(self._thermal_dump_path)
self.a_ket_mpo = dipole_mpo.apply(ket_mpo, canonicalise=True)
self.cv_mpo = Mpo.finiteT_cv(self.mol_list,
1,
self.m_max,
self.spectratype,
percent=1.0)
self.cv_mps = self.cv_mpo
def init_oper(self):
pass
@property
def _thermal_dump_path(self):
assert self._defined_output_path
return os.path.join(self.dump_dir, self.job_name + "_impo.npz")
def oper_prepare(self, omega):
omega_minus_H = copy.deepcopy(self.h_mpo)
for ibra in range(self.h_mpo.pbond_list[0]):
omega_minus_H[0][0, ibra, ibra, 0] -= omega
omega_minus_H = omega_minus_H.scale(-1)
self.a_oper = omega_minus_H.apply(omega_minus_H)
for ibra in range(self.a_oper[0].shape[1]):
self.a_oper[0][0, ibra, ibra, 0] += (self.eta**2)
self.b_oper = omega_minus_H
def optimize_cv(self, lr_group, direction, isite, num, percent=0):
if self.spectratype == "abs":
# quantum number restriction, |1><0|
up_exciton, down_exciton = 1, 0
elif self.spectratype == "emi":
# quantum number restriction, |0><1|
up_exciton, down_exciton = 0, 1
nexciton = 1
first_LR, second_LR, third_LR, forth_LR = lr_group
if self.method == "1site":
add_list = [isite - 1]
first_L = asxp(first_LR[isite - 1])
first_R = asxp(first_LR[isite])
second_L = asxp(second_LR[isite - 1])
second_R = asxp(second_LR[isite])
third_L = asxp(third_LR[isite - 1])
third_R = asxp(third_LR[isite])
forth_L = asxp(forth_LR[isite - 1])
forth_R = asxp(forth_LR[isite])
else:
add_list = [isite - 2, isite - 1]
first_L = asxp(first_LR[isite - 2])
first_R = asxp(first_LR[isite])
second_L = asxp(second_LR[isite - 2])
second_R = asxp(second_LR[isite])
third_L = asxp(third_LR[isite - 2])
third_R = asxp(third_LR[isite])
forth_L = asxp(forth_LR[isite - 2])
forth_R = asxp(forth_LR[isite])
xqnmat, xqnbigl, xqnbigr, xshape = \
self.construct_X_qnmat(add_list, direction)
dag_qnmat, dag_qnbigl, dag_qnbigr = self.swap(xqnmat, xqnbigl, xqnbigr,
direction)
nonzeros = np.sum(self.condition(dag_qnmat,
[down_exciton, up_exciton]))
if self.method == "1site":
guess = moveaxis(self.cv_mpo[isite - 1], (1, 2), (2, 1))
else:
guess = tensordot(moveaxis(self.cv_mpo[isite - 2], (1, 2), (2, 1)),
moveaxis(self.cv_mpo[isite - 1]),
axes=(-1, 0))
guess = guess[self.condition(dag_qnmat,
[down_exciton, up_exciton])].reshape(
nonzeros, 1)
if self.method == "1site":
# define dot path
path_1 = [([0, 1], "abc, adef -> bcdef"),
([2, 0], "bcdef, begh -> cdfgh"),
([1, 0], "cdfgh, fhi -> cdgi")]
path_2 = [([0, 1], "abcd, aefg -> bcdefg"),
([3, 0], "bcdefg, bfhi -> cdeghi"),
([2, 0], "cdeghi, djek -> cghijk"),
([1, 0], "cghijk, gilk -> chjl")]
path_4 = [([0, 1], "ab, acde -> bcde"), ([1,
0], "bcde, ef -> bcdf")]
vecb = multi_tensor_contract(
path_4, forth_L,
moveaxis(self.a_ket_mpo[isite - 1], (1, 2), (2, 1)), forth_R)
vecb = -self.eta * vecb
a_oper_isite = asxp(self.a_oper[isite - 1])
b_oper_isite = asxp(self.b_oper[isite - 1])
h_mpo_isite = asxp(self.h_mpo[isite - 1])
# construct preconditioner
Idt = xp.identity(h_mpo_isite.shape[1])
M1_1 = xp.einsum('aea->ae', first_L)
M1_2 = xp.einsum('eccf->ecf', a_oper_isite)
M1_3 = xp.einsum('dfd->df', first_R)
M1_4 = xp.einsum('bb->b', Idt)
path_m1 = [([0, 1], "ae,b->aeb"), ([2, 0], "aeb,ecf->abcf"),
([1, 0], "abcf, df->abcd")]
pre_M1 = multi_tensor_contract(path_m1, M1_1, M1_4, M1_2, M1_3)
pre_M1 = pre_M1[self.condition(dag_qnmat, [down_exciton, up_exciton])]
M2_1 = xp.einsum('aeag->aeg', second_L)
M2_2 = xp.einsum('eccf->ecf', b_oper_isite)
M2_3 = xp.einsum('gbbh->gbh', h_mpo_isite)
M2_4 = xp.einsum('dfdh->dfh', second_R)
path_m2 = [([0, 1], "aeg,gbh->aebh"), ([2, 0], "aebh,ecf->abchf"),
([1, 0], "abhcf,dfh->abcd")]
pre_M2 = multi_tensor_contract(path_m2, M2_1, M2_3, M2_2, M2_4)
pre_M2 = pre_M2[self.condition(dag_qnmat, [down_exciton, up_exciton])]
M4_1 = xp.einsum('faah->fah', third_L)
M4_4 = xp.einsum('gddi->gdi', third_R)
M4_5 = xp.einsum('cc->c', Idt)
M4_path = [([0, 1], "fah,febg->ahebg"), ([2, 0], "ahebg,hjei->abgji"),
([1, 0], "abgji,gdi->abjd")]
pre_M4 = multi_tensor_contract(M4_path, M4_1, h_mpo_isite, h_mpo_isite,
M4_4)
pre_M4 = xp.einsum('abbd->abd', pre_M4)
pre_M4 = xp.tensordot(pre_M4, M4_5, axes=0)
pre_M4 = xp.moveaxis(pre_M4, [2, 3], [3, 2])[self.condition(
dag_qnmat, [down_exciton, up_exciton])]
pre_M = (pre_M1 + 2 * pre_M2 + pre_M4)
indices = np.array(range(nonzeros))
indptr = np.array(range(nonzeros + 1))
pre_M = scipy.sparse.csc_matrix((asnumpy(pre_M), indices, indptr),
shape=(nonzeros, nonzeros))
M_x = lambda x: scipy.sparse.linalg.spsolve(pre_M, x)
M = scipy.sparse.linalg.LinearOperator((nonzeros, nonzeros), M_x)
count = 0
def hop(x):
nonlocal count
count += 1
dag_struct = asxp(self.dag2mat(xshape, x, dag_qnmat, direction))
if self.method == "1site":
M1 = multi_tensor_contract(path_1, first_L, dag_struct,
a_oper_isite, first_R)
M2 = multi_tensor_contract(path_2, second_L, dag_struct,
b_oper_isite, h_mpo_isite, second_R)
M2 = xp.moveaxis(M2, (1, 2), (2, 1))
M3 = multi_tensor_contract(path_2, third_L, h_mpo_isite,
dag_struct, h_mpo_isite, third_R)
M3 = xp.moveaxis(M3, (1, 2), (2, 1))
cout = M1 + 2 * M2 + M3
cout = cout[self.condition(dag_qnmat,
[down_exciton, up_exciton])].reshape(
nonzeros, 1)
return asnumpy(cout)
# Matrix A and Vector b
vecb = asnumpy(vecb)[self.condition(
dag_qnmat, [down_exciton, up_exciton])].reshape(nonzeros, 1)
mata = scipy.sparse.linalg.LinearOperator((nonzeros, nonzeros),
matvec=hop)
# conjugate gradient method
# x, info = scipy.sparse.linalg.cg(MatA, VecB, atol=0)
if num == 1:
x, info = scipy.sparse.linalg.cg(mata,
vecb,
tol=1.e-5,
maxiter=500,
M=M,
atol=0)
else:
x, info = scipy.sparse.linalg.cg(mata,
vecb,
tol=1.e-5,
x0=guess,
maxiter=500,
M=M,
atol=0)
# logger.info(f"linear eq dim: {nonzeros}")
# logger.info(f'times for hop:{count}')
self.hop_time.append(count)
if info != 0:
logger.warning(
f"cg not converged, vecb.norm:{np.linalg.norm(vecb)}")
l_value = np.inner(
hop(x).reshape(1, nonzeros), x.reshape(1, nonzeros)) - \
2 * np.inner(vecb.reshape(1, nonzeros), x.reshape(1, nonzeros))
x = self.dag2mat(xshape, x, dag_qnmat, direction)
if self.method == "1site":
x = np.moveaxis(x, [1, 2], [2, 1])
x, xdim, xqn, compx = self.x_svd(x,
xqnbigl,
xqnbigr,
nexciton,
direction,
percent=percent)
if self.method == "1site":
self.cv_mpo[isite - 1] = x
if direction == "left":
if isite != 1:
self.cv_mpo[isite - 2] = \
tensordot(self.cv_mpo[isite - 2], compx, axes=(-1, 0))
self.cv_mpo.qn[isite - 1] = xqn
else:
self.cv_mpo[isite - 1] = \
tensordot(compx, self.cv_mpo[isite - 1], axes=(-1, 0))
elif direction == "right":
if isite != len(self.cv_mpo):
self.cv_mpo[isite] = \
tensordot(compx, self.cv_mpo[isite], axes=(-1, 0))
self.cv_mpo.qn[isite] = xqn
else:
self.cv_mpo[isite - 1] = \
tensordot(self.cv_mpo[isite - 1], compx, axes=(-1, 0))
else:
if direction == "left":
self.cv_mpo[isite - 2] = compx
self.cv_mpo[isite - 1] = x
else:
self.cv_mpo[isite - 2] = x
self.cv_mpo[isite - 1] = compx
self.cv_mpo.qn[isite - 1] = xqn
return l_value[0][0]
def construct_X_qnmat(self, addlist, direction):
pbond = self.mol_list.pbond_list
xqnl = np.array(self.cv_mpo.qn[addlist[0]])
xqnr = np.array(self.cv_mpo.qn[addlist[-1] + 1])
xqnmat = xqnl.copy()
xqnsigmalist = []
for idx in addlist:
if self.mol_list.ephtable.is_electron(idx):
xqnsigma = np.array([[[0, 0], [0, 1]], [[1, 0], [1, 1]]])
else:
xqnsigma = []
for i in range((pbond[idx])**2):
xqnsigma.append([0, 0])
xqnsigma = np.array(xqnsigma)
xqnsigma = xqnsigma.reshape(pbond[idx], pbond[idx], 2)
xqnmat = self.qnmat_add(xqnmat, xqnsigma)
xqnsigmalist.append(xqnsigma)
xqnmat = self.qnmat_add(xqnmat, xqnr)
matshape = list(xqnmat.shape)
if self.method == "1site":
if xqnmat.ndim == 4:
if direction == "left":
xqnmat = np.moveaxis(xqnmat.reshape(matshape + [1]), -1,
-2)
else:
xqnmat = xqnmat.reshape([1] + matshape)
if direction == "left":
xqnbigl = xqnl.copy()
xqnbigr = self.qnmat_add(xqnsigmalist[0], xqnr)
if xqnbigr.ndim == 3:
rshape = list(xqnbigr.shape)
xqnbigr = np.moveaxis(xqnbigr.reshape(rshape + [1]), -1,
-2)
else:
xqnbigl = self.qnmat_add(xqnl, xqnsigmalist[0])
xqnbigr = xqnr.copy()
if xqnbigl.ndim == 3:
lshape = list(xqnbigl.shape)
xqnbigl = xqnbigl.reshape([1] + lshape)
else:
if xqnmat.ndim == 6:
if addlist[0] != 0:
xqnmat = np.moveaxis(xqnmat.resahpe(matshape + [1]), -1,
-2)
else:
xqnmat = xqnmat.reshape([1] + matshape)
xqnbigl = self.qnmat_add(xqnl, xqnsigmalist[0])
if xqnbigl.ndim == 3:
lshape = list(xqnbigl.shape)
xqnbigl = xqnbigl.reshape([1] + lshape)
xqnbigr = self.qnmat_add(xqnsigmalist[-1], xqnr)
if xqnbigr.ndim == 3:
rshape = list(xqnbigr.shape)
xqnbigr = np.moveaxis(xqnbigr.reshape(rshape + [1]), -1, -2)
xshape = list(xqnmat.shape)
del xshape[-1]
if len(xshape) == 3:
if direction == "left":
xshape = xshape + [1]
elif direction == "right":
xshape = [1] + xshape
return xqnmat, xqnbigl, xqnbigr, xshape
def swap(self, mat, qnbigl, qnbigr, direction):
def inter_change(ori_mat):
matshape = ori_mat.shape
len_mat = int(np.prod(np.array(matshape[:-1])))
ori_mat = ori_mat.reshape(len_mat, 2)
change_mat = copy.deepcopy(ori_mat)
change_mat[:, 0], change_mat[:, 1] = ori_mat[:, 1], ori_mat[:, 0]
return change_mat.reshape(matshape)
dag_qnmat = inter_change(mat)
if self.method == "1site":
dag_qnmat = np.moveaxis(dag_qnmat, [1, 2], [2, 1])
dag_qnbigl = inter_change(qnbigl)
dag_qnbigr = inter_change(qnbigr)
if direction == "left":
dag_qnbigr = np.moveaxis(dag_qnbigr, [0, 1], [1, 0])
else:
dag_qnbigl = np.moveaxis(dag_qnbigl, [1, 2], [2, 1])
else:
raise NotImplementedError
# we don't recommend 2-site CV-DMRG, which is a huge cost
return dag_qnmat, dag_qnbigl, dag_qnbigr
def condition(self, mat, qn):
condition = (mat == qn)
mat_shape = list(condition.shape)
del mat_shape[-1]
condition = condition.all(axis=-1)
condition = condition.reshape(mat_shape)
return condition
def qnmat_add(self, mat_l, mat_r):
lshape, rshape = mat_l.shape, mat_r.shape
lena = int(np.prod(np.array(lshape)) / 2)
lenb = int(np.prod(np.array(rshape)) / 2)
matl = mat_l.reshape(lena, 2)
matr = mat_r.reshape(lenb, 2)
lr1 = np.add.outer(matl[:, 0], matr[:, 0]).flatten()
lr2 = np.add.outer(matl[:, 1], matr[:, 1]).flatten()
lr = np.zeros((len(lr1), 2))
lr[:, 0] = lr1
lr[:, 1] = lr2
shapel = list(mat_l.shape)
del shapel[-1]
shaper = list(mat_r.shape)
del shaper[-1]
lr = lr.reshape(shapel + shaper + [2])
return lr
def dag2mat(self, xshape, x, dag_qnmat, direction):
if self.spectratype == "abs":
up_exciton, down_exciton = 1, 0
else:
up_exciton, down_exciton = 0, 1
xdag = np.zeros(xshape, dtype=x.dtype)
mask = self.condition(dag_qnmat, [down_exciton, up_exciton])
np.place(xdag, mask, x)
shape = list(xdag.shape)
if xdag.ndim == 3:
if direction == 'left':
xdag = xdag.reshape(shape + [1])
else:
xdag = xdag.reshape([1] + shape)
return xdag
def x_svd(self, xstruct, xqnbigl, xqnbigr, nexciton, direction, percent=0):
Gamma = xstruct.reshape(
np.prod(xqnbigl.shape) // 2,
np.prod(xqnbigr.shape) // 2)
localXqnl = xqnbigl.ravel()
localXqnr = xqnbigr.ravel()
list_locall = []
list_localr = []
for i in range(0, len(localXqnl), 2):
list_locall.append([localXqnl[i], localXqnl[i + 1]])
for i in range(0, len(localXqnr), 2):
list_localr.append([localXqnr[i], localXqnr[i + 1]])
localXqnl = copy.deepcopy(list_locall)
localXqnr = copy.deepcopy(list_localr)
xuset = []
xuset0 = []
xvset = []
xvset0 = []
xsset = []
xsuset0 = []
xsvset0 = []
xqnlset = []
xqnlset0 = []
xqnrset = []
xqnrset0 = []
if self.spectratype == "abs":
combine = [[[y, 0], [nexciton - y, 0]]
for y in range(nexciton + 1)]
elif self.spectratype == "emi":
combine = [[[0, y], [0, nexciton - y]]
for y in range(nexciton + 1)]
for nl, nr in combine:
lset = np.where(self.condition(np.array(localXqnl), [nl]))[0]
rset = np.where(self.condition(np.array(localXqnr), [nr]))[0]
if len(lset) != 0 and len(rset) != 0:
Gamma_block = Gamma.ravel().take(
(lset * Gamma.shape[1]).reshape(-1, 1) + rset)
try:
U, S, Vt = \
scipy.linalg.svd(Gamma_block, full_matrices=True,
lapack_driver='gesdd')
except:
U, S, Vt = \
scipy.linalg.svd(Gamma_block, full_matrices=True,
lapack_driver='gesvd')
dim = S.shape[0]
xsset.append(S)
# U part quantum number
xuset.append(
svd_qn.blockrecover(lset, U[:, :dim], Gamma.shape[0]))
xqnlset += [nl] * dim
xuset0.append(
svd_qn.blockrecover(lset, U[:, dim:], Gamma.shape[0]))
xqnlset0 += [nl] * (U.shape[0] - dim)
xsuset0.append(np.zeros(U.shape[0] - dim))
# V part quantum number
VT = Vt.T
xvset.append(
svd_qn.blockrecover(rset, VT[:, :dim], Gamma.shape[1]))
xqnrset += [nr] * dim
xvset0.append(
svd_qn.blockrecover(rset, VT[:, dim:], Gamma.shape[1]))
xqnrset0 += [nr] * (VT.shape[0] - dim)
xsvset0.append(np.zeros(VT.shape[0] - dim))
xuset = np.concatenate(xuset + xuset0, axis=1)
xvset = np.concatenate(xvset + xvset0, axis=1)
xsuset = np.concatenate(xsset + xsuset0)
xsvset = np.concatenate(xsset + xsvset0)
xqnlset = xqnlset + xqnlset0
xqnrset = xqnrset + xqnrset0
bigl_shape = list(xqnbigl.shape)
del bigl_shape[-1]
bigr_shape = list(xqnbigr.shape)
del bigr_shape[-1]
if direction == "left":
x, xdim, xqn, compx = update_cv(xvset,
xsvset,
xqnrset,
xuset,
nexciton,
self.m_max,
self.spectratype,
percent=percent)
if (self.method == "1site") and (len(bigr_shape + [xdim]) == 3):
return np.moveaxis(
x.reshape(bigr_shape + [1] + [xdim]), -1, 0),\
xdim, xqn, compx.reshape(bigl_shape + [xdim])
else:
return np.moveaxis(x.reshape(bigr_shape + [xdim]), -1, 0),\
xdim, xqn, compx.reshape(bigl_shape + [xdim])
elif direction == "right":
x, xdim, xqn, compx = update_cv(xuset,
xsuset,
xqnlset,
xvset,
nexciton,
self.m_max,
self.spectratype,
percent=percent)
if (self.method == "1site") and (len(bigl_shape + [xdim]) == 3):
return x.reshape([1] + bigl_shape + [xdim]), xdim, xqn, \
np.moveaxis(compx.reshape(bigr_shape + [xdim]), -1, 0)
else:
return x.reshape(bigl_shape + [xdim]), xdim, xqn, \
np.moveaxis(compx.reshape(bigr_shape + [xdim]), -1, 0)
def initialize_LR(self, direction):
first_LR = [np.ones((1, 1, 1))]
second_LR = [np.ones((1, 1, 1, 1))]
forth_LR = [np.ones((1, 1))]
for isite in range(1, len(self.cv_mpo)):
first_LR.append(None)
second_LR.append(None)
forth_LR.append(None)
first_LR.append(np.ones((1, 1, 1)))
second_LR.append(np.ones((1, 1, 1, 1)))
third_LR = copy.deepcopy(second_LR)
forth_LR.append(np.ones((1, 1)))
if direction == "right":
for isite in range(len(self.cv_mpo), 1, -1):
path1 = [([0, 1], "abc, defa -> bcdef"),
([2, 0], "bcdef, gfhb -> cdegh"),
([1, 0], "cdegh, ihec -> dgi")]
first_LR[isite - 1] = asnumpy(
multi_tensor_contract(
path1, first_LR[isite],
moveaxis(self.cv_mpo[isite - 1], (1, 2), (2, 1)),
self.a_oper[isite - 1], self.cv_mpo[isite - 1]))
path2 = [([0, 1], "abcd, efga -> bcdefg"),
([3, 0], "bcdefg, hgib -> cdefhi"),
([2, 0], "cdefhi, jikc -> defhjk"),
([1, 0], "defhjk, lkfd -> ehjl")]
path4 = [([0, 1], "ab, cdea->bcde"), ([1,
0], "bcde, fedb->cf")]
second_LR[isite - 1] = asnumpy(
multi_tensor_contract(
path2, second_LR[isite],
moveaxis(self.cv_mpo[isite - 1], (1, 2),
(2, 1)), self.b_oper[isite - 1],
self.cv_mpo[isite - 1], self.h_mpo[isite - 1]))
third_LR[isite - 1] = asnumpy(
multi_tensor_contract(
path2, third_LR[isite], self.h_mpo[isite - 1],
moveaxis(self.cv_mpo[isite - 1], (1, 2), (2, 1)),
self.cv_mpo[isite - 1], self.h_mpo[isite - 1]))
forth_LR[isite - 1] = asnumpy(
multi_tensor_contract(
path4, forth_LR[isite],
moveaxis(self.a_ket_mpo[isite - 1], (1, 2), (2, 1)),
self.cv_mpo[isite - 1]))
if direction == "left":
for isite in range(1, len(self.cv_mpo)):
path1 = [([0, 1], "abc, adef -> bcdef"),
([2, 0], "bcdef, begh -> cdfgh"),
([1, 0], "cdfgh, cgdi -> fhi")]
first_LR[isite] = asnumpy(
multi_tensor_contract(
path1, first_LR[isite - 1],
moveaxis(self.cv_mpo[isite - 1], (1, 2), (2, 1)),
self.a_oper[isite - 1], self.cv_mpo[isite - 1]))
path2 = [([0, 1], "abcd, aefg -> bcdefg"),
([3, 0], "bcdefg, bfhi -> cdeghi"),
([2, 0], "cdeghi, chjk -> degijk"),
([1, 0], "degijk, djel -> gikl")]
path4 = [([0, 1], "ab, acde->bcde"), ([1,
0], "bcde, bdcf->ef")]
second_LR[isite] = asnumpy(
multi_tensor_contract(
path2, second_LR[isite - 1],
moveaxis(self.cv_mpo[isite - 1], (1, 2),
(2, 1)), self.b_oper[isite - 1],
self.cv_mpo[isite - 1], self.h_mpo[isite - 1]))
third_LR[isite] = asnumpy(
multi_tensor_contract(
path2, third_LR[isite - 1], self.h_mpo[isite - 1],
moveaxis(self.cv_mpo[isite - 1], (1, 2), (2, 1)),
self.cv_mpo[isite - 1], self.h_mpo[isite - 1]))
forth_LR[isite] = asnumpy(
multi_tensor_contract(
path4, forth_LR[isite - 1],
moveaxis(self.a_ket_mpo[isite - 1], (1, 2), (2, 1)),
self.cv_mpo[isite - 1]))
return [first_LR, second_LR, third_LR, forth_LR]
def update_LR(self, lr_group, direction, isite):
first_LR, second_LR, third_LR, forth_LR = lr_group
assert direction in ["left", "right"]
if self.method == "1site":
if direction == "left":
path1 = [([0, 1], "abc, defa -> bcdef"),
([2, 0], "bcdef, gfhb -> cdegh"),
([1, 0], "cdegh, ihec -> dgi")]
first_LR[isite - 1] = multi_tensor_contract(
path1, first_LR[isite],
moveaxis(self.cv_mpo[isite - 1], (1, 2), (2, 1)),
self.a_oper[isite - 1], self.cv_mpo[isite - 1])
path2 = [([0, 1], "abcd, efga -> bcdefg"),
([3, 0], "bcdefg, hgib -> cdefhi"),
([2, 0], "cdefhi, jikc -> defhjk"),
([1, 0], "defhjk, lkfd -> ehjl")]
path4 = [([0, 1], "ab, cdea->bcde"), ([1,
0], "bcde, fedb->cf")]
second_LR[isite - 1] = multi_tensor_contract(
path2, second_LR[isite],
moveaxis(self.cv_mpo[isite - 1], (1, 2),
(2, 1)), self.b_oper[isite - 1],
self.cv_mpo[isite - 1], self.h_mpo[isite - 1])
third_LR[isite - 1] = multi_tensor_contract(
path2, third_LR[isite], self.h_mpo[isite - 1],
moveaxis(self.cv_mpo[isite - 1], (1, 2), (2, 1)),
self.cv_mpo[isite - 1], self.h_mpo[isite - 1])
forth_LR[isite - 1] = multi_tensor_contract(
path4, forth_LR[isite],
moveaxis(self.a_ket_mpo[isite - 1], (1, 2), (2, 1)),
self.cv_mpo[isite - 1])
elif direction == "right":
path1 = [([0, 1], "abc, adef -> bcdef"),
([2, 0], "bcdef, begh -> cdfgh"),
([1, 0], "cdfgh, cgdi -> fhi")]
first_LR[isite] = multi_tensor_contract(
path1, first_LR[isite - 1],
moveaxis(self.cv_mpo[isite - 1], (1, 2), (2, 1)),
self.a_oper[isite - 1], self.cv_mpo[isite - 1])
path2 = [([0, 1], "abcd, aefg -> bcdefg"),
([3, 0], "bcdefg, bfhi -> cdeghi"),
([2, 0], "cdeghi, chjk -> degijk"),
([1, 0], "degijk, djel -> gikl")]
path4 = [([0, 1], "ab, acde->bcde"), ([1,
0], "bcde, bdcf->ef")]
second_LR[isite] = multi_tensor_contract(
path2, second_LR[isite - 1],
moveaxis(self.cv_mpo[isite - 1], (1, 2),
(2, 1)), self.b_oper[isite - 1],
self.cv_mpo[isite - 1], self.h_mpo[isite - 1])
third_LR[isite] = multi_tensor_contract(
path2, third_LR[isite - 1], self.h_mpo[isite - 1],
moveaxis(self.cv_mpo[isite - 1], (1, 2), (2, 1)),
self.cv_mpo[isite - 1], self.h_mpo[isite - 1])
forth_LR[isite] = multi_tensor_contract(
path4, forth_LR[isite - 1],
moveaxis(self.a_ket_mpo[isite - 1], (1, 2), (2, 1)),
self.cv_mpo[isite - 1])
else:
# 2site for finite temperature is too expensive, so I drop it
# (at least for now)
raise NotImplementedError
return first_LR, second_LR, third_LR, forth_LR
class SpectraFtCV(SpectraCv):
r"""
Use DDMRG to calculate the finite temperature spectrum from frequency domain
Args:
model (:class:`~renormalizer.model.Model`): system information.
spectratype (string): "abs" or "emi".
m_max (int): maximal bond dimension of correction vector.
eta (float): Lorentzian broadening width (a.u.).
temperature (:class:`~renormalizer.utils.Quantity`): simulation temperature.
h_mpo (:class:`~renormalizer.mps.Mpo`): system Hamiltonian.
method (str): "1site" or "2site".
procedure_cv (list): percent used for each sweep.
rtol (float): the relative tolerance of the spectrum strength, default: 1e-5.
b_mps (:class:`~renormalizer.mps.Mps`): the b vector -eta * dipole * \psi_0, default: None.
(Holstein model could construct b_mps implicitly).
cv_mps (:class:`~renormalizer.mps.Mps`): initial guess of cv_mps, default: None.
icompress_config (:class:`~renormalizer.utils.CompressConfig`): config when compressing MPS/MPO during the imaginary time evolution..
ievolve_config (:class:`~renormalizer.utils.EvolveConfig`): evolution config for imaginary time evolution.
insteps (int): evolve steps for imaginary time evolution. have to be provided when calculating emission.
dump_dir (str): the directory for logging and numerical result output.
Also the directory from which to load previous thermal propagated initial state (if exists).
job_name (str): the name of the calculation job which determines the file name of the logging and numerical result output.
Example::
see test/test_abs.py for example
"""
def __init__(
self,
model,
spectratype,
m_max,
eta,
temperature,
h_mpo=None,
method='1site',
procedure_cv=None,
rtol=1e-5,
b_mps=None,
cv_mps=None,
icompress_config=None,
ievolve_config=None,
insteps=None,
dump_dir: str = None,
job_name=None,
):
self.temperature = temperature
self.evolve_config = ievolve_config
self.compress_config = icompress_config
if self.evolve_config is None:
self.evolve_config = \
EvolveConfig()
if self.compress_config is None:
self.compress_config = \
CompressConfig(CompressCriteria.fixed,
max_bonddim=m_max)
self.compress_config.set_bonddim(len(model.pbond_list))
self.insteps = insteps
self.job_name = job_name
self.dump_dir = dump_dir
super().__init__(
model,
spectratype,
m_max,
eta,
h_mpo=h_mpo,
method=method,
procedure_cv=procedure_cv,
rtol=rtol,
b_mps=b_mps,
cv_mps=cv_mps,
)
self.cv_mpo = self.cv_mps
self.b_mpo = self.b_mps
self.a_oper = None
def init_cv_mpo(self):
cv_mpo = Mpo.finiteT_cv(self.model,
1,
self.m_max,
self.spectratype,
percent=1.0)
return cv_mpo
init_cv_mps = init_cv_mpo
def init_b_mpo(self):
# get the right hand site vector b, Ax=b
# b = -eta * dipole * \psi_0
# only support Holstien model 0/1 exciton manifold
beta = self.temperature.to_beta()
if self.spectratype == "abs":
dipole_mpo = Mpo.onsite(self.model, r"a^\dagger", dipole=True)
i_mpo = MpDm.max_entangled_gs(self.model)
tp = ThermalProp(i_mpo, self.h_mpo, exact=True, space='GS')
tp.evolve(None, 1, beta / 2j)
ket_mpo = tp.latest_mps
elif self.spectratype == "emi":
dipole_mpo = Mpo.onsite(self.model, "a", dipole=True)
if self._defined_output_path:
ket_mpo = \
load_thermal_state(self.model, self._thermal_dump_path)
else:
ket_mpo = None
if ket_mpo is None:
impo = MpDm.max_entangled_ex(self.model)
impo.compress_config = self.compress_config
if self.job_name is None:
job_name = None
else:
job_name = self.job_name + "_thermal_prop"
tp = ThermalProp(impo,
self.h_mpo,
evolve_config=self.evolve_config,
dump_dir=self.dump_dir,
job_name=job_name)
tp.evolve(None, self.insteps, beta / 2j)
ket_mpo = tp.latest_mps
if self._defined_output_path:
ket_mpo.dump(self._thermal_dump_path)
else:
assert False
ket_mpo = dipole_mpo.apply(ket_mpo.scale(-self.eta))
return ket_mpo, None
init_b_mps = init_b_mpo
@property
def _thermal_dump_path(self):
assert self._defined_output_path
return os.path.join(self.dump_dir, self.job_name + "_impo.npz")
@property
def _defined_output_path(self):
return self.dump_dir is not None and self.job_name is not None
def oper_prepare(self, omega):
identity = Mpo.identity(self.model).scale(omega)
self.a_oper = identity.add(self.h_mpo.scale(-1, inplace=False))
def optimize_cv(self, lr_group, isite, percent=0):
if self.spectratype == "abs":
# quantum number restriction, |1><0|
up_exciton, down_exciton = 1, 0
elif self.spectratype == "emi":
# quantum number restriction, |0><1|
up_exciton, down_exciton = 0, 1
nexciton = 1
first_LR, second_LR, third_LR, forth_LR = lr_group
if self.method == "1site":
add_list = [isite - 1]
first_L = asxp(first_LR[isite - 1])
first_R = asxp(first_LR[isite])
second_L = asxp(second_LR[isite - 1])
second_R = asxp(second_LR[isite])
third_L = asxp(third_LR[isite - 1])
third_R = asxp(third_LR[isite])
forth_L = asxp(forth_LR[isite - 1])
forth_R = asxp(forth_LR[isite])
else:
add_list = [isite - 2, isite - 1]
first_L = asxp(first_LR[isite - 2])
first_R = asxp(first_LR[isite])
second_L = asxp(second_LR[isite - 2])
second_R = asxp(second_LR[isite])
third_L = asxp(third_LR[isite - 2])
third_R = asxp(third_LR[isite])
forth_L = asxp(forth_LR[isite - 2])
forth_R = asxp(forth_LR[isite])
xqnmat, xqnbigl, xqnbigr, xshape = \
self.construct_X_qnmat(add_list)
dag_qnmat, dag_qnbigl, dag_qnbigr = self.swap(xqnmat, xqnbigl, xqnbigr)
nonzeros = int(
np.sum(self.condition(dag_qnmat, [down_exciton, up_exciton])))
if self.method == "1site":
guess = moveaxis(self.cv_mpo[isite - 1], (1, 2), (2, 1))
else:
guess = tensordot(moveaxis(self.cv_mpo[isite - 2], (1, 2), (2, 1)),
moveaxis(self.cv_mpo[isite - 1]),
axes=(-1, 0))
guess = guess[self.condition(dag_qnmat, [down_exciton, up_exciton])]
if self.method == "1site":
# define dot path
path_1 = [([0, 1], "abcd, aefg -> bcdefg"),
([3, 0], "bcdefg, bfhi -> cdeghi"),
([2, 0], "cdeghi, chjk -> degijk"),
([1, 0], "degijk, gikl -> dejl")]
path_2 = [([0, 1], "abcd, aefg -> bcdefg"),
([3, 0], "bcdefg, bfhi -> cdeghi"),
([2, 0], "cdeghi, djek -> cghijk"),
([1, 0], "cghijk, gilk -> chjl")]
path_3 = [([0, 1], "ab, acde -> bcde"), ([1,
0], "bcde, ef -> bcdf")]
vecb = multi_tensor_contract(
path_3, forth_L, moveaxis(self.b_mpo[isite - 1], (1, 2),
(2, 1)),
forth_R)[self.condition(dag_qnmat, [down_exciton, up_exciton])]
a_oper_isite = asxp(self.a_oper[isite - 1])
h_mpo_isite = asxp(self.h_mpo[isite - 1])
# construct preconditioner
Idt = xp.identity(h_mpo_isite.shape[1])
M1_1 = xp.einsum('abca->abc', first_L)
path_m1 = [([0, 1], "abc, bdef->acdef"), ([1,
0], "acdef, cegh->adfgh")]
M1_2 = multi_tensor_contract(path_m1, M1_1, a_oper_isite, a_oper_isite)
M1_2 = xp.einsum("abcbd->abcd", M1_2)
M1_3 = xp.einsum('ecde->ecd', first_R)
M1_4 = xp.einsum('ff->f', Idt)
path_m1 = [([0, 1], "abcd,ecd->abe"), ([1, 0], "abe,f->abef")]
pre_M1 = multi_tensor_contract(path_m1, M1_2, M1_3, M1_4)
pre_M1 = xp.moveaxis(pre_M1, [-2, -1], [-1, -2])[self.condition(
dag_qnmat, [down_exciton, up_exciton])]
M2_1 = xp.einsum('aeag->aeg', second_L)
M2_2 = xp.einsum('eccf->ecf', a_oper_isite)
M2_3 = xp.einsum('gbbh->gbh', h_mpo_isite)
M2_4 = xp.einsum('dfdh->dfh', second_R)
path_m2 = [([0, 1], "aeg,gbh->aebh"), ([2, 0], "aebh,ecf->abchf"),
([1, 0], "abhcf,dfh->abcd")]
pre_M2 = multi_tensor_contract(path_m2, M2_1, M2_3, M2_2, M2_4)
pre_M2 = pre_M2[self.condition(dag_qnmat, [down_exciton, up_exciton])]
M4_1 = xp.einsum('faah->fah', third_L)
M4_4 = xp.einsum('gddi->gdi', third_R)
M4_5 = xp.einsum('cc->c', Idt)
M4_path = [([0, 1], "fah,febg->ahebg"), ([2, 0], "ahebg,hjei->abgji"),
([1, 0], "abgji,gdi->abjd")]
pre_M4 = multi_tensor_contract(M4_path, M4_1, h_mpo_isite, h_mpo_isite,
M4_4)
pre_M4 = xp.einsum('abbd->abd', pre_M4)
pre_M4 = xp.tensordot(pre_M4, M4_5, axes=0)
pre_M4 = xp.moveaxis(pre_M4, [2, 3], [3, 2])[self.condition(
dag_qnmat, [down_exciton, up_exciton])]
M_x = lambda x: asnumpy(
asxp(x) /
(pre_M1 + 2 * pre_M2 + pre_M4 + xp.ones(nonzeros) * self.eta**2))
pre_M = scipy.sparse.linalg.LinearOperator((nonzeros, nonzeros), M_x)
count = 0
def hop(x):
nonlocal count
count += 1
dag_struct = asxp(self.dag2mat(xshape, x, dag_qnmat))
if self.method == "1site":
M1 = multi_tensor_contract(path_1, first_L, dag_struct,
a_oper_isite, a_oper_isite, first_R)
M2 = multi_tensor_contract(path_2, second_L, dag_struct,
a_oper_isite, h_mpo_isite, second_R)
M2 = xp.moveaxis(M2, (1, 2), (2, 1))
M3 = multi_tensor_contract(path_2, third_L, h_mpo_isite,
dag_struct, h_mpo_isite, third_R)
M3 = xp.moveaxis(M3, (1, 2), (2, 1))
cout = M1 + 2 * M2 + M3 + dag_struct * self.eta**2
cout = cout[self.condition(dag_qnmat, [down_exciton, up_exciton])]
return asnumpy(cout)
# Matrix A
mat_a = scipy.sparse.linalg.LinearOperator((nonzeros, nonzeros),
matvec=hop)
x, info = scipy.sparse.linalg.cg(mat_a,
asnumpy(vecb),
tol=1.e-5,
x0=asnumpy(guess),
maxiter=500,
M=pre_M,
atol=0)
# logger.info(f"linear eq dim: {nonzeros}")
# logger.info(f'times for hop:{count}')
self.hop_time.append(count)
if info != 0:
logger.warning(
f"cg not converged, vecb.norm:{xp.linalg.norm(vecb)}")
l_value = xp.dot(asxp(hop(x)), asxp(x)) - 2 * xp.dot(vecb, asxp(x))
x = self.dag2mat(xshape, x, dag_qnmat)
if self.method == "1site":
x = np.moveaxis(x, [1, 2], [2, 1])
x, xdim, xqn, compx = self.x_svd(x,
xqnbigl,
xqnbigr,
nexciton,
percent=percent)
if self.method == "1site":
self.cv_mpo[isite - 1] = x
if not self.cv_mpo.to_right:
if isite != 1:
self.cv_mpo[isite - 2] = \
tensordot(self.cv_mpo[isite - 2], compx, axes=(-1, 0))
self.cv_mpo.qn[isite - 1] = xqn
self.cv_mpo.qnidx = isite - 2
else:
self.cv_mpo[isite - 1] = \
tensordot(compx, self.cv_mpo[isite - 1], axes=(-1, 0))
self.cv_mpo.qnidx = 0
else:
if isite != len(self.cv_mpo):
self.cv_mpo[isite] = \
tensordot(compx, self.cv_mpo[isite], axes=(-1, 0))
self.cv_mpo.qn[isite] = xqn
self.cv_mpo.qnidx = isite
else:
self.cv_mpo[isite - 1] = \
tensordot(self.cv_mpo[isite - 1], compx, axes=(-1, 0))
self.cv_mpo.qnidx = self.cv_mpo.site_num - 1
else:
if not self.cv_mpo.to_right:
self.cv_mpo[isite - 2] = compx
self.cv_mpo[isite - 1] = x
self.cv_mpo.qnidx = isite - 2
else:
self.cv_mpo[isite - 2] = x
self.cv_mpo[isite - 1] = compx
self.cv_mpo.qnidx = isite - 1
self.cv_mpo.qn[isite - 1] = xqn
return float(l_value)
def construct_X_qnmat(self, addlist):
pbond = self.model.pbond_list
xqnl = np.array(self.cv_mpo.qn[addlist[0]])
xqnr = np.array(self.cv_mpo.qn[addlist[-1] + 1])
xqnmat = xqnl.copy()
xqnsigmalist = []
for idx in addlist:
sigmaqn = self.model.basis[idx].sigmaqn
xqnsigma = np.array(list(product(sigmaqn, repeat=2)))
xqnsigma = xqnsigma.reshape(pbond[idx], pbond[idx], 2)
xqnmat = self.qnmat_add(xqnmat, xqnsigma)
xqnsigmalist.append(xqnsigma)
xqnmat = self.qnmat_add(xqnmat, xqnr)
matshape = list(xqnmat.shape)
if self.method == "1site":
if xqnmat.ndim == 4:
if not self.cv_mpo.to_right:
xqnmat = np.moveaxis(xqnmat.reshape(matshape + [1]), -1,
-2)
else:
xqnmat = xqnmat.reshape([1] + matshape)
if not self.cv_mpo.to_right:
xqnbigl = xqnl.copy()
xqnbigr = self.qnmat_add(xqnsigmalist[0], xqnr)
if xqnbigr.ndim == 3:
rshape = list(xqnbigr.shape)
xqnbigr = np.moveaxis(xqnbigr.reshape(rshape + [1]), -1,
-2)
else:
xqnbigl = self.qnmat_add(xqnl, xqnsigmalist[0])
xqnbigr = xqnr.copy()
if xqnbigl.ndim == 3:
lshape = list(xqnbigl.shape)
xqnbigl = xqnbigl.reshape([1] + lshape)
else:
if xqnmat.ndim == 6:
if addlist[0] != 0:
xqnmat = np.moveaxis(xqnmat.resahpe(matshape + [1]), -1,
-2)
else:
xqnmat = xqnmat.reshape([1] + matshape)
xqnbigl = self.qnmat_add(xqnl, xqnsigmalist[0])
if xqnbigl.ndim == 3:
lshape = list(xqnbigl.shape)
xqnbigl = xqnbigl.reshape([1] + lshape)
xqnbigr = self.qnmat_add(xqnsigmalist[-1], xqnr)
if xqnbigr.ndim == 3:
rshape = list(xqnbigr.shape)
xqnbigr = np.moveaxis(xqnbigr.reshape(rshape + [1]), -1, -2)
xshape = list(xqnmat.shape)
del xshape[-1]
if len(xshape) == 3:
if not self.cv_mpo.to_right:
xshape = xshape + [1]
else:
xshape = [1] + xshape
return xqnmat, xqnbigl, xqnbigr, xshape
def swap(self, mat, qnbigl, qnbigr):
def inter_change(ori_mat):
matshape = ori_mat.shape
len_mat = int(np.prod(np.array(matshape[:-1])))
ori_mat = ori_mat.reshape(len_mat, 2)
change_mat = copy.deepcopy(ori_mat)
change_mat[:, 0], change_mat[:, 1] = ori_mat[:, 1], ori_mat[:, 0]
return change_mat.reshape(matshape)
dag_qnmat = inter_change(mat)
if self.method == "1site":
dag_qnmat = np.moveaxis(dag_qnmat, [1, 2], [2, 1])
dag_qnbigl = inter_change(qnbigl)
dag_qnbigr = inter_change(qnbigr)
if not self.cv_mpo.to_right:
dag_qnbigr = np.moveaxis(dag_qnbigr, [0, 1], [1, 0])
else:
dag_qnbigl = np.moveaxis(dag_qnbigl, [1, 2], [2, 1])
else:
raise NotImplementedError
# we don't recommend 2-site CV-DMRG, which is a huge cost
return dag_qnmat, dag_qnbigl, dag_qnbigr
def condition(self, mat, qn):
condition = (mat == qn)
mat_shape = list(condition.shape)
del mat_shape[-1]
condition = condition.all(axis=-1)
condition = condition.reshape(mat_shape)
return condition
def qnmat_add(self, mat_l, mat_r):
lshape, rshape = mat_l.shape, mat_r.shape
lena = int(np.prod(np.array(lshape)) / 2)
lenb = int(np.prod(np.array(rshape)) / 2)
matl = mat_l.reshape(lena, 2)
matr = mat_r.reshape(lenb, 2)
lr1 = np.add.outer(matl[:, 0], matr[:, 0]).flatten()
lr2 = np.add.outer(matl[:, 1], matr[:, 1]).flatten()
lr = np.zeros((len(lr1), 2))
lr[:, 0] = lr1
lr[:, 1] = lr2
shapel = list(mat_l.shape)
del shapel[-1]
shaper = list(mat_r.shape)
del shaper[-1]
lr = lr.reshape(shapel + shaper + [2])
return lr
def dag2mat(self, xshape, x, dag_qnmat):
if self.spectratype == "abs":
up_exciton, down_exciton = 1, 0
else:
up_exciton, down_exciton = 0, 1
xdag = np.zeros(xshape, dtype=x.dtype)
mask = self.condition(dag_qnmat, [down_exciton, up_exciton])
np.place(xdag, mask, x)
shape = list(xdag.shape)
if xdag.ndim == 3:
if not self.cv_mpo.to_right:
xdag = xdag.reshape(shape + [1])
else:
xdag = xdag.reshape([1] + shape)
return xdag
def x_svd(self, xstruct, xqnbigl, xqnbigr, nexciton, percent=0):
Gamma = xstruct.reshape(
np.prod(xqnbigl.shape) // 2,
np.prod(xqnbigr.shape) // 2)
localXqnl = xqnbigl.ravel()
localXqnr = xqnbigr.ravel()
list_locall = []
list_localr = []
for i in range(0, len(localXqnl), 2):
list_locall.append([localXqnl[i], localXqnl[i + 1]])
for i in range(0, len(localXqnr), 2):
list_localr.append([localXqnr[i], localXqnr[i + 1]])
localXqnl = copy.deepcopy(list_locall)
localXqnr = copy.deepcopy(list_localr)
xuset = []
xuset0 = []
xvset = []
xvset0 = []
xsset = []
xsuset0 = []
xsvset0 = []
xqnlset = []
xqnlset0 = []
xqnrset = []
xqnrset0 = []
if self.spectratype == "abs":
combine = [[[y, 0], [nexciton - y, 0]]
for y in range(nexciton + 1)]
elif self.spectratype == "emi":
combine = [[[0, y], [0, nexciton - y]]
for y in range(nexciton + 1)]
for nl, nr in combine:
lset = np.where(self.condition(np.array(localXqnl), [nl]))[0]
rset = np.where(self.condition(np.array(localXqnr), [nr]))[0]
if len(lset) != 0 and len(rset) != 0:
Gamma_block = Gamma.ravel().take(
(lset * Gamma.shape[1]).reshape(-1, 1) + rset)
try:
U, S, Vt = \
scipy.linalg.svd(Gamma_block, full_matrices=True,
lapack_driver='gesdd')
except:
U, S, Vt = \
scipy.linalg.svd(Gamma_block, full_matrices=True,
lapack_driver='gesvd')
dim = S.shape[0]
xsset.append(S)
# U part quantum number
xuset.append(
svd_qn.blockrecover(lset, U[:, :dim], Gamma.shape[0]))
xqnlset += [nl] * dim
xuset0.append(
svd_qn.blockrecover(lset, U[:, dim:], Gamma.shape[0]))
xqnlset0 += [nl] * (U.shape[0] - dim)
xsuset0.append(np.zeros(U.shape[0] - dim))
# V part quantum number
VT = Vt.T
xvset.append(
svd_qn.blockrecover(rset, VT[:, :dim], Gamma.shape[1]))
xqnrset += [nr] * dim
xvset0.append(
svd_qn.blockrecover(rset, VT[:, dim:], Gamma.shape[1]))
xqnrset0 += [nr] * (VT.shape[0] - dim)
xsvset0.append(np.zeros(VT.shape[0] - dim))
xuset = np.concatenate(xuset + xuset0, axis=1)
xvset = np.concatenate(xvset + xvset0, axis=1)
xsuset = np.concatenate(xsset + xsuset0)
xsvset = np.concatenate(xsset + xsvset0)
xqnlset = xqnlset + xqnlset0
xqnrset = xqnrset + xqnrset0
bigl_shape = list(xqnbigl.shape)
del bigl_shape[-1]
bigr_shape = list(xqnbigr.shape)
del bigr_shape[-1]
if not self.cv_mpo.to_right:
x, xdim, xqn, compx = update_cv(xvset,
xsvset,
xqnrset,
xuset,
nexciton,
self.m_max,
self.spectratype,
percent=percent)
if (self.method == "1site") and (len(bigr_shape + [xdim]) == 3):
return np.moveaxis(
x.reshape(bigr_shape + [1] + [xdim]), -1, 0),\
xdim, xqn, compx.reshape(bigl_shape + [xdim])
else:
return np.moveaxis(x.reshape(bigr_shape + [xdim]), -1, 0),\
xdim, xqn, compx.reshape(bigl_shape + [xdim])
else:
x, xdim, xqn, compx = update_cv(xuset,
xsuset,
xqnlset,
xvset,
nexciton,
self.m_max,
self.spectratype,
percent=percent)
if (self.method == "1site") and (len(bigl_shape + [xdim]) == 3):
return x.reshape([1] + bigl_shape + [xdim]), xdim, xqn, \
np.moveaxis(compx.reshape(bigr_shape + [xdim]), -1, 0)
else:
return x.reshape(bigl_shape + [xdim]), xdim, xqn, \
np.moveaxis(compx.reshape(bigr_shape + [xdim]), -1, 0)
def initialize_LR(self):
first_LR = [np.ones((1, 1, 1, 1))]
forth_LR = [np.ones((1, 1))]
for isite in range(1, len(self.cv_mpo)):
first_LR.append(None)
forth_LR.append(None)
first_LR.append(np.ones((1, 1, 1, 1)))
second_LR = copy.deepcopy(first_LR)
third_LR = copy.deepcopy(first_LR)
forth_LR.append(np.ones((1, 1)))
if self.cv_mpo.to_right:
for isite in range(len(self.cv_mpo), 1, -1):
cv_isite = self.cv_mpo[isite - 1]
dag_cv_isite = moveaxis(cv_isite, (1, 2), (2, 1))
path1 = [([0, 1], "abcd, efga -> bcdefg"),
([3, 0], "bcdefg, hgib -> cdefhi"),
([2, 0], "cdefhi, jikc -> defhjk"),
([1, 0], "defhjk, lkfd -> ehjl")]
path2 = [([0, 1], "ab, cdea->bcde"), ([1,
0], "bcde, fedb->cf")]
first_LR[isite - 1] = asnumpy(
multi_tensor_contract(path1, first_LR[isite], dag_cv_isite,
self.a_oper[isite - 1],
self.a_oper[isite - 1], cv_isite))
second_LR[isite - 1] = asnumpy(
multi_tensor_contract(path1, second_LR[isite],
dag_cv_isite, self.a_oper[isite - 1],
cv_isite, self.h_mpo[isite - 1]))
third_LR[isite - 1] = asnumpy(
multi_tensor_contract(path1, third_LR[isite],
self.h_mpo[isite - 1], dag_cv_isite,
cv_isite, self.h_mpo[isite - 1]))
forth_LR[isite - 1] = asnumpy(
multi_tensor_contract(
path2, forth_LR[isite],
moveaxis(self.b_mpo[isite - 1], (1, 2), (2, 1)),
cv_isite))
else:
for isite in range(1, len(self.cv_mpo)):
cv_isite = self.cv_mpo[isite - 1]
dag_cv_isite = moveaxis(cv_isite, (1, 2), (2, 1))
path1 = [([0, 1], "abcd, aefg -> bcdefg"),
([3, 0], "bcdefg, bfhi -> cdeghi"),
([2, 0], "cdeghi, chjk -> degijk"),
([1, 0], "degijk, djel -> gikl")]
path2 = [([0, 1], "ab, acde->bcde"), ([1,
0], "bcde, bdcf->ef")]
first_LR[isite] = asnumpy(
multi_tensor_contract(path1, first_LR[isite - 1],
dag_cv_isite, self.a_oper[isite - 1],
self.a_oper[isite - 1], cv_isite))
second_LR[isite] = asnumpy(
multi_tensor_contract(path1, second_LR[isite - 1],
dag_cv_isite, self.a_oper[isite - 1],
cv_isite, self.h_mpo[isite - 1]))
third_LR[isite] = asnumpy(
multi_tensor_contract(path1, third_LR[isite - 1],
self.h_mpo[isite - 1], dag_cv_isite,
cv_isite, self.h_mpo[isite - 1]))
forth_LR[isite] = asnumpy(
multi_tensor_contract(
path2, forth_LR[isite - 1],
moveaxis(self.b_mpo[isite - 1], (1, 2), (2, 1)),
cv_isite))
return [first_LR, second_LR, third_LR, forth_LR]
def update_LR(self, lr_group, isite):
first_LR, second_LR, third_LR, forth_LR = lr_group
cv_isite = self.cv_mpo[isite - 1]
dag_cv_isite = moveaxis(cv_isite, (1, 2), (2, 1))
if self.method == "1site":
if not self.cv_mpo.to_right:
path1 = [([0, 1], "abcd, efga -> bcdefg"),
([3, 0], "bcdefg, hgib -> cdefhi"),
([2, 0], "cdefhi, jikc -> defhjk"),
([1, 0], "defhjk, lkfd -> ehjl")]
path2 = [([0, 1], "ab, cdea->bcde"), ([1,
0], "bcde, fedb->cf")]
first_LR[isite - 1] = multi_tensor_contract(
path1, first_LR[isite], dag_cv_isite,
self.a_oper[isite - 1], self.a_oper[isite - 1], cv_isite)
second_LR[isite - 1] = multi_tensor_contract(
path1, second_LR[isite], dag_cv_isite,
self.a_oper[isite - 1], cv_isite, self.h_mpo[isite - 1])
third_LR[isite - 1] = multi_tensor_contract(
path1, third_LR[isite], self.h_mpo[isite - 1],
dag_cv_isite, cv_isite, self.h_mpo[isite - 1])
forth_LR[isite - 1] = multi_tensor_contract(
path2, forth_LR[isite],
moveaxis(self.b_mpo[isite - 1], (1, 2), (2, 1)), cv_isite)
else:
path1 = [([0, 1], "abcd, aefg -> bcdefg"),
([3, 0], "bcdefg, bfhi -> cdeghi"),
([2, 0], "cdeghi, chjk -> degijk"),
([1, 0], "degijk, djel -> gikl")]
path2 = [([0, 1], "ab, acde->bcde"), ([1,
0], "bcde, bdcf->ef")]
first_LR[isite] = multi_tensor_contract(
path1, first_LR[isite - 1], dag_cv_isite,
self.a_oper[isite - 1], self.a_oper[isite - 1], cv_isite)
second_LR[isite] = multi_tensor_contract(
path1, second_LR[isite - 1], dag_cv_isite,
self.a_oper[isite - 1], cv_isite, self.h_mpo[isite - 1])
third_LR[isite] = multi_tensor_contract(
path1, third_LR[isite - 1], self.h_mpo[isite - 1],
dag_cv_isite, cv_isite, self.h_mpo[isite - 1])
forth_LR[isite] = multi_tensor_contract(
path2, forth_LR[isite - 1],
moveaxis(self.b_mpo[isite - 1], (1, 2), (2, 1)), cv_isite)
else:
# 2site for finite temperature is too expensive, so I drop it
# (at least for now)
raise NotImplementedError
return first_LR, second_LR, third_LR, forth_LR