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
def renormalization_svd(cstruct,
qnbigl,
qnbigr,
domain,
nexciton,
Mmax,
percent=0):
"""
get the new mps, mpsdim, mpdqn, complementary mps to get the next guess
with singular value decomposition method (1 root)
"""
assert domain in ["R", "L"]
Uset, SUset, qnlnew, Vset, SVset, qnrnew = svd_qn.Csvd(cstruct,
qnbigl,
qnbigr,
nexciton,
system=domain)
if domain == "R":
mps, mpsdim, mpsqn, compmps = updatemps(Vset,
SVset,
qnrnew,
Uset,
nexciton,
Mmax,
percent=percent)
return (
moveaxis(mps.reshape(list(qnbigr.shape) + [mpsdim]), -1, 0),
mpsdim,
mpsqn,
compmps.reshape(list(qnbigl.shape) + [mpsdim]),
)
else:
mps, mpsdim, mpsqn, compmps = updatemps(Uset,
SUset,
qnlnew,
Vset,
nexciton,
Mmax,
percent=percent)
return (
mps.reshape(list(qnbigl.shape) + [mpsdim]),
mpsdim,
mpsqn,
moveaxis(compmps.reshape(list(qnbigr.shape) + [mpsdim]), -1, 0),
)
def conj_trans(self):
new_mpo = self.metacopy()
for i in range(new_mpo.site_num):
new_mpo[i] = moveaxis(self[i], (1, 2), (2, 1)).conj()
new_mpo.qn = [[-i for i in mt_qn] for mt_qn in new_mpo.qn]
return new_mpo
def renormalization_ddm(cstruct,
qnbigl,
qnbigr,
domain,
nexciton,
Mmax,
percent=0):
"""
get the new mps, mpsdim, mpdqn, complementary mps to get the next guess
with diagonalize reduced density matrix method (> 1 root)
"""
nroots = len(cstruct)
ddm = 0.0
for iroot in range(nroots):
if domain == "R":
ddm += np.tensordot(
cstruct[iroot],
cstruct[iroot],
axes=(range(qnbigl.ndim), range(qnbigl.ndim)),
)
else:
ddm += np.tensordot(
cstruct[iroot],
cstruct[iroot],
axes=(
range(qnbigl.ndim, cstruct[0].ndim),
range(qnbigl.ndim, cstruct[0].ndim),
),
)
ddm /= float(nroots)
if domain == "L":
Uset, Sset, qnnew = svd_qn.Csvd(ddm,
qnbigl,
qnbigl,
nexciton,
ddm=True)
else:
Uset, Sset, qnnew = svd_qn.Csvd(ddm,
qnbigr,
qnbigr,
nexciton,
ddm=True)
mps, mpsdim, mpsqn, compmps = updatemps(Uset,
Sset,
qnnew,
None,
nexciton,
Mmax,
percent=percent)
if domain == "R":
return (
moveaxis(mps.reshape(list(qnbigr.shape) + [mpsdim]), -1, 0),
mpsdim,
mpsqn,
tensordot(
Matrix(cstruct[0]),
mps.reshape(list(qnbigr.shape) + [mpsdim]),
axes=(range(qnbigl.ndim, cstruct[0].ndim), range(qnbigr.ndim)),
),
)
else:
return (
mps.reshape(list(qnbigl.shape) + [mpsdim]),
mpsdim,
mpsqn,
tensordot(
mps.reshape(list(qnbigl.shape) + [mpsdim]),
Matrix(cstruct[0]),
axes=(range(qnbigl.ndim), range(qnbigl.ndim)),
),
)
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
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 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 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 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)