def ph_onsite(cls, mol_list: MolList, opera: str, mol_idx:int, ph_idx=0):
assert opera in ["b", r"b^\dagger", r"b^\dagger b"]
mpo = cls()
mpo.mol_list = mol_list
for imol, mol in enumerate(mol_list):
if mol_list.scheme < 4:
mpo.append(xp.eye(2).reshape(1, 2, 2, 1))
elif mol_list.scheme == 4:
if len(mpo) == mol_list.e_idx():
n = mol_list.mol_num
mpo.append(xp.eye(n).reshape(1, n, n, 1))
else:
assert False
iph = 0
for ph in mol.dmrg_phs:
for iqph in range(ph.nqboson):
ph_pbond = ph.pbond[iqph]
if imol == mol_idx and iph == ph_idx:
mt = ph_op_matrix(opera, ph_pbond)
else:
mt = ph_op_matrix("Iden", ph_pbond)
mpo.append(mt.reshape(1, ph_pbond, ph_pbond, 1))
iph += 1
mpo.build_empty_qn()
return mpo
def identity(cls, mol_list: MolList):
mpo = cls()
mpo.mol_list = mol_list
for p in mol_list.pbond_list:
mpo.append(xp.eye(p).reshape(1, p, p, 1))
mpo.build_empty_qn()
return mpo
def check_rortho(self):
"""
check R-orthogonal
"""
tensm = self.array.reshape([self.shape[0], np.prod(self.shape[1:])])
s = xp.dot(tensm, tensm.T.conj())
return allclose(s, xp.eye(s.shape[0]), atol=1e-3)
def check_lortho(self):
"""
check L-orthogonal
"""
tensm = self.array.reshape([np.prod(self.shape[:-1]), self.shape[-1]])
s = xp.dot(tensm.T.conj(), tensm)
return allclose(s, xp.eye(s.shape[0]), atol=1e-3)
def check_lortho(self, rtol=1e-5, atol=1e-8):
"""
check L-orthogonal
"""
tensm = asxp(
self.array.reshape([np.prod(self.shape[:-1]), self.shape[-1]]))
s = tensm.T.conj() @ tensm
return xp.allclose(s, xp.eye(s.shape[0]), rtol=rtol, atol=atol)
def check_rortho(self, rtol=1e-5, atol=1e-8):
"""
check R-orthogonal
"""
tensm = asxp(
self.array.reshape([self.shape[0],
np.prod(self.shape[1:])]))
s = tensm @ tensm.T.conj()
return xp.allclose(s, xp.eye(s.shape[0]), rtol=rtol, atol=atol)
def dot(self, other: "MatrixProduct") -> complex:
"""
dot product of two mps / mpo
"""
assert len(self) == len(other)
e0 = xp.eye(1, 1)
# for debugging. It has little computational cost anyway
debug_t = []
for mt1, mt2 in zip(self, other):
# sum_x e0[:,x].m[x,:,:]
debug_t.append(e0)
e0 = tensordot(e0, mt2.array, 1)
# sum_ij e0[i,p,:] self[i,p,:]
# note, need to flip a (:) index onto top,
# therefore take transpose
if mt1.ndim == 3:
e0 = tensordot(e0, mt1.array, ([0, 1], [0, 1])).T
elif mt1.ndim == 4:
e0 = tensordot(e0, mt1.array, ([0, 1, 2], [0, 1, 2])).T
else:
assert False
return complex(e0[0, 0])
def eye(N, M=None, dtype=None):
if dtype is None:
dtype = backend.real_dtype
return Matrix(xp.eye(N, M), dtype=dtype)