def mat_fn_offdiag(self, d1, d2):
'''Calculate an off-diagonal Hamiltonian matrix element.
:type d1: iterable of :class:`BasisFn` objects
:param d1: a Slater determinant basis function, `|d_1\\rangle`
:type d2: iterable of :class:`BasisFn` objects
:param d2: a Slater determinant basis function, `|d_2\\rangle`
:rtype: float
:returns: `\langle d_1|H|d_2 \\rangle`.
'''
# <D|H|D'> = 1/2 <ij|ij> - <ij|ji>
# if |D> and |D'> are related by a double excitation, assuming |D> and
# |D'> are in maximum coincidence.
(from_1, to_2, nperm) = hamil.determinant_excitation(d1, d2)
hmatel = 0
if len(from_1) == 2:
if all(total_momentum(from_1) == total_momentum(to_2)):
if from_1[0].spin == to_2[0].spin and from_1[1].spin == to_2[1].spin:
# Coulomb
hmatel += self.sys.coulomb_int(from_1[0].kp - to_2[0].kp)
if from_1[0].spin == to_2[1].spin and from_1[1].spin == to_2[0].spin:
# Exchange
hmatel -= self.sys.coulomb_int(from_1[0].kp - to_2[1].kp)
if nperm % 2 == 1:
hmatel = -hmatel
return hmatel
def mat_fn_offdiag(self, bi, bj):
'''Calculate an off-diagonal Hamiltonian matrix element.
:type bi: iterable of :class:`LatticeSite` objects
:param bi: a Slater determinant basis function, `|b_i\\rangle`
:type bj: iterable of :class:`LatticeSite` objects
:param bj: a Slater determinant basis function, `|b_j\\rangle`
:rtype: float
:returns: `\langle b_i|H|b_j \\rangle`.
'''
# H = - \sum_{<ij>} (c_i^\dagger c_j + c_j^\dagger c_i - n_i n_j)
# Coulomb operator is diagonal in this basis.
# Kinetic term only if excitation involves moving a fermion from
# a lattice site to a connected lattice site.
(from_i, to_j, nperm) = hamil.determinant_excitation(bi, bj)
if len(from_i) == 1:
hmatel = self.sys.hopping_int(from_i[0], to_j[0])
else:
hmatel = 0
if nperm % 2 == 1:
hmatel = -hmatel
return hmatel
def mat_fn_offdiag(self, d1, d2):
'''Calculate an off-diagonal Hamiltonian matrix element.
:type d1: iterable of :class:`BasisFn` objects
:param d1: a Slater determinant basis function, `|d_1\\rangle`
:type d2: iterable of :class:`BasisFn` objects
:param d2: a Slater determinant basis function, `|d_2\\rangle`
:rtype: float
:returns: `\langle d_1|H|d_2 \\rangle`.
'''
# <D|H|D'> = 1/2 <ij|ij> - <ij|ji>
# if |D> and |D'> are related by a double excitation, assuming |D> and
# |D'> are in maximum coincidence.
(from_1, to_2, nperm) = hamil.determinant_excitation(d1, d2)
hmatel = 0
if len(from_1) == 2:
if all(total_momentum(from_1) == total_momentum(to_2)):
if from_1[0].spin == to_2[0].spin and from_1[1].spin == to_2[
1].spin:
# Coulomb
hmatel += self.sys.coulomb_int(from_1[0].kp - to_2[0].kp)
if from_1[0].spin == to_2[1].spin and from_1[1].spin == to_2[
0].spin:
# Exchange
hmatel -= self.sys.coulomb_int(from_1[0].kp - to_2[1].kp)
if nperm % 2 == 1:
hmatel = -hmatel
return hmatel
def mat_fn_offdiag(self, bi, bj):
'''Calculate an off-diagonal Hamiltonian matrix element.
:type bi: iterable of :class:`LatticeSite` objects
:param bi: a Slater determinant basis function, `|b_i\\rangle`
:type bj: iterable of :class:`LatticeSite` objects
:param bj: a Slater determinant basis function, `|b_j\\rangle`
:rtype: float
:returns: `\langle b_i|H|b_j \\rangle`.
'''
# H = - \sum_{<ij>} (c_i^\dagger c_j + c_j^\dagger c_i - n_i n_j)
# Coulomb operator is diagonal in this basis.
# Kinetic term only if excitation involves moving a fermion from
# a lattice site to a connected lattice site.
(from_i, to_j, nperm) = hamil.determinant_excitation(bi, bj)
if len(from_i) == 1:
hmatel = self.sys.hopping_int(from_i[0], to_j[0])
else:
hmatel = 0
if nperm % 2 == 1:
hmatel = -hmatel
return hmatel