def mat_fn_offdiag(self, p1, p2):
'''Calculate an off-diagonal matrix element.
:type p1: iterable of :class:`BasisFn` objects
:param p1: a Hartree product basis function, `|p_1\\rangle`
:type p2: iterable of :class:`BasisFn` objects
:param p2: a Hartree product basis function, `|p_2\\rangle`
:rtype: float
:returns: `\langle p_1|H|p_2 \\rangle`
'''
# <p|H|p'> = <ij|U|ab>
# Matrix element non-zero if exactly two spin-orbitals differ.
# Order matters in Hartree products, so the differing spin-orbitals
# must appear in the same place.
# Kinetic operator is diagonal in a plane-wave basis, so only have
# Coulomb integrals.
# No exchange integrals in a Hartree product basis, of course.
(from_1, to_2) = hamil.hartree_excitation(p1, p2)
hmatel = 0
if len(from_1) == 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)
return hmatel
def mat_fn_offdiag(self, p1, p2):
'''Calculate an off-diagonal matrix element.
:type p1: iterable of :class:`BasisFn` objects
:param p1: a Hartree product basis function, `|p_1\\rangle`
:type p2: iterable of :class:`BasisFn` objects
:param p2: a Hartree product basis function, `|p_2\\rangle`
:rtype: float
:returns: `\langle p_1|H|p_2 \\rangle`
'''
# <p|H|p'> = <ij|U|ab>
# Matrix element non-zero if exactly two spin-orbitals differ.
# Order matters in Hartree products, so the differing spin-orbitals
# must appear in the same place.
# Kinetic operator is diagonal in a plane-wave basis, so only have
# Coulomb integrals.
# No exchange integrals in a Hartree product basis, of course.
(from_1, to_2) = hamil.hartree_excitation(p1, p2)
hmatel = 0
if len(from_1) == 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)
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 Hartree product basis function, `|b_i\\rangle`
:type bj: iterable of :class:`LatticeSite` objects
:param bj: a Hartree product 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) = hamil.hartree_excitation(bi, bj)
if len(from_i) == 1:
hmatel = self.sys.hopping_int(from_i[0], to_j[0])
else:
hmatel = 0
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 Hartree product basis function, `|b_i\\rangle`
:type bj: iterable of :class:`LatticeSite` objects
:param bj: a Hartree product 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) = hamil.hartree_excitation(bi, bj)
if len(from_i) == 1:
hmatel = self.sys.hopping_int(from_i[0], to_j[0])
else:
hmatel = 0
return hmatel