def test_strong_interaction_hubbard_VT_order_gives_larger_error(self):
hamiltonian = normal_ordered(fermi_hubbard(4, 4, 1., 10.0))
TV_error_operator = (
split_operator_trotter_error_operator_diagonal_two_body(
hamiltonian, order='T+V'))
TV_error_bound = numpy.sum(numpy.absolute(
list(TV_error_operator.terms.values())))
VT_error_operator = (
split_operator_trotter_error_operator_diagonal_two_body(
hamiltonian, order='V+T'))
VT_error_bound = numpy.sum(numpy.absolute(
list(VT_error_operator.terms.values())))
self.assertGreater(VT_error_bound, TV_error_bound)
def test_intermediate_interaction_hubbard_TV_order_has_larger_error(self):
hamiltonian = normal_ordered(fermi_hubbard(4, 4, 1., 4.0))
TV_error_operator = (
split_operator_trotter_error_operator_diagonal_two_body(
hamiltonian, order='T+V'))
TV_error_bound = numpy.sum(numpy.absolute(
list(TV_error_operator.terms.values())))
VT_error_operator = (
split_operator_trotter_error_operator_diagonal_two_body(
hamiltonian, order='V+T'))
VT_error_bound = numpy.sum(numpy.absolute(
list(VT_error_operator.terms.values())))
self.assertAlmostEqual(TV_error_bound, 1706.66666666666)
self.assertAlmostEqual(VT_error_bound, 1365.33333333333)
def test_1d_jellium_wigner_seitz_10_VT_order_gives_larger_error(self):
hamiltonian = normal_ordered(jellium_model(
hypercube_grid_with_given_wigner_seitz_radius_and_filling(
1, 5, wigner_seitz_radius=10.,
spinless=True), spinless=True, plane_wave=False))
TV_error_operator = (
split_operator_trotter_error_operator_diagonal_two_body(
hamiltonian, order='T+V'))
TV_error_bound = numpy.sum(numpy.absolute(
list(TV_error_operator.terms.values())))
VT_error_operator = (
split_operator_trotter_error_operator_diagonal_two_body(
hamiltonian, order='V+T'))
VT_error_bound = numpy.sum(numpy.absolute(
list(VT_error_operator.terms.values())))
self.assertGreater(VT_error_bound, TV_error_bound)
def test_split_operator_error_operator_VT_order_against_definition(self):
hamiltonian = (normal_ordered(fermi_hubbard(3, 3, 1., 4.0)) -
2.3 * FermionOperator.identity())
potential_terms, kinetic_terms = (
diagonal_coulomb_potential_and_kinetic_terms_as_arrays(
hamiltonian))
potential = sum(potential_terms, FermionOperator.zero())
kinetic = sum(kinetic_terms, FermionOperator.zero())
error_operator = (
split_operator_trotter_error_operator_diagonal_two_body(
hamiltonian, order='V+T'))
# V-then-T ordered double commutators: [V, [T, V]] + [T, [T, V]] / 2
inner_commutator = normal_ordered(commutator(kinetic, potential))
error_operator_definition = normal_ordered(
commutator(potential, inner_commutator))
error_operator_definition += normal_ordered(
commutator(kinetic, inner_commutator)) / 2.0
error_operator_definition /= 12.0
self.assertEqual(error_operator, error_operator_definition)