def fermi_hubbard_from_general(x_dimension, y_dimension, tunneling, coulomb,
chemical_potential=0.,
periodic=True, spinless=False, magnetic_field=0):
lattice = HubbardSquareLattice(x_dimension, y_dimension,
periodic=periodic, spinless=spinless)
interaction_edge_type = 'neighbor' if spinless else 'onsite'
model = FermiHubbardModel(lattice,
tunneling_parameters=(('neighbor', (0, 0), tunneling),),
interaction_parameters=((interaction_edge_type, (0, 0), coulomb),),
potential_parameters=((0, chemical_potential),),
magnetic_field=magnetic_field)
return model.hamiltonian()
def test_fermi_hubbard_square_lattice_random_parameters(
lattice, parameters, distinguish_edges):
model = FermiHubbardModel(lattice, **parameters)
hamiltonian = model.hamiltonian()
terms_per_parameter = defaultdict(int)
for term, coefficient in hamiltonian.terms.items():
spin_orbitals = set(i for i, _ in term)
if len(spin_orbitals) == 2:
(i, a, s), (ii, aa, ss) = (lattice.from_spin_orbital_index(i)
for i in spin_orbitals)
edge_type = ({
(0, 0): 'onsite',
(0, 1): 'vertical_neighbor',
(1, 0): 'horizontal_neighbor'
} if distinguish_edges else {
(0, 0): 'onsite',
(0, 1): 'neighbor',
(1, 0): 'neighbor'
})[lattice.delta_mag(i, ii, True)]
dofs = tuple(sorted((a, aa)))
if len(term) == 2:
parameter = (edge_type, dofs, -coefficient)
assert parameter in parameters['tunneling_parameters']
terms_per_parameter['tunneling', parameter] += 1
else:
assert len(term) == 4
spin_pairs = (SpinPairs.ALL if lattice.spinless else
(SpinPairs.SAME if s == ss else SpinPairs.DIFF))
parameter = (edge_type, dofs, coefficient, spin_pairs)
assert parameter in parameters['interaction_parameters']
terms_per_parameter['interaction', parameter] += 1
else:
assert len(term) == 2
assert len(spin_orbitals) == 1
spin_orbital = spin_orbitals.pop()
_, dof, spin_index = lattice.from_spin_orbital_index(spin_orbital)
potential_coefficient = -coefficient
if not lattice.spinless:
(-1)**spin_index
potential_coefficient -= (((-1)**spin_index) *
parameters.get('magnetic_field', 0))
if not potential_coefficient:
continue
parameter = (dof, potential_coefficient)
assert parameter in parameters['potential_parameters']
terms_per_parameter['potential', parameter] += 1
edge_type_to_n_site_pairs = {
'onsite': lattice.n_sites,
'neighbor': lattice.n_neighbor_pairs(False),
'vertical_neighbor': lattice.n_vertical_neighbor_pairs(False),
'horizontal_neighbor': lattice.n_horizontal_neighbor_pairs(False)
}
for (term_type, parameter), n_terms in terms_per_parameter.items():
if term_type == 'potential':
assert n_terms == lattice.n_sites * lattice.n_spin_values
continue
n_site_pairs = edge_type_to_n_site_pairs[parameter[0]]
if term_type == 'tunneling':
assert n_terms == 2 * n_site_pairs * lattice.n_spin_values
else:
assert term_type == 'interaction'
parameter = InteractionParameter(*parameter)
expected_n_terms = n_site_pairs
if parameter.edge_type == 'neighbor':
expected_n_terms *= len(set(parameter.dofs))
if not lattice.spinless:
assert parameter.spin_pairs != SpinPairs.ALL
if (parameter.edge_type == 'onsite'
and parameter.spin_pairs == SpinPairs.DIFF):
expected_n_terms *= len(set(parameter.dofs))
else:
expected_n_terms *= 2
assert n_terms == expected_n_terms