def test_line():
"""1D shape with 1D lattice"""
model = pb.Model(examples.chain_lattice(a=1), pb.line(0, 4.5))
assert model.system.num_sites == 4
model = pb.Model(examples.chain_lattice(a=1), pb.line([0, -0.5], [5, 0.5]))
assert model.system.num_sites == 6
def test_hopping_generator():
"""Generated next-nearest hoppings should produce the same result as the builtin lattice"""
from scipy.spatial import cKDTree
@pb.hopping_generator("tnn_test", energy=graphene.t_nn)
def next_nearest(x, y, z):
pos = np.stack([x, y, z], axis=1)
dmin = graphene.a * 0.95
dmax = graphene.a * 1.05
kdtree = cKDTree(pos)
coo = kdtree.sparse_distance_matrix(kdtree, dmax).tocoo()
idx = coo.data > dmin
return coo.row[idx], coo.col[idx]
@pb.onsite_energy_modifier
def onsite_offset(energy):
return energy + 3 * graphene.t_nn
model = pb.Model(graphene.monolayer(), next_nearest, onsite_offset,
graphene.hexagon_ac(1))
expected = pb.Model(graphene.monolayer(2), graphene.hexagon_ac(1))
assert pytest.fuzzy_equal(model.hamiltonian, expected.hamiltonian)
@pb.hopping_generator("t_new", energy=1.0)
def bad_generator():
"""Different array lengths"""
return [0, 1, 2], [0, 1]
model = pb.Model(graphene.monolayer(), pb.primitive(3, 3), bad_generator)
with pytest.raises(RuntimeError) as excinfo:
model.eval()
assert "the number of `from` and `to` indices must be equal" in str(
excinfo.value)
def test_multiorbital_hamiltonian():
"""For multi-orbital lattices the Hamiltonian size is larger than the number of sites"""
def lattice():
lat = pb.Lattice([1])
lat.add_sublattices(("A", [0], [[1, 3j], [0, 2]]))
lat.register_hopping_energies({
"t22": [[0, 1], [2, 3]],
"t11":
1, # incompatible hopping - it's never used so it shouldn't raise any errors
})
lat.add_hoppings(([1], "A", "A", "t22"))
return lat
model = pb.Model(lattice(), pb.primitive(3))
h = model.hamiltonian.toarray()
assert model.system.num_sites == 3
assert h.shape[0] == 6
assert pytest.fuzzy_equal(h, h.T.conjugate())
assert pytest.fuzzy_equal(h[:2, :2], h[-2:, -2:])
assert pytest.fuzzy_equal(h[:2, :2], [[1, 3j], [-3j, 2]])
assert pytest.fuzzy_equal(h[:2, 2:4], [[0, 1], [2, 3]])
@pb.onsite_energy_modifier
def onsite(energy, x, sub_id):
return 3 * energy + sub_id.eye * 0 * x
@pb.hopping_energy_modifier
def hopping(energy):
return 2 * energy
model = pb.Model(lattice(), pb.primitive(3), onsite, hopping)
h = model.hamiltonian.toarray()
assert model.system.num_sites == 3
assert h.shape[0] == 6
assert pytest.fuzzy_equal(h, h.T.conjugate())
assert pytest.fuzzy_equal(h[:2, :2], h[-2:, -2:])
assert pytest.fuzzy_equal(h[:2, :2], [[3, 9j], [-9j, 6]])
assert pytest.fuzzy_equal(h[:2, 2:4], [[0, 2], [4, 6]])
assert pytest.fuzzy_equal(h[2:4, 4:6], [[0, 2], [4, 6]])
def lattice_with_zero_diagonal():
lat = pb.Lattice([1])
lat.add_sublattices(("A", [0], [[0, 3j], [0, 0]]))
return lat
model = pb.Model(lattice_with_zero_diagonal(), pb.primitive(3))
h = model.hamiltonian.toarray()
assert model.system.num_sites == 3
assert h.shape[0] == 6
assert pytest.fuzzy_equal(h, h.T.conjugate())
assert pytest.fuzzy_equal(h[:2, :2], h[-2:, -2:])
assert pytest.fuzzy_equal(h[:2, :2], [[0, 3j], [-3j, 0]])
def test_primitive():
"""The primitive shape can be positioned using the lattice origin"""
model = pb.Model(graphene.monolayer(), pb.primitive(2, 2))
assert model.system.num_sites == 8
assert np.isclose(model.system.x.min(), -1.5 * graphene.a, rtol=1e-3)
assert np.isclose(model.system.y.min(), -2 * graphene.a_cc, rtol=1e-3)
model = pb.Model(
graphene.monolayer().with_offset(
[0.5 * graphene.a, 0.5 * graphene.a_cc]), pb.primitive(2, 2))
assert model.system.num_sites == 8
assert np.isclose(model.system.x.min(), -graphene.a, rtol=1e-3)
assert np.isclose(model.system.y.min(), -1.5 * graphene.a_cc, rtol=1e-3)
def test_hopping_buffer():
"""The energy passed to hopping modifiers is buffered, but users should not be aware of it"""
def lattice():
lat = pb.Lattice([1, 0], [0, 1])
lat.add_sublattices(("A", [0, 0], [0, 0, 0, 0]))
lat.register_hopping_energies({
"t44": [[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11],
[12, 13, 14, 15]]
})
lat.add_hoppings(([1, 0], "A", "A", "t44"), ([0, 1], "A", "A", "t44"))
return lat
capture = {}
@pb.hopping_energy_modifier
def check_buffer(energy, hop_id):
capture.setdefault(hop_id, [])
capture[hop_id] += [energy.copy()]
energy[0] = 99
return energy
model = pb.Model(lattice(), pb.primitive(3000, 2), check_buffer)
assert model.system.num_sites == 6000
assert model.hamiltonian.shape[0] == 24000
energies = capture["t44"]
assert len(energies) >= 2
assert energies[0].shape == (6250, 4, 4)
for energy in energies:
assert np.argwhere(energy == 99).size == 0
def test_structure_map_plot(compare_figure):
model = pb.Model(graphene.monolayer(), pb.rectangle(0.8))
structure_map = model.structure_map(model.system.x * model.system.y)
with compare_figure() as chk:
structure_map.plot(site_radius=(0.03, 0.05))
assert chk.passed
def test_ldos_sublattice():
"""LDOS for A and B sublattices should be antisymmetric for graphene with a mass term"""
model = pb.Model(graphene.monolayer(), graphene.hexagon_ac(10), graphene.mass_term(1))
kpm = pb.chebyshev.kpm(model)
a, b = (kpm.calc_ldos(np.linspace(-5, 5, 50), 0.1, [0, 0], sub) for sub in ('A', 'B'))
assert pytest.fuzzy_equal(a.ldos, b.ldos[::-1], rtol=1e-3, atol=1e-6)
def test_complex_multiorbital_hamiltonian():
def checkerboard_lattice(delta, t):
lat = pb.Lattice(a1=[1, 0], a2=[0, 1])
lat.add_sublattices(('A', [0, 0], -delta),
('B', [1 / 2, 1 / 2], delta))
lat.add_hoppings(
([0, 0], 'A', 'B', t),
([0, -1], 'A', 'B', t),
([-1, 0], 'A', 'B', t),
([-1, -1], 'A', 'B', t),
)
return lat
hopp_t = np.array([[2 + 2j, 3 + 3j], [4 + 4j,
5 + 5j]]) # multi-orbital hopping
onsite_en = np.array([[1, 1j], [-1j, 1]]) # onsite energy
model = pb.Model(checkerboard_lattice(onsite_en, hopp_t),
pb.translational_symmetry(True, True))
h = model.hamiltonian.toarray()
assert model.system.num_sites == 2
assert h.shape[0] == 4
assert pytest.fuzzy_equal(h, h.T.conjugate()) # check if Hermitian
assert pytest.fuzzy_equal(
h[:2, :2], -h[-2:, -2:]) # onsite energy on A and B is opposite
assert pytest.fuzzy_equal(h[:2, 2:4],
4 * hopp_t) # hopping A <-> B is 4 * hopp_t
def test_dos(params, baseline, plot_if_fails):
configurations = [
{
'matrix_format': "ELL",
'optimal_size': False,
'interleaved': False
},
{
'matrix_format': "ELL",
'optimal_size': True,
'interleaved': True
},
]
model = pb.Model(*params)
kernel = pb.lorentz_kernel()
strategies = [
pb.kpm(model, kernel=kernel, silent=True, **c) for c in configurations
]
energy = np.linspace(0, 2, 25)
results = [kpm.calc_dos(energy, broadening=0.15) for kpm in strategies]
expected = results[0].with_data(
baseline(results[0].data.astype(np.float32)))
for i in range(len(results)):
plot_if_fails(results[i], expected, 'plot', label=i)
for result in results:
assert pytest.fuzzy_equal(result, expected, rtol=1e-3, atol=1e-6)
def factory(v1, v2, energy=np.linspace(0, 0.1, 10)):
model = pb.Model(graphene.monolayer(),
graphene.hexagon_ac(side_width=15),
pb.constant_potential(v1), pb.constant_potential(v2))
kpm = pb.greens.kpm(model)
return kpm.deferred_ldos(energy, broadening=0.15, position=[0, 0])
def test_api():
model = pb.Model(graphene.monolayer(), pb.primitive(2, 2))
system = model.system
idx = system.num_sites // 2
assert idx == system.find_nearest(system.xyz[idx])
assert idx == system.find_nearest(system.xyz[idx], 'B')
assert system.find_nearest([0, 0], 'A') != system.find_nearest([0, 0], 'B')
with pytest.raises(IndexError) as excinfo:
system.find_nearest([0, 0], 'invalid_sublattice')
assert "There is no Site named" in str(excinfo.value)
assert np.allclose(system.expanded_positions.x, system.positions.x)
s = pb.Model(group6_tmd.monolayer_3band("MoS2"), pb.primitive(2, 2)).system
assert s.expanded_positions.x.size == s.positions.x.size * 3
def test_hamiltonian_submatrix_sites():
"""The `to_sites` and `from_sites` arguments are not supported"""
kwant_sys = pb.Model(graphene.monolayer(), pb.rectangle(1,
1)).tokwant()
with pytest.raises(RuntimeError) as excinfo:
kwant_sys.hamiltonian_submatrix(to_sites=1, from_sites=1)
assert "not supported" in str(excinfo.value)
def test_warnings():
"""Extra arguments and ignored by pybinding -- warn users"""
kwant_sys = pb.Model(graphene.monolayer(), pb.rectangle(1,
1)).tokwant()
with pytest.warns(UserWarning):
kwant_sys.hamiltonian_submatrix(sparse=True, args=(1, ))
with pytest.warns(UserWarning):
kwant_sys.hamiltonian_submatrix(sparse=True, params=dict(v=1))
def test_structure_map_plot(compare_figure):
model = pb.Model(graphene.monolayer(), pb.rectangle(0.8))
system = model.system
data = np.arange(system.num_sites)
structure_map = pb.results.StructureMap.from_system(data, system)
with compare_figure() as chk:
structure_map.plot_structure(site_radius=(0.03, 0.05), cbar_props=False)
assert chk.passed
def test_structure_map_plot(compare_figure):
model = pb.Model(graphene.monolayer(), pb.rectangle(0.8))
data = [3, 11, 19, 26, 5, 13, 21, 0, 7, 15, 23, 2, 9, 17,
10, 18, 25, 4, 12, 20, 27, 6, 14, 22, 1, 8, 16, 24]
structure_map = model.structure_map(data)
with compare_figure() as chk:
structure_map.plot(site_radius=(0.03, 0.05))
assert chk.passed
def test_sites():
model = pb.Model(graphene.monolayer(), pb.primitive(2, 2))
system = model.system
sites = pb.system.Sites(system.positions, system.sublattices)
idx = system.num_sites // 2
assert idx == sites.find_nearest(system.xyz[idx])
assert idx == sites.find_nearest(system.xyz[idx], system.sublattices[idx])
assert sites.find_nearest([0, 0], 'A') != sites.find_nearest([0, 0], 'B')
def test_site_and_hopping_interaction():
"""Add a new row of sites and connect them just like the rest of the lattice"""
d = 1.0
v = 1.5
t = 1.0
def square_lattice():
lat = pb.Lattice(a1=[d, 0], a2=[0, d])
lat.add_sublattices(("A", [0, 0], v))
lat.add_hoppings(([0, 1], "A", "A", t), ([1, 0], "A", "A", t))
return lat
@pb.site_generator(name="B", energy=v)
def edge_sites(system):
edge_atoms = system.count_neighbors() < 4
x, y, z = (v[edge_atoms] for v in system.positions)
top_edge_only = np.isclose(y, y.max())
x, y, z = (v[top_edge_only] for v in (x, y, z))
y += d
return x, y, z
@pb.hopping_generator(name="t_edge", energy=t)
def edge_hoppings(system, y):
new_sites = system.sub == "B"
edge_atoms = np.logical_and(system.sub != "B",
system.count_neighbors() < 4)
top_edge_only = np.logical_and(edge_atoms,
np.isclose(y, y[edge_atoms].max()))
return new_sites, top_edge_only
@pb.hopping_generator(name="t_edge2", energy=t)
def edge_hoppings2(system):
edge_idx = np.flatnonzero(system.sub == "B")
to_idx = edge_idx[1:]
from_idx = edge_idx[:-1]
return to_idx, from_idx
model = pb.Model(square_lattice(), pb.primitive(6, 4), edge_sites,
edge_hoppings, edge_hoppings2)
expected = pb.Model(square_lattice(), pb.primitive(6, 5))
assert pytest.fuzzy_equal(model.hamiltonian, expected.hamiltonian)
def factory(v, energy=np.linspace(0, 0.1, 10)):
model = pb.Model(graphene.monolayer(),
graphene.hexagon_ac(side_width=15),
pb.constant_potential(v))
kpm = pb.kpm(model, kernel=pb.lorentz_kernel())
return kpm.deferred_ldos(energy,
broadening=0.15,
position=[0, 0],
sublattice="B")
def test_structure_map_plot(compare_figure):
import matplotlib.pyplot as plt
model = pb.Model(graphene.monolayer(), pb.rectangle(0.8))
structure_map = model.structure_map(model.system.x * model.system.y)
with compare_figure() as chk:
structure_map.plot(site_radius=(0.03, 0.05))
plt.gca().set_aspect("equal", "datalim")
assert chk.passed
def test_optimized_hamiltonian():
"""Currently available only in internal interface"""
from pybinding import _cpp
model = pb.Model(graphene.monolayer(), graphene.hexagon_ac(10))
h = model.hamiltonian
oh = _cpp.OptimizedHamiltonian(model.raw_hamiltonian, 0)
assert oh.matrix.shape == h.shape
assert oh.sizes[-1] == h.shape[0]
assert len(oh.indices) == h.shape[0]
def model():
def ring(inner_radius, outer_radius):
def contains(x, y, _):
r = np.sqrt(x**2 + y**2)
return np.logical_and(inner_radius < r, r < outer_radius)
return pb.FreeformShape(contains,
width=[2 * outer_radius, 2 * outer_radius])
return pb.Model(graphene.monolayer(), ring(3, 5))
def make_model(v0=0):
model = pb.Model(
graphene.monolayer().with_min_neighbors(1),
pb.rectangle(length, width),
potential_barrier(v0),
)
model.attach_lead(
-1, pb.line([-length / 2, -width / 2], [-length / 2, width / 2]))
model.attach_lead(
+1, pb.line([length / 2, -width / 2], [length / 2, width / 2]))
return model
def square_model(width=2, height=3):
def square_lattice(d=1, t=1):
lat = pb.Lattice(a1=[d, 0], a2=[0, d])
lat.add_sublattices(('A', [0, 0]))
lat.add_hoppings(
([0, 1], 'A', 'A', -t),
([1, 0], 'A', 'A', -t),
)
return lat
return pb.Model(square_lattice(), pb.rectangle(width, height))
def test_kpm_reuse():
"""KPM should return the same result when a single object is used for multiple calculations"""
model = pb.Model(graphene.monolayer(), graphene.hexagon_ac(10))
kpm = pb.chebyshev.kpm(model)
energy = np.linspace(-5, 5, 50)
broadening = 0.1
for position in [0, 0], [6, 0]:
actual = kpm.calc_ldos(energy, broadening, position)
expected = pb.chebyshev.kpm(model).calc_ldos(energy, broadening, position)
assert pytest.fuzzy_equal(actual, expected, rtol=1e-3, atol=1e-6)
def test_add_sublattice_alias(mock_lattice):
c_position = [0, 9]
mock_lattice.add_one_sublattice('c', c_position, alias='a')
model = pb.Model(mock_lattice)
c_index = model.system.find_nearest(c_position)
assert mock_lattice['c'] != mock_lattice['a']
assert model.system.sublattices[c_index] == mock_lattice['a']
with pytest.raises(IndexError) as excinfo:
mock_lattice.add_one_sublattice('d', [0, 0], alias='bad_name')
assert "There is no sublattice named 'bad_name'" in str(excinfo.value)
def test_api():
model = pb.Model(graphene.monolayer(), pb.primitive(2, 2))
system = model.system
idx = system.num_sites // 2
assert idx == system.find_nearest(system.xyz[idx])
assert idx == system.find_nearest(system.xyz[idx], 'B')
assert system.find_nearest([0, 0], 'A') != system.find_nearest([0, 0], 'B')
with pytest.raises(IndexError) as excinfo:
system.find_nearest([0, 0], 'invalid_sublattice')
assert "There is no sublattice" in str(excinfo.value)
def test_hopping_generator():
"""Generated next-nearest hoppings should produce the same result as the builtin lattice"""
from scipy.spatial import cKDTree
@pb.hopping_generator("tnn_test", energy=graphene.t_nn)
def next_nearest(x, y, z):
pos = np.stack([x, y, z], axis=1)
dmin = graphene.a * 0.95
dmax = graphene.a * 1.05
kdtree = cKDTree(pos)
coo = kdtree.sparse_distance_matrix(kdtree, dmax).tocoo()
idx = coo.data > dmin
return coo.row[idx], coo.col[idx]
@pb.onsite_energy_modifier
def onsite_offset(energy):
return energy + 3 * graphene.t_nn
model = pb.Model(graphene.monolayer(), next_nearest, onsite_offset, graphene.hexagon_ac(1))
expected = pb.Model(graphene.monolayer(2), graphene.hexagon_ac(1))
assert pytest.fuzzy_equal(model.hamiltonian, expected.hamiltonian)
def test_hamiltonian_submatrix_orbitals(lattice, norb):
"""Return the number of orbitals at each site in addition to the Hamiltonian"""
model = pb.Model(lattice, pb.rectangle(1, 1))
kwant_sys = model.tokwant()
matrix, to_norb, from_norb = kwant_sys.hamiltonian_submatrix(
sparse=True, return_norb=True)
assert matrix.shape == model.hamiltonian.shape
assert to_norb.size == model.system.num_sites
assert from_norb.size == model.system.num_sites
assert np.all(to_norb == norb)
assert np.all(from_norb == norb)
def test_multiorbital_onsite():
def multi_orbital_lattice():
lat = pb.Lattice([1, 0], [0, 1])
tau_z = np.array([[1, 0],
[0, -1]])
tau_x = np.array([[0, 1],
[1, 0]])
lat.add_sublattices(("A", [0, 0], tau_z + 2 * tau_x),
("B", [0, 0.1], 0.5),
("C", [0, 0.2], [1, 2, 3]))
lat.add_hoppings(([0, -1], "A", "A", 3 * tau_z),
([1, 0], "A", "A", 3 * tau_z),
([0, 0], "B", "C", [[2, 3, 4]]))
return lat
capture = {}
@pb.onsite_energy_modifier
def onsite(energy, x, y, z, sub_id):
capture[sub_id] = [v.copy() for v in (energy, x, y, z)]
return energy
def assert_onsite(name, **expected):
energy, x, y, z = capture[name]
assert energy.shape == expected["shape"]
expected_energy = np.array(expected["energy"])
for index in np.ndindex(*expected_energy.shape):
expected_slice = np.full(energy.shape[-1], expected_energy[index])
assert pytest.fuzzy_equal(energy[index], expected_slice)
assert pytest.fuzzy_equal(x, expected["x"])
assert pytest.fuzzy_equal(y, expected["y"])
assert pytest.fuzzy_equal(z, expected["z"])
model = pb.Model(multi_orbital_lattice(), pb.rectangle(2, 1), onsite)
assert model.system.num_sites == 6
assert model.hamiltonian.shape[0] == 12
assert_onsite("A", shape=(2, 2, 2), energy=[[1, 2],
[2, -1]],
x=[0, 1], y=[0, 0], z=[0, 0])
assert_onsite("B", shape=(2,), energy=[0.5],
x=[0, 1], y=[0.1, 0.1], z=[0, 0])
assert_onsite("C", shape=(3, 3, 2), energy=[[1, 0, 0],
[0, 2, 0],
[0, 0, 3]],
x=[0, 1], y=[0.2, 0.2], z=[0, 0])
def test_api(ring_model):
with pytest.raises(RuntimeError) as excinfo:
ring_model.attach_lead(0, pb.line(0, 0))
assert "Lead direction must be one of" in str(excinfo.value)
for direction in [3, -3]:
with pytest.raises(RuntimeError) as excinfo:
ring_model.attach_lead(direction, pb.line(0, 0))
assert "not valid for a 2D lattice" in str(excinfo.value)
with pytest.raises(RuntimeError) as excinfo:
pb.Model(examples.chain_lattice()).attach_lead(2, pb.line(0, 0))
assert "Attaching leads to 1D lattices is not supported" in str(
excinfo.value)
