def test_site_state():
@pb.site_state_modifier
def mod(state):
return np.ones_like(state)
assert np.all(mod(zero))
assert np.all(mod.apply(zero, one, one, one, one))
capture = {}
@pb.site_state_modifier
def check_args(state, x, y, z, sub_id, sites):
capture[sub_id] = [v.copy() for v in (state, x, y, z)]
capture[sub_id].append(sites.argsort_nearest([0, graphene.a_cc / 2]))
return state
def assert_state(name, **kwargs):
state, x, y, z, nearest = capture[name]
assert state.shape == kwargs["shape"]
assert pytest.fuzzy_equal(state, kwargs["state"])
assert x.shape == kwargs["shape"]
assert pytest.fuzzy_equal(x, kwargs["x"])
assert pytest.fuzzy_equal(y, kwargs["y"])
assert pytest.fuzzy_equal(z, kwargs["z"])
assert np.all(nearest == kwargs["nearest"])
model = build_model(check_args, pb.primitive(1, 2))
assert model.hamiltonian.dtype == np.float32
assert_state("A",
shape=(2, ),
state=[True] * 2,
nearest=[1, 0],
x=[-graphene.a / 2, 0],
y=[-2 * graphene.a_cc, -graphene.a_cc / 2],
z=[0, 0])
assert_state("B",
shape=(2, ),
state=[True] * 2,
nearest=[1, 0],
x=[-graphene.a / 2, 0],
y=[-graphene.a_cc, graphene.a_cc / 2],
z=[0, 0])
@pb.site_state_modifier
def remove_site(state):
state[0] = False
return state
model = build_model(remove_site, pb.primitive(2, 2))
assert model.system.num_sites == 6
@pb.site_state_modifier(min_neighbors=1)
def remove_dangling(state, sub_id):
state[sub_id == "A"] = False
return state
with pytest.raises(RuntimeError) as excinfo:
build_model(remove_dangling, pb.primitive(3, 3))
assert "0 sites" 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_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_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_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_sites():
model = pb.Model(graphene.monolayer(), pb.primitive(2, 2))
system = model.system
sites = pb.system.Sites(system.positions, system.sublattices, system.lattice)
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_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 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_site_position():
@pb.site_position_modifier
def mod(x, y, z):
return x + 1, y + 1, z + 1
assert (one, ) * 3 == mod(zero, zero, zero)
assert (one, ) * 3 == mod.apply(zero, zero, zero, one)
capture = {}
@pb.site_position_modifier
def check_args(x, y, z, sub_id, sites):
capture[sub_id] = [v.copy() for v in (x, y, z)]
capture[sub_id].append(sites.argsort_nearest([0, graphene.a_cc / 2]))
return x, y, z
def assert_positions(name, **kwargs):
x, y, z, nearest = capture[name]
assert x.shape == kwargs["shape"]
assert y.shape == kwargs["shape"]
assert z.shape == kwargs["shape"]
assert pytest.fuzzy_equal(x, kwargs["x"])
assert pytest.fuzzy_equal(y, kwargs["y"])
assert pytest.fuzzy_equal(z, kwargs["z"])
assert np.all(nearest == kwargs["nearest"])
model = build_model(check_args, pb.primitive(1, 2))
assert model.hamiltonian.dtype == np.float32
assert_positions("A",
shape=(2, ),
nearest=[1, 0],
x=[-graphene.a / 2, 0],
y=[-2 * graphene.a_cc, -graphene.a_cc / 2],
z=[0, 0])
assert_positions("B",
shape=(2, ),
nearest=[1, 0],
x=[-graphene.a / 2, 0],
y=[-graphene.a_cc, graphene.a_cc / 2],
z=[0, 0])
@pb.site_position_modifier
def shift(x, y, z):
return x + 1, y + 1, z + 1
model = build_model(check_args, shift)
assert pytest.fuzzy_equal(model.system.x, [1, 1])
assert pytest.fuzzy_equal(model.system.y,
[1 - graphene.a_cc / 2, 1 + graphene.a_cc / 2])
assert pytest.fuzzy_equal(model.system.z, [1, 1])
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]]})
lat.add_hoppings(([1], "A", "A", "t22"))
return lat
model = pb.Model(lattice(), pb.primitive(3))
h = model.hamiltonian.todense()
assert model.system.num_sites == 3
assert h.shape[0] == 6
assert pytest.fuzzy_equal(h, h.H)
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):
return 3 * energy
@pb.hopping_energy_modifier
def hopping(energy):
return 2 * energy
model = pb.Model(lattice(), pb.primitive(3), onsite, hopping)
h = model.hamiltonian.todense()
assert model.system.num_sites == 3
assert h.shape[0] == 6
assert pytest.fuzzy_equal(h, h.H)
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 test_wrapper_return():
"""Make sure the boost python wrapper return type conversion is working"""
@pb.hopping_energy_modifier
def mul(energy):
"""Returning a non-contiguous view will force the wrapper to create a copy"""
energy = np.concatenate([energy, energy])
energy *= 3
return energy[::2]
lattice = pb.Lattice([1, 0])
lattice.add_sublattices(("A", [0, 0]), ("B", [0, 0]))
lattice.add_one_hopping([0], "A", "B", 1.0)
model = pb.Model(lattice, mul, pb.primitive(2))
assert pytest.fuzzy_equal(model.hamiltonian.data, [3, 3, 3, 3])
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], system.sublattices[idx])
assert system.find_nearest([0, 0], 'A') != system.find_nearest([0, 0], 'B')
invalid_sublattice = 99
with pytest.raises(KeyError) as excinfo:
system.find_nearest([0, 0], invalid_sublattice)
assert "There is no sublattice" in str(excinfo.value)
with pytest.raises(KeyError) as excinfo:
system.find_nearest([0, 0], 'invalid_sublattice')
assert "There is no sublattice" in str(excinfo.value)
def mymodel(dim=20, theta=0, B=0.0):
# Pauli matrices
S1 = array([[0, 1], [1, 0]])
S2 = array([[0, -1j], [1j, 0]])
S3 = array([[1, 0], [0, -1]])
Tx = -S3 # Hopping in the x direction
Ty = -S3 # Hopping in the y direction
Tz = -S3 - 1j * S1 # Hopping in the z direction
U = 5 * S3 # Onsite term
# Building the lattice model
lat = pb.Lattice(a1=[1, 0, 0], a2=[0, 1, 0], a3=[0, 0, 1])
lat.add_sublattices(('A', [0, 0, 0], U))
lat.add_hoppings(([1, 0, 0], 'A', 'A', Tx), ([0, 1, 0], 'A', 'A', Ty),
([0, 0, 1], 'A', 'A', Tz))
# generating the model object by combinig the lattice and the Peierls field
model = pb.Model(lat, pb.primitive(a1=dim, a2=dim, a3=dim),
constant_magnetic_field(B=B, theta=theta))
return model
import pytest
import pybinding as pb
from pybinding.repository import graphene
models = {
'graphene-monolayer': [graphene.monolayer(), graphene.hexagon_ac(1)],
'graphene-monolayer-alt': [graphene.monolayer_alt(), pb.rectangle(1.6, 1.4)],
'graphene-monolayer-4atom': [graphene.monolayer_4atom()],
'graphene-monolayer-nn': [graphene.monolayer(2), pb.regular_polygon(6, 0.9)],
'graphene-monolayer-periodic-1d': [graphene.monolayer(), pb.primitive(5, 5),
pb.translational_symmetry(a1=True, a2=False)],
'graphene-monolayer-periodic-1d-alt': [graphene.monolayer_4atom(), pb.rectangle(1),
pb.translational_symmetry(a1=False, a2=0.6)],
'graphene-monolayer-periodic-2d': [graphene.monolayer(), pb.primitive(a1=5, a2=5),
pb.translational_symmetry(a1=1, a2=1)],
'graphene-monolayer-4atom-periodic-2d': [graphene.monolayer_4atom(), pb.rectangle(1),
pb.translational_symmetry(a1=0.6, a2=0.6)],
'graphene-bilayer': [graphene.bilayer(), graphene.hexagon_ac(0.6)],
}
@pytest.fixture(scope='module', ids=list(models.keys()), params=models.values())
def model(request):
return pb.Model(*request.param)
def test_api():
model = pb.Model(graphene.monolayer(), pb.primitive(2, 2))
system = model.system
import pytest
import numpy as np
import pybinding as pb
from pybinding.repository import graphene, group6_tmd
models = {
'graphene-monolayer': [graphene.monolayer(), graphene.hexagon_ac(1)],
'graphene-monolayer-alt': [graphene.monolayer_alt(), pb.rectangle(1.6, 1.4)],
'graphene-monolayer-4atom': [graphene.monolayer_4atom()],
'graphene-monolayer-nn': [graphene.monolayer(2), pb.regular_polygon(6, 0.9)],
'graphene-monolayer-periodic-1d': [graphene.monolayer(), pb.primitive(5, 5),
pb.translational_symmetry(a1=True, a2=False)],
'graphene-monolayer-periodic-1d-alt': [graphene.monolayer_4atom(), pb.rectangle(1),
pb.translational_symmetry(a1=False, a2=0.6)],
'graphene-monolayer-periodic-2d': [graphene.monolayer(), pb.primitive(a1=5, a2=5),
pb.translational_symmetry(a1=1, a2=1)],
'graphene-monolayer-4atom-periodic-2d': [graphene.monolayer_4atom(), pb.rectangle(1),
pb.translational_symmetry(a1=0.6, a2=0.6)],
'graphene-bilayer': [graphene.bilayer(), graphene.hexagon_ac(0.6)],
}
@pytest.fixture(scope='module', ids=list(models.keys()), params=models.values())
def model(request):
return pb.Model(*request.param)
def test_pickle_round_trip(model):
import pickle
unpickled = pickle.loads(pickle.dumps(model.system))
import numpy as np
import pybinding as pb
from pybinding.repository import graphene, group6_tmd
models = {
'graphene-monolayer': [graphene.monolayer(),
graphene.hexagon_ac(1)],
'graphene-monolayer-alt':
[graphene.monolayer_alt(),
pb.rectangle(1.6, 1.4)],
'graphene-monolayer-4atom': [graphene.monolayer_4atom()],
'graphene-monolayer-nn':
[graphene.monolayer(2), pb.regular_polygon(6, 0.9)],
'graphene-monolayer-periodic-1d': [
graphene.monolayer(),
pb.primitive(5, 5),
pb.translational_symmetry(a1=True, a2=False)
],
'graphene-monolayer-periodic-1d-alt': [
graphene.monolayer_4atom(),
pb.rectangle(1),
pb.translational_symmetry(a1=False, a2=0.6)
],
'graphene-monolayer-periodic-2d': [
graphene.monolayer(),
pb.primitive(a1=5, a2=5),
pb.translational_symmetry(a1=1, a2=1)
],
'graphene-monolayer-4atom-periodic-2d': [
graphene.monolayer_4atom(),
pb.rectangle(1),
import pybinding as pb
import numpy as np
import matplotlib.pyplot as plt
d = 1
pb.pltutils.use_style()
lattice = pb.Lattice(a1=[d,0], a2=[d/2, d*np.math.sqrt(3)/2])
lattice.add_sublattices(("A", [0,0]))
lattice.add_hoppings(([0,1], "A", "A", 1), ([1,0], "A", "A", 1))
model = pb.Model(lattice, pb.primitive(a1=5, a2=5))
model.plot()
plt.show()
def test_multiorbital_hoppings():
"""For multi-orbital lattices, hopping modifiers get `energy` as 3D array"""
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", [-0.25, 0.0], tau_z + 2 * tau_x),
("B", [0.0, 0.5], 0.5),
("C", [0.25, 0.0], [1, 2, 3]))
lat.register_hopping_energies({
"t11": 1,
"t1|2": 2,
"t1|3": 3,
"t22": 3 * tau_z,
"t23": [[0, 1, 2], [3, 4, 5]],
"t13": [[11, 12, 13]],
})
lat.add_hoppings(([1, 0], "B", "B", "t11"), ([0, 1], "B", "B", "t11"),
([1, 1], "B", "B", "t1|2"),
([1, -1], "B", "B", "t1|3"),
([0, 1], "A", "A", "t22"), ([0, 0], "A", "C", "t23"),
([0, 0], "B", "C", "t13"))
return lat
capture = {}
@pb.hopping_energy_modifier
def hopping(energy, hop_id, x1, y1, z1, x2, y2, z2):
capture[hop_id] = [v.copy() for v in (energy, x1, y1, z1, x2, y2, z2)]
return energy
def assert_positions(name, **expected):
_, x1, y1, z1, x2, y2, z2 = capture[name]
assert pytest.fuzzy_equal(x1.squeeze(), expected["x1"])
assert pytest.fuzzy_equal(y1.squeeze(), expected["y1"])
assert pytest.fuzzy_equal(z1.squeeze(), expected["z1"])
assert pytest.fuzzy_equal(x2.squeeze(), expected["x2"])
assert pytest.fuzzy_equal(y2.squeeze(), expected["y2"])
assert pytest.fuzzy_equal(z1.squeeze(), expected["z2"])
def assert_hoppings(name, **expected):
energy, *_ = capture[name]
assert energy.shape == expected["shape"]
for i in range(energy.shape[0]):
assert pytest.fuzzy_equal(energy[i], expected["energy"])
model = pb.Model(multi_orbital_lattice(), pb.primitive(2, 2), hopping)
assert model.system.num_sites == 12
assert model.hamiltonian.shape[0] == 24
assert_positions("t11",
x1=[-1, -1, 0, -1],
y1=[-0.5, -0.5, -0.5, 0.5],
z1=[0, 0, 0, 0],
x2=[0, -1, 0, 0],
y2=[-0.5, 0.5, 0.5, 0.5],
z2=[0, 0, 0, 0])
assert_positions("t22",
x1=[-1.25, -0.25],
y1=[-1, -1],
z1=[0, 0],
x2=[-1.25, -0.25],
y2=[0, 0],
z2=[0, 0])
assert_positions("t23",
x1=[-1.25, -0.25, -1.25, -0.25],
y1=[-1, -1, 0, 0],
z1=[0, 0, 0, 0],
x2=[-0.75, 0.25, -0.75, 0.25],
y2=[-1, -1, 0, 0],
z2=[0, 0, 0, 0])
assert_positions("t13",
x1=[-1, 0, -1, 0],
y1=[-0.5, -0.5, 0.5, 0.5],
z1=[0, 0, 0, 0],
x2=[-0.75, 0.25, -0.75, 0.25],
y2=[-1, -1, 0, 0],
z2=[0, 0, 0, 0])
assert_hoppings("t11", shape=(4, ), energy=[1])
assert_hoppings("t22", shape=(2, 2, 2), energy=[[3, 0], [0, -3]])
assert_hoppings("t23", shape=(4, 2, 3), energy=[[0, 1, 2], [3, 4, 5]])
assert_hoppings("t13", shape=(4, 1, 3), energy=[[11, 12, 13]])
@pb.hopping_energy_modifier
def hopping_mod(energy, hop_id, x1, y1, z1, x2, y2, z2):
if hop_id == "t11":
energy *= x1 * 0
elif hop_id == "t1":
energy *= 3
elif hop_id == "t22":
energy += [[0, 1], [1, 0]]
elif hop_id == "t23":
energy += [[1, 0, 0]]
elif hop_id == "t13":
energy *= 2
capture[hop_id] = [v.copy() for v in (energy, x1, y1, z1, x2, y2, z2)]
return energy
model = pb.Model(multi_orbital_lattice(), pb.primitive(2, 2), hopping_mod)
assert model.system.num_sites == 12
assert model.hamiltonian.shape[0] == 24
assert_hoppings("t11", shape=(4, ), energy=[0])
assert_hoppings("t1|2", shape=(1, ), energy=[6])
assert_hoppings("t1|3", shape=(1, ), energy=[9])
assert_hoppings("t22", shape=(2, 2, 2), energy=[[3, 1], [1, -3]])
assert_hoppings("t23", shape=(4, 2, 3), energy=[[1, 1, 2], [4, 4, 5]])
assert_hoppings("t13", shape=(4, 1, 3), energy=[[22, 24, 26]])
def test_multiorbital_hoppings():
"""For multi-orbital lattices, hopping modifiers get `energy` as 3D array"""
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", [-0.25, 0.0], tau_z + 2 * tau_x),
("B", [0.0, 0.5], 0.5),
("C", [0.25, 0.0], [1, 2, 3]))
lat.register_hopping_energies({
"t11": 1,
"t22": 3 * tau_z,
"t23": [[0, 1, 2],
[3, 4, 5]],
"t13": [[11, 12, 13]],
})
lat.add_hoppings(([1, 0], "B", "B", "t11"),
([0, 1], "B", "B", "t11"),
([0, 1], "A", "A", "t22"),
([0, 0], "A", "C", "t23"),
([0, 0], "B", "C", "t13"))
return lat
capture = {}
@pb.hopping_energy_modifier
def hopping(energy, hop_id, x1, y1, z1, x2, y2, z2):
capture[hop_id] = [v.copy() for v in (energy, x1, y1, z1, x2, y2, z2)]
return energy
def assert_hoppings(name, **expected):
energy, x1, y1, z1, x2, y2, z2 = 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(x1, expected["x1"])
assert pytest.fuzzy_equal(y1, expected["y1"])
assert pytest.fuzzy_equal(z1, expected["z1"])
assert pytest.fuzzy_equal(x2, expected["x2"])
assert pytest.fuzzy_equal(y2, expected["y2"])
assert pytest.fuzzy_equal(z1, expected["z2"])
model = pb.Model(multi_orbital_lattice(), pb.primitive(2, 2), hopping)
assert model.system.num_sites == 12
assert model.hamiltonian.shape[0] == 24
assert_hoppings("t11", shape=(4,), energy=[1, 1, 1, 1],
x1=[-1, -1, 0, -1], y1=[-0.5, -0.5, -0.5, 0.5], z1=[0, 0, 0, 0],
x2=[0, -1, 0, 0], y2=[-0.5, 0.5, 0.5, 0.5], z2=[0, 0, 0, 0])
assert_hoppings("t22", shape=(2, 2, 2), energy=[[3, 0],
[0, -3]],
x1=[-1.25, -0.25], y1=[-1, -1], z1=[0, 0],
x2=[-1.25, -0.25], y2=[0, 0], z2=[0, 0])
assert_hoppings("t23", shape=(2, 3, 4), energy=[[0, 1, 2],
[3, 4, 5]],
x1=[-1.25, -0.25, -1.25, -0.25], y1=[-1, -1, 0, 0], z1=[0, 0, 0, 0],
x2=[-0.75, 0.25, -0.75, 0.25], y2=[-1, -1, 0, 0], z2=[0, 0, 0, 0])
assert_hoppings("t13", shape=(1, 3, 4), energy=[[11, 12, 13]],
x1=[-1, 0, -1, 0], y1=[-0.5, -0.5, 0.5, 0.5], z1=[0, 0, 0, 0],
x2=[-0.75, 0.25, -0.75, 0.25], y2=[-1, -1, 0, 0], z2=[0, 0, 0, 0])
