def test_time_reversal(orbitals, result_repr_matrix, numeric):
"""
Test the generation of a representation matrix for time-reversal.
"""
result = sr.get_time_reversal(orbitals=orbitals, numeric=numeric)
if numeric:
assert isinstance(result.repr.matrix, np.ndarray)
assert np.allclose(result.repr.matrix,
np.array(result_repr_matrix).astype(complex))
assert isinstance(result.real_space_operator.rotation_matrix,
np.ndarray)
assert np.allclose(result.real_space_operator.rotation_matrix,
np.eye(3))
assert isinstance(result.real_space_operator.translation_vector,
np.ndarray)
assert np.allclose(result.real_space_operator.translation_vector,
np.zeros(3))
else:
assert isinstance(result.repr.matrix, sp.Matrix)
assert result.repr.matrix == result_repr_matrix
assert isinstance(result.real_space_operator.rotation_matrix,
sp.Matrix)
assert result.real_space_operator.rotation_matrix.equals(sp.eye(3, 3))
assert isinstance(result.real_space_operator.translation_vector,
sp.Matrix)
assert result.real_space_operator.translation_vector.equals(
sp.zeros(3, 1))
assert result.repr.has_cc
sr.Orbital(position=pos_In, function_string="y", spin=spin_up),
sr.Orbital(position=pos_In, function_string="z", spin=spin_up),
sr.Orbital(position=pos_As, function_string="x", spin=spin_up),
sr.Orbital(position=pos_As, function_string="y", spin=spin_up),
sr.Orbital(position=pos_As, function_string="z", spin=spin_up),
sr.Orbital(position=pos_In, function_string="1", spin=spin_down),
sr.Orbital(position=pos_In, function_string="x", spin=spin_down),
sr.Orbital(position=pos_In, function_string="y", spin=spin_down),
sr.Orbital(position=pos_In, function_string="z", spin=spin_down),
sr.Orbital(position=pos_As, function_string="x", spin=spin_down),
sr.Orbital(position=pos_As, function_string="y", spin=spin_down),
sr.Orbital(position=pos_As, function_string="z", spin=spin_down),
]
# set up symmetry operations
time_reversal = sr.get_time_reversal(orbitals=orbitals, numeric=True)
assert np.allclose(time_reversal.repr.matrix,
np.kron([[0, -1j], [1j, 0]], np.eye(7)))
structure = mg.Structure(
lattice=model_nosym.uc,
species=["In", "As"],
coords=np.array([[0, 0, 0], [0.25, 0.25, 0.25]]),
)
# get real-space representations
analyzer = mg.symmetry.analyzer.SpacegroupAnalyzer(structure)
symops = analyzer.get_symmetry_operations(cartesian=False)
symops_cart = analyzer.get_symmetry_operations(cartesian=True)
symmetries = []
),
rotation_matrix_cartesian=sp.Matrix([[-1, 0, 0], [0, 1, 0], [0, 0,
1]]),
numeric=False
),
sr.SymmetryOperation.from_orbitals(
orbitals=orbitals,
real_space_operator=sr.RealSpaceOperator(
rotation_matrix=sp.Matrix([[1, 0, 0], [-1, -1, -1], [0, 0, 1]]),
translation_vector=sp.Matrix([0, 0, 0]),
),
rotation_matrix_cartesian=sp.Matrix([[0, 0, -1], [0, 1, 0], [-1, 0,
0]]),
numeric=False
),
sr.get_time_reversal(orbitals=orbitals, numeric=False)
]
def print_result(order):
"""prints the basis for a given order of k"""
print('Order:', order)
for m in kp.symmetric_hamiltonian(
*symmetry_generators,
expr_basis=kp.monomial_basis(order),
repr_basis=kp.hermitian_basis(len(orbitals))
):
print(m)
print()