def get_C4z_symmetry_map(config):
assert config.n_sublattices == 1
geometry = 'square'
mapping = np.zeros((config.total_dof // 2, config.total_dof // 2)) + 0.0j # trivial mapping
rotation_matrix = np.array([[np.cos(2 * np.pi / 4.), np.sin(2 * np.pi / 4.)], \
[-np.sin(2 * np.pi / 4.), np.cos(2 * np.pi / 4.)]])
if config.n_orbitals == 2:
rotation_matrix_orbital = rotation_matrix
else:
rotation_matrix_orbital = np.eye(1)
for preindex in range(config.total_dof // 2):
orbit_preimage, sublattice_preimage, x_preimage, y_preimage = \
models.from_linearized_index(preindex, config.Ls, config.n_orbitals, config.n_sublattices)
orbit_preimage_vector = np.zeros(config.n_orbitals); orbit_preimage_vector[orbit_preimage] = 1.
r_preimage = models.lattice_to_physical([x_preimage, y_preimage, sublattice_preimage], geometry)
orbit_image_vector = np.einsum('ij,j->i', rotation_matrix_orbital, orbit_preimage_vector)
r_image = np.einsum('ij,j->i', rotation_matrix, r_preimage)
x_image, y_image, sublattice_image = models.physical_to_lattice(r_image, geometry)
x_image = int(np.rint(x_image)); y_image = int(np.rint(y_image))
x_image = (x_image % config.Ls); y_image = (y_image % config.Ls)
for orbit_image in range(config.n_orbitals):
coefficient = orbit_image_vector[orbit_image]
index = models.to_linearized_index(x_image, y_image, sublattice_image, orbit_image, \
config.Ls, config.n_orbitals, config.n_sublattices)
mapping[preindex, index] += coefficient
assert np.sum(np.abs(mapping.dot(mapping).dot(mapping).dot(mapping) - np.eye(mapping.shape[0]))) < 1e-5 # C_4z^4 = I
return mapping + 0.0j
def get_TRS_symmetry_map_chiral_jastrow(config):
assert config.n_sublattices == 2
geometry = 'hexagonal'
mapping = np.zeros(
(config.total_dof // 2, config.total_dof // 2)) # trivial mapping
for preindex in range(config.total_dof // 2):
orbit_preimage, sublattice_preimage, x_preimage, y_preimage = \
models.from_linearized_index(preindex, config.Ls, config.n_orbitals, config.n_sublattices)
r_preimage = models.lattice_to_physical(
[x_preimage, y_preimage, sublattice_preimage], geometry)
r_image = r_preimage
x_image, y_image, sublattice_image = models.physical_to_lattice(
r_image, geometry)
x_image = int(np.rint(x_image))
y_image = int(np.rint(y_image))
x_image = (x_image % config.Ls)
y_image = (y_image % config.Ls)
index = models.to_linearized_index(x_image, y_image, sublattice_image, 1 - orbit_preimage, \
config.Ls, config.n_orbitals, config.n_sublattices)
mapping[preindex, index] = 1.
assert np.sum(np.abs(mapping.dot(mapping) -
np.eye(mapping.shape[0]))) < 1e-12 # T^2 = I
return mapping
def get_C2y_symmetry_map_chiral_jastrow(config):
mapping = np.zeros((config.total_dof // 2, config.total_dof // 2))
for preindex in range(config.total_dof // 2):
orbit_preimage, sublattice_preimage, x_preimage, y_preimage = \
models.from_linearized_index(preindex, config.Ls, config.n_orbitals, config.n_sublattices)
orbit_image = 1 - orbit_preimage
r_preimage = np.array(
models.lattice_to_physical(
[x_preimage, y_preimage, sublattice_preimage],
'hexagonal'))
r_preimage -= np.array([1. / np.sqrt(3) / 2, 0.0])
r_image = np.array([-r_preimage[0], r_preimage[1]]) + np.array(
[1. / np.sqrt(3) / 2, 0.0])
x_image, y_image, sublattice_image = models.physical_to_lattice(
r_image, 'hexagonal')
x_image = int(np.rint(x_image))
y_image = int(np.rint(y_image))
x_image = (x_image % config.Ls)
y_image = (y_image % config.Ls)
index = models.to_linearized_index(x_image, y_image, sublattice_image, orbit_image, \
config.Ls, config.n_orbitals, config.n_sublattices)
mapping[preindex, index] += 1.
assert np.sum(np.abs(mapping.dot(mapping) -
np.eye(mapping.shape[0]))) < 1e-12 # C_2y^2 = I
return mapping
def get_C3z_symmetry_map_chiral_jastrow(config):
assert config.n_sublattices == 2
geometry = 'hexagonal'
mapping = np.zeros(
(config.total_dof // 2, config.total_dof // 2)) # trivial mapping
rotation_matrix = np.array([[np.cos(2 * np.pi / 3.), np.sin(2 * np.pi / 3.)], \
[-np.sin(2 * np.pi / 3.), np.cos(2 * np.pi / 3.)]])
for preindex in range(config.total_dof // 2):
orbit_preimage, sublattice_preimage, x_preimage, y_preimage = \
models.from_linearized_index(preindex, config.Ls, config.n_orbitals, config.n_sublattices)
r_preimage = models.lattice_to_physical(
[x_preimage, y_preimage, sublattice_preimage], geometry)
r_image = np.einsum('ij,j->i', rotation_matrix, r_preimage)
x_image, y_image, sublattice_image = models.physical_to_lattice(
r_image, geometry)
x_image = int(np.rint(x_image))
y_image = int(np.rint(y_image))
x_image = (x_image % config.Ls)
y_image = (y_image % config.Ls)
index = models.to_linearized_index(x_image, y_image, sublattice_image, orbit_preimage, \
config.Ls, config.n_orbitals, config.n_sublattices)
mapping[preindex, index] = 1.
assert np.sum(
np.abs(
mapping.dot(mapping).dot(mapping) -
np.eye(mapping.shape[0]))) < 1e-12 # C_3z^3 = I
return mapping
def get_C2y_symmetry_map(config, chiral = False):
if config.n_sublattices == 2:
geometry = 'hexagonal'
else:
geometry = 'square'
mapping = np.zeros((config.total_dof // 2, config.total_dof // 2)) + 0.0j # trivial mapping
for preindex in range(config.total_dof // 2):
orbit_preimage, sublattice_preimage, x_preimage, y_preimage = \
models.from_linearized_index(preindex, config.Ls, config.n_orbitals, config.n_sublattices)
if config.n_orbitals == 2:
if not chiral:
orbit_image = orbit_preimage
coefficient = -1.0 if orbit_image == 0 else 1.0
else:
orbit_image = 1 - orbit_preimage
coefficient = -1.0
else:
orbit_image = orbit_preimage
coefficient = 1.0
r_preimage = np.array(models.lattice_to_physical([x_preimage, y_preimage, sublattice_preimage], geometry))
if geometry == 'hexagonal':
r_preimage -= np.array([1. / np.sqrt(3) / 2, 0.0])
r_image = np.array([-r_preimage[0], r_preimage[1]]) + np.array([1. / np.sqrt(3) / 2, 0.0])
else:
r_image = np.array([-r_preimage[0], r_preimage[1]])
x_image, y_image, sublattice_image = models.physical_to_lattice(r_image, geometry)
x_image = int(np.rint(x_image)); y_image = int(np.rint(y_image))
x_image = (x_image % config.Ls); y_image = (y_image % config.Ls)
index = models.to_linearized_index(x_image, y_image, sublattice_image, orbit_image, \
config.Ls, config.n_orbitals, config.n_sublattices)
mapping[preindex, index] += coefficient
assert np.sum(np.abs(mapping.dot(mapping) - np.eye(mapping.shape[0]))) < 1e-5 # C_2y^2 = I
return mapping + 0.0j