def Pyrochlore(extent: Sequence[int],
*,
pbc: Union[bool, Sequence[bool]] = True,
**kwargs) -> Lattice:
"""Constructs a pyrochlore lattice of a given spatial extent.
Periodic boundary conditions can also be imposed.
Sites are returned at the 16c Wyckoff positions of the FCC lattice
([111]/8, [1 -1 -1]/8, [-1 1 -1]/8, [-1 -1 1]/8, and translations thereof).
Arguments:
extent: Number of primitive unit cells along each direction, needs to be
an array of length 3
pbc: If `True`, the lattice will have periodic boundary conditions (PBC);
if `False`, the lattice will have open boundary conditions (OBC).
This parameter can also be a list of booleans with same length as
the parameter `length`, in which case each dimension will have
PBC/OBC depending on the corresponding entry of `pbc`.
kwargs: Additional keyword arguments are passed on to the constructor of
:ref:`netket.graph.Lattice`.
Example:
Construct a pyrochlore lattice with 3×3×3 primitive unit cells:
>>> from netket.graph import Pyrochlore
>>> g = Pyrochlore(extent=[3,3,3])
>>> print(g.n_nodes)
108
"""
basis = [[0, 0.5, 0.5], [0.5, 0, 0.5], [0.5, 0.5, 0]]
sites = np.array([[1, 1, 1], [1, 3, 3], [3, 1, 3], [3, 3, 1]]) / 8
# determine if full point group is realised by the simulation box
point_group = cubic.Fd3m() if np.all(pbc) and len(
set(extent)) == 1 else None
return Lattice(
basis_vectors=basis,
site_offsets=sites,
extent=extent,
pbc=pbc,
point_group=point_group,
**kwargs,
)
def Diamond(extent: Sequence[int],
*,
pbc: Union[bool, Sequence[bool]] = True) -> Lattice:
"""Constructs a diamond lattice of a given spatial extent.
Periodic boundary conditions can also be imposed.
Sites are returned at the 8a Wyckoff positions of the FCC lattice
([000], [1/4,1/4,1/4], and translations thereof).
Arguments:
extent: Number of primitive unit cells along each direction, needs to
be an array of length 3
pbc: If `True`, the lattice will have periodic boundary conditions (PBC);
if `False`, the lattice will have open boundary conditions (OBC).
This parameter can also be a list of booleans with same length as
the parameter `length`, in which case each dimension will have
PBC/OBC depending on the corresponding entry of `pbc`.
Example:
Construct a diamond lattice with 3×3×3 primitive unit cells:
>>> from netket.graph import Diamond
>>> g = Diamond(extent=[3,3,3])
>>> print(g.n_nodes)
54
"""
basis = [[0, 0.5, 0.5], [0.5, 0, 0.5], [0.5, 0.5, 0]]
sites = [[0, 0, 0], [0.25, 0.25, 0.25]]
# determine if full point group is realised by the simulation box
point_group = cubic.Fd3m() if np.all(pbc) and len(
set(extent)) == 1 else None
return Lattice(
basis_vectors=basis,
site_offsets=sites,
extent=extent,
pbc=pbc,
point_group=point_group,
)