SimpleBZ

full name: tenpy.models.lattice.SimpleBZ
parent module: tenpy.models.lattice
type: class

Inheritance Diagram

Methods

`SimpleBZ.__init__`(vertices, basis, dim)
`SimpleBZ.contains_points`(points)	Checks whether given points lie inside the 1st Brillouin Zone.
`SimpleBZ.from_recip_basis_vectors`(...)
`SimpleBZ.lagrange_lattice_reduction`(basis)	Short implementation of Lagrange's algorithm for 2D lattice reduction.
`SimpleBZ.order_vertices`(vertices)
`SimpleBZ.plot_brillouin_zone`(args, *kwargs)	Plot the brillouin zone of the lattice.
`SimpleBZ.reduce_points`(points)	Bring a set of points into 1st Brillouin Zone.

Class Attributes and Properties

SimpleBZ.area

class tenpy.models.lattice.SimpleBZ(vertices, basis, dim: int)[source]

Bases: object

Helper class to provide an interface for the Brillouin Zone of a given lattice.

The Brillouin Zone is the Wigner-Seitz Cell of the reciprocal lattice. For a given lattice with basis vectors \(a_i\), the reciprocal lattice is generated by the reciprocal basis vectors \(b_i\), which obey \(a_i b_j = 2 \pi \delta_{i j}\).

Parameters:

vertices (array_like) – a list of the vertices of the 1st BZ with shape (N, d) where d is the dimension and N the number of vertices.
basis (array_like) – the reciprocal basis of the real space lattice, i.e. the basis in reciprocal space
dim (int) – dimension of the Brillouin Zone

contains_points(points) → ndarray[source]

Checks whether given points lie inside the 1st Brillouin Zone.

Parameters:: points (array_like) – points of shape (…, 2) for 2D or shape(…) for 1D that will be checked
Returns:: boolean array of shape points.shape[:-1] if 2D or points.shape if 1D, indicating whether the corresponding point in points is contained in the Brillouin Zone
Return type:: ndarray

reduce_points(points)[source]

Bring a set of points into 1st Brillouin Zone.

This is done by applying multiples of the reciprocal basis vectors, for points that lie outside the 1st Brillouin Zone.

Parameters:: points (array_like) – points to reduce given in the shape (…, 2) for 2D or (…) for 1D
Returns:: reduced_points – of shape points.shape the array of the points now reduced to the 1st BZ
Return type:: ndarray

plot_brillouin_zone(*args, **kwargs)[source]

Plot the brillouin zone of the lattice.

See _plot_brillouin_zone_1d() and _plot_brillouin_zone_2d().

static lagrange_lattice_reduction(basis)[source]

Short implementation of Lagrange’s algorithm for 2D lattice reduction.

Parameters:: basis (array_like) – basis of a lattice in reciprocal space, s.t. the basis vectors are b1 = basis[0], b2 = basis[1]
Returns:: out – the reduced basis. If \(\{i b_1 + j b_2 | i, j \in \mathbb{Z}\}\) define a lattice L, the reduced basis vectors will generate the same lattice, albeit being the shortest and “most orthogonal” ones to define the lattice
Return type:: ndarray