qml.spin.Lattice

class Lattice(n_cells, vectors, positions=None, boundary_condition=False, neighbour_order=1, custom_edges=None, custom_nodes=None, distance_tol=1e-05)

Bases: object

Constructs a Lattice object.

Parameters

• n_cells (list[int]) – Number of cells in each direction of the grid.

• vectors (list[list[float]]) – Primitive vectors for the lattice.

• positions (list[list[float]]) – Initial positions of the lattice nodes. Default value is [[0.0] \(\times\) number of dimensions].

• boundary_condition (bool or list[bool]) – Specifies whether or not to enforce periodic boundary conditions for the different lattice axes. Default is False indicating open boundary condition.

• neighbour_order (int) – Specifies the interaction level for neighbors within the lattice. Default is 1, indicating nearest neighbour. Must be 1 if custom_edges is defined.

• custom_edges (Optional[list(list(tuples))]) – Specifies the edges to be added in the lattice. Default value is None, which adds the edges based on neighbour_order. Each element in the list is for a separate edge, and can contain 1 or 2 tuples. First tuple contains the indices of the starting and ending vertices of the edge. Second tuple is optional and contains the operator on that edge and coefficient of that operator. Default value is the index of edge in custom_edges list.

• custom_nodes (Optional(list(list(int, tuples)))) – Specifies the on-site potentials and operators for nodes in the lattice. The default value is None, which means no on-site potentials. Each element in the list is for a separate node. For each element, the first value is the index of the node, and the second element is a tuple which contains the operator and coefficient.

• distance_tol (float) – Distance below which spatial points are considered equal for the purpose of identifying nearest neighbours. Default value is 1e-5.

Raises

• TypeError – if n_cells contains numbers other than positive integers.

• ValueError – if positions doesn’t have a dimension of 2.

• ValueError – if vectors doesn’t have a dimension of 2 or the length of vectors is not equal to the number of vectors.

• ValueError – if boundary_condition is not a bool or a list of bools with length equal to the number of vectors.

• ValueError – if custom_nodes contains nodes with negative indices or indices greater than number of sites

Returns

Lattice object

Example

We can define the positions of nodes in the lattice unit cell along with the lattice vectors to create a custom lattice layout.

from pennylane.spin import Lattice

positions = [[0.2, 0.5],
             [0.5, 0.2],
             [0.5, 0.8],
             [0.8, 0.5]]

vectors = [[1, 0], [0, 1]]

n_cells = [2, 2]

# periodic boundary conditions applied along the [1,0] axis only
boundary_condition = [True, False]

lattice = Lattice(n_cells, vectors, positions, boundary_condition=boundary_condition)

>>> lattice.edges
[(10, 13, 0), (0, 11, 0), (4, 15, 0), (2, 5, 0), (3, 8, 0), (7, 12, 0)]

Usage Details

Unless otherwise specified, the edges will be added based on the neighbour_order, which defaults to 1. Increasing neighbour_order will add additional connections in the lattice.

positions = [[0.2, 0.5],
             [0.5, 0.2],
             [0.5, 0.8],
             [0.8, 0.5]]

lattice = Lattice(n_cells=[2, 2],
                  vectors=[[1, 0], [0, 1]],
                  positions=positions,
                  neighbour_order=2,
                  boundary_condition=[True, False])

>>> len(lattice.edges)
22

We can also define edges with custom interactions, as well as adding on-site potentials for the nodes:

# defining on-site potential at each node in the unit cell
custom_nodes = [[(0), ('X', 0.5)],
                [(1), ('X', 0.6)],
                [(2), ('X', 0.7)],
                [(3), ('X', 0.8)]]

# defining custom edges (instead of nearest-neigbour connections) and their interactions
custom_edges = [[(0, 1), ('XX', 0.5)],
                [(0, 2), ('YY', 0.6)],
                [(1, 3), ('ZZ', 0.7)],
                [(2, 3), ('ZZ', 0.7)]]

>>> lattice = Lattice(n_cells,
...                   vectors,
...                   positions,
...                   custom_edges=custom_edges,
...                   custom_nodes=custom_nodes)
>>> lattice.edges
[(0, 1, ('XX', 0.5)),
(4, 5, ('XX', 0.5)),
(8, 9, ('XX', 0.5)),
(12, 13, ('XX', 0.5)),
(0, 2, ('YY', 0.6)),
(4, 6, ('YY', 0.6)),
(8, 10, ('YY', 0.6)),
(12, 14, ('YY', 0.6)),
(1, 3, ('ZZ', 0.7)),
(5, 7, ('ZZ', 0.7)),
(9, 11, ('ZZ', 0.7)),
(13, 15, ('ZZ', 0.7)),
(2, 3, ('ZZ', 0.7)),
(6, 7, ('ZZ', 0.7)),
(10, 11, ('ZZ', 0.7)),
(14, 15, ('ZZ', 0.7))]

Methods

add_edge(edge_indices)

Adds a specific edge based on the site index without translating it.

add_edge(edge_indices)

Adds a specific edge based on the site index without translating it.

Parameters

edge_indices – List of edges to be added, an edge is defined as a list of integers specifying the corresponding node indices.

Returns

Updates the edges attribute to include provided edges.

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