# netket.operator.GraphOperator¶

class netket.operator.GraphOperator

A custom graph based operator.

__init__(self: netket._C_netket.operator.GraphOperator, hilbert: netket._C_netket.hilbert.Hilbert, siteops: List[List[List[complex]]] = [], bondops: List[List[List[complex]]] = [], bondops_colors: List[int] = []) → None

Constructs a new GraphOperator given a hilbert space and either a list of operators acting on sites or a list acting on the bonds. Users can specify the color of the bond that an operator acts on, if desired. If none are specified, the bond operators act on all edges.

Parameters
• hilbert – Hilbert space the operator acts on.

• siteops – A list of operators that act on the nodes of the graph. The default is an empty list. Note that if no siteops are specified, the user must give a list of bond operators.

• bondops – A list of operators that act on the edges of the graph. The default is an empty list. Note that if no bondops are specified, the user must give a list of site operators.

• bondops_colors – A list of edge colors, specifying the color each bond operator acts on. The defualt is an empty list.

Examples

Constructs a BosGraphOperator operator for a 2D system.

>>> import netket as nk
>>> sigmax = [[0, 1], [1, 0]]
>>> mszsz = [[1, 0, 0, 0], [0, -1, 0, 0], [0, 0, -1, 0], [0, 0, 0, 1]]
>>> edges = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8],
... [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15],
... [15, 16], [16, 17], [17, 18], [18, 19], [19, 0]]
>>> g = nk.graph.CustomGraph(edges=edges)
>>> hi = nk.hilbert.CustomHilbert(local_states=[-1, 1], graph=g)
>>> op = nk.operator.GraphOperator(
... hi, siteops=[sigmax], bondops=[mszsz], bondops_colors=[0])
>>> print(op.hilbert.size)
20


Methods

 __init__(self, hilbert, siteops, bondops, …) Constructs a new GraphOperator given a hilbert space and either a list of operators acting on sites or a list acting on the bonds. get_conn(self, v, 1]]) Member function finding the connected elements of the Operator. to_dense(self) Returns the dense matrix representation of the operator. Converts Operator to scipy.sparse.linalg.LinearOperator. to_sparse(self) Returns the sparse matrix representation of the operator.

Attributes

 hilbert Hilbert space of operator.
get_conn(self: netket._C_netket.Operator, v: numpy.ndarray[float64[m, 1]]) → Tuple[scipy.sparse.csc_matrix[float64], numpy.ndarray[complex128[m, 1]]]

Member function finding the connected elements of the Operator. Starting from a given visible state v, it finds all other visible states v’ such that the matrix element $$O(v,v')$$ is different from zero. In general there will be several different connected visible units satisfying this condition, and they are denoted here $$v'(k)$$, for $$k=0,1...N_{\mathrm{connected}}$$.

Parameters

v – A constant reference to the visible configuration.

property hilbert

Hilbert space of operator.

Type

netket.hilbert.Hilbert

to_dense(self: netket._C_netket.Operator) → numpy.ndarray[complex128[m, n]]

Returns the dense matrix representation of the operator. Note that, in general, the size of the matrix is exponential in the number of quantum numbers, and this operation should thus only be performed for low-dimensional Hilbert spaces.

This method requires an indexable Hilbert space.

to_linear_operator(self: object) → object

Converts Operator to scipy.sparse.linalg.LinearOperator.

This method requires an indexable Hilbert space.

to_sparse(self: netket._C_netket.Operator) → scipy.sparse.csr_matrix[complex128]

Returns the sparse matrix representation of the operator. Note that, in general, the size of the matrix is exponential in the number of quantum numbers, and this operation should thus only be performed for low-dimensional Hilbert spaces or sufficiently sparse operators.

This method requires an indexable Hilbert space.