Defining tensor networks

abstract type AbstractUnitCell{G<:AbstractUnitCellGeometry, ElType, A} <: AbstractArray{ElType, 2}

Abstract supertype of all unit cells (periodic boundary conditions) defined on a lattice with geometry G.

struct UnitCell{G<:AbstractUnitCellGeometry, ElType, A} <: AbstractUnitCell{G<:AbstractUnitCellGeometry, ElType, A}

Container AbstractMatrix type with periodic boundary conditions, and a lattice geometry specific by type parameter G.

abstract type AbstractUnitCellGeometry

Abstract supertype of all unit cell lattice geometries.

struct Square <: AbstractUnitCellGeometry

Singleton type representing a standard square lattice geometry with coordination number 4.

struct SquareSymmetric <: AbstractUnitCellGeometry

Singleton type representing a square lattice with reverse cyclic symmetry. For (2,2) unit cell sizes, this defines a checkerboard lattice geometry.

Examples

julia> UnitCell{SquareSymmetric}([1 2 3; 2 3 1; 3 1 2])
3×3 UnitCell{SquareSymmetric, Int64, Matrix{Int64}}:
 1  2  3
 2  3  1
 3  1  2

julia> UnitCell{SquareSymmetric}([1 2; 3 4])
ERROR: ArgumentError: data does not have the required cyclic symmetry for this lattice geometry.

CompositeTensor{M,T,S<:IndexSpace,N₁,N₂, ...} <: AbstractTensorMap{T,S,N₁,N₂}

Subtype of AbstractTensorMap for representing a M-layered tensor map, e.g. a tensor and it's conjugate.

tensortype(x) -> AbstractTensorMap

Return the type of tensor associated with object x, if any. Similar to eltype for container types but always returns an AbstractTensorMap. Defined in both the value and type domains.

virtualspace(tensor, [dir::Integer])

Return an NTuple{4,<:VectorSpace} containing the east, south, west, and north vector spaces associated with the respective bonds, in that order. If dir is provided, then return the corresponding VectorSpace in that tuple.

swapaxes(tensor)

Swap the horizontal and the vertical virtual bonds of an object.

invertaxes(tensor)

Invert the horizontal and the vertical bonds of an object t, that is, south ↔ north and east ↔ west.