The TTN object

mutable struct TTN{T}
    sites::Vector{Index{T}}
    graph::Graph{Int2}
    tensors::Dict{Int2, ITensor}
    orthocenter::Int2
end

Tree Tensor Network (TTN) object.

Each tensor is indexed by the tuple of integers (::Int2), (ll, nn), where (usually) ll denotes the layer index and nn denotes the tensor index at each layer.

• sites::Vector{Index}: Physical site Indexs.
• graph::Graph{Int2}: Underlying structure of the network defined by Graph{Int2}.
• tensors::Dict{Int2, ITensor}: Tensors in the TTN.
• orthocenter::Int2: Orthogonality center of the TTN.

function ITensors.siteinds(ttn::TTN)

Returns the site Indexs of the TTN.

function ITensors.siteind(ttn::TTN, n::Int)

Returns the nth site Index of the TTN.

function numsites(ttn::TTN)

Returns the number of physical sites in the TTN.

function getgraph(ttn::TTN)

Returns (shallow copy of) the underlying graph of the TTN.

function Base.getindex(ttn::TTN, node::Int2)
function Base.getindex(ttn::TTN, ll::Int, nn::Int)

Returns the tensor at the node::Int2 = (ll, nn).

function Base.setindex!(ttn::TTN, tensor::ITensor, node::Int2)
function Base.setindex!(ttn::TTN, tensor::ITensor, ll::Int, nn::Int)

Sets the tensor at the node::Int2 = (ll, nn). If the node is not the orthogonality center, orthogonality center is set to (typemin(Int), typemin(Int)).

function orthocenter(ttn::TTN)

Returns the orthogonality center of the TTN.

Base.copy(ttn::TTN)

Shallow copy of TTN.

function isvalidnode(ttn::TTN, node::Int2)

Checks whether the input node::Int2 is a valid node in the TTN graph.

function isneighbor(ttn::TTN, node1::Int2, node2::Int2)

Checks whether node1 and node2 are neighboring nodes in the TTN.

function ITensors.findsite(ttn::TTN, is)

Returns the first site of the TTN that has at least one Index in common with the Index or ITensor or their collection is.

function ITensors.findsites(ttn::TTN, is)

Returns the sites of the TTN that have Indexs in common with the Index or ITensor or their collection is.

function findnode(ttn::TTN, is)

Returns the first node of the TTN that has at least one Index in common with the Index or ITensor or their collection is.

function findnodes(ttn::TTN, is)

Returns the nodes of the TTN that have Indexs in common with the Index or ITensor or their collection is.

function find_sitenode(ttn::TTN, n::Int)

Return node of the TTN that is associated with the site n.

function find_sitenodes(ttn::TTN, ns)

Returns nodes of the TTN that are associated with the sites ns (a collection of Ints).

function ITensors.maxlinkdim(ttn::TTN)

Returns the maximum bond/link dimension of the TTN.

function LinearAlgebra.normalize!(ttn::TTN)

Normalizes the TTN. The TTN must have well-defined orthogonality center.

function ITensors.hasqns(ttn::TTN)

Checks whether the TTN has QNs.

function find_qnnode(ttn::TTN)

Returns the node where the a dummy QN Index is attached to fix the QN sector. Returns nothing if the TTN does not have QN.

function moveisometry_to_next!(ttn::TTN, node1::Int2, node2::Int2; kwargs...)

Moves the isometry / orthogonality center of the TTN from node1::Int2 to the neighboring node2::Int. node1 and node2 must be neighboring nodes. node1 must be the orthogonality center unless ignore_orthocenter = true.

Note: Does not normalize the TTN afterwards.

Named arguments and their default values.

• ignore_orthocenter::Bool = false: If set to true, node1 is not required to be the orthogonality center.
• maxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.
• mindim::Int = 1: Minimum bond dimension after SVD truncation.
• cutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.
• svd_alg::String = "divide_and_conquer".

function isometrize_full!(ttn::TTN, node::Int2; kwargs...)

Isometrizes the TTN from scratch with respect to the orthogonality center node::Int2.

Named arguments and their default values.

• normalize::Bool = true: Whether to normalize the TTN afterwards.
• maxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.
• mindim::Int = 1: Minimum bond dimension after SVD truncation.
• cutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.
• svd_alg::String = "divide_and_conquer".

function isometrize!(ttn::TTN, node::Int2; kwargs...)

Moves the isometry / orthogonality center of the TTN to a new center node. If the TTN does not have proper orthoginality center, Isometrizes the TTN from scratch.

Named arguments and their default values.

• normalize::Bool = true: Whether to normalize the TTN afterwards.
• maxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.
• mindim::Int = 1: Minimum bond dimension after SVD truncation.
• cutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.
• svd_alg::String = "divide_and_conquer".