Generating `TTN`

TenNetLib.jl defines following functions to generate TTNs with random entries.

For the standard TTN with the default hierarchical binary tree structure, follwoing function can be used.

TenNetLib.default_randomTTN — Function

function default_randomTTN(sites::Vector{Index{T}}, chi::Int, qn::QN = QN()) where T

Returns a TTN object, having random elements, from site Indexs sites, initial bond dimension chi and (optional) global QN sector qn. The structure is a default hierarchical binary tree graph. Automatically handles situations where the number of sites is not a power of 2.

Note: For QN conserving TTN, the bond dimension might be off by one or two from chi.

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The underlying default binary tree for the function above is generated by the following function.

TenNetLib.default_graph_sitenodes — Method

function default_graph_sitenodes(N::Int)

Given the total number of sites, N::Int, generates the default hierarchical binary tree graph and a Dict{Int, Int2} object that maps each site to the corresponding node. Automatically handles situations where the number of sites is not a power of 2.

Return values:

::Graph{Int2}: Default hierarchical tree graph to accomodate N number of sites in a TTN.
::Dict{Int, Int2}: Maps each site to the corresponding node.

Example:

graph, sitenodes = default_graph_sitenodes(32)

sitenodes[1] == (1,1) # true
sitenodes[2] == (1,1) # true
sitenodes[3] == (1,2) # true
sitenodes[4] == (1,2) # true
sitenodes[31] == (1,16) # true
sitenodes[32] == (1,16) # true

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In the generic scenario, a random TTN with user-defined structure can be generated by the following function.

TenNetLib.randomTTN — Function

function randomTTN(sites::Vector{Index{T}}, graph::Graph{Int2},
                   sitenodes::Dict{Int, Int2}, chi::Int, qn::QN = QN()) where T

Returns a TTN object, having random elements, from site Indexs sites, the underlyting graph, sitenodes::Dict{Int, Int2} that maps each site to the corresponding node, initial bond dimension chi, and (optional) global QN sector qn. The structure is determined by the input graph object.

Note: This function can be used to generate any loop-free tensor network.

Note: For QN conserving TTN, the bond dimension might be off by one or two from chi.

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Info

The above function can be used to generate any loop-free tensor network.

Generating TTN

Generating `TTN`