MPS

julia

MPO <: AbstractAnsatz

A Matrix Product Operator (MPO) Ansatz Tensor Network.

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Tenet.MPO Method

julia

MPO(arrays::Vector{<:AbstractArray}; order=defaultorder(MPO))

Create a NonCanonical MPO from a vector of arrays.

Keyword Arguments

order The order of the indices in the arrays. Defaults to (:o, :i, :l, :r).

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Tenet.MPS Type

julia

MPS <: AbstractAnsatz

A Matrix Product State Ansatz Tensor Network.

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Tenet.MPS Method

julia

MPS(arrays::Vector{<:AbstractArray}; order=defaultorder(MPS))

Create a NonCanonical MPS from a vector of arrays.

Keyword Arguments

order The order of the indices in the arrays. Defaults to (:o, :l, :r).

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Tenet.MPS Method

julia

MPS(::typeof(identity), n::Integer; physdim=2, maxdim=physdim^(n ÷ 2))

Returns an MPS of n sites whose tensors are initialized to COPY-tensors.

Keyword Arguments

physdim The physical or output dimension of each site. Defaults to 2.
maxdim The maximum bond dimension. Defaults to physdim^(n ÷ 2).

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Base.rand Method

julia

Base.rand(rng::Random.AbstractRNG, ::Type{MPO}; n, maxdim, eltype=Float64, physdim=2)

Create a random MPO Tensor Network. In order to avoid norm explosion issues, the tensors are orthogonalized by QR factorization so its normalized and mixed canonized to the last site.

Keyword Arguments

n The number of sites.
maxdim The maximum bond dimension. If it is nothing, the maximum bond dimension increases exponentially with the number of sites up to (physdim^2)^(n ÷ 2).
eltype The element type of the tensors. Defaults to Float64.
physdim The physical or output dimension of each site. Defaults to 2.

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Base.rand Method

julia

Base.rand(rng::Random.AbstractRNG, ::Type{MPS}; n, maxdim, eltype=Float64, physdim=2)

Create a random MPS Tensor Network in the MixedCanonical form where all tensors are right-canonical (ortogonality center at the first site). In order to avoid norm explosion issues, the tensors are orthogonalized by LQ factorization.

Keyword Arguments

n The number of sites.
maxdim The maximum bond dimension. If it is nothing, the maximum bond dimension increases exponentially with the number of sites up to physdim^(n ÷ 2).
eltype The element type of the tensors. Defaults to Float64.
physdim The physical or output dimension of each site. Defaults to 2.

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Tenet.absorb! Method

julia

absorb!(tn::AbstractMPO; bond=(lane1, lane2), dir::Symbol = :left, delete_Λ = true)

For a given AbstractMPO Tensor Network, contract the singular values Λ located in the bond between lanes lane1 and lane2.

Keyword arguments

- `bond` The bond between the singular values tensor and the tensors to be contracted.
- `dir` The direction of the contraction. Defaults to `:left`.
- `delete_Λ` Whether to delete the singular values tensor after the contraction. Defaults to `true`.

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Tenet.absorb Method

julia

absorb(tn::AbstractMPO; kwargs...)

Non-mutating version of absorb!.

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Tenet.check_form Method

julia

check_form(mps::AbstractMPO)

Check if the tensors in the mps are in the proper Form.

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Tenet.evolve! Method

julia

evolve!(ψ::AbstractAnsatz, mpo::AbstractMPO; threshold=nothing, maxdim=nothing, normalize=true, reset_index=true)

Evolve the AbstractAnsatz ψ with the AbstractMPO mpo along the output indices of ψ. If threshold or maxdim are not nothing, the tensors are truncated after each sweep at the proper value, and the bond is normalized if normalize=true. If reset_index=true, the indices of the ψ are reset to the original ones.

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Tenet.truncate_sweep! Method

julia

truncate_sweep!

Do a right-to-left QR sweep on the AbstractMPO ψ and then left-to-right SVD sweep and truncate the tensors according to the threshold or maxdim values. The bond is normalized if normalize=true.

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MPS ​

MPS