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TensorKit.jl

A Julia package for large-scale tensor computations, with a hint of category theory.

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Release notes for v0.13

TensorKit v0.13 brings a number of performance improvements, but also comes with a number of breaking changes:

1. The scalar type (the eltype of the tensor data) is now an explicit parameter of the the TensorMap type, and appears in the first position. As a consequence, TensorMap{T}(undef, codomain ← domain) can and should now be used to create a TensorMap with uninitialised data with scalar type T.

2. The constructors for creating tensors with randomly initialised data, of the form TensorMap(randn, T, codomain ← domain), are being replaced with randn(T, codomain ← domain). Hence, we overload the methods rand and randn from Base (actually, Random, and also Random.randexp) and mimick the Array constructors, relying on the fact that we use spaces instead of integers to characterise the tensor structure. As with integer-based rand and randn, a custom random number generator from the Random module can be passed as the first argument, and the scalar type T is optional, defaulting to Float64. The old constructors TensorMap(randn, T, codomain ← domain) still exist in deprecation mode, and will be removed in the 1.0 release.

3. The TensorMap data structure has been changed (simplified), so that all tensor data now resides in a single array of type <:DenseVector. While this does not lead to breaking changes in the interface, it does mean that TensorMap objects from TensorKit.jl v0.12.7 or earlier that were saved to disk using e.g. JLD2.jl, cannot simply be read back in using the new version of TensorKit.jl. We provide a script below to export data in a format that can be read back in by TensorKit.jl v0.13.

Major non-breaking changes include:

• Support for TensorOperations.jl v5, and with this the new backend and allocator support within the @tensor macro.
• The part of TensorKit.jl that defines the Sector type hierarchy and its corresponding interface, as well as the implementation of all of the standard symmetries, has been moved to a separate package called TensorKitSectors.jl, so that it can also be used by other packages and is a more lightweight dependency. TensorKitSectors.jl is a direct dependency and is automatically installed when installing TensorKit.jl. Furthermore, its public interface is re-exported by TensorKit.jl, so that this should not have any observable consequences.
• The fusiontrees iterator now iterates over FusionTree objects in a different order, which will facilitate speeding up certain operations in the future. Furthermore, it now also accepts a ProductSpace object as first input, instead of simply a tuple of Sector objects. This also affects the data ordering in the TensorMap objects.
• The structural information associated with a TensorMap object (or rather with the HomSpace instance that represents the space to which the tensor belongs) is no longer stored within the tensor, but is cached in a global (or task local) dictionary. As a result, this information does not need to be recomputed when new TensorMap objects are created, thus eliminating some overhead that can be significant in certain applications.

Transferring TensorMap data from older versions to v0.13:

To export TensorMap data from TensorKit.jl v0.12.7 or earlier, you should first export the data there in a format that is explicit about how tensor data is associated with the structural part of the tensor, i.e. the splitting and fusion tree pairs. Therefore, on the older version of TensorKit.jl, use the following code to save the data

using JLD2
filename = "choose_some_filename.jld2"
t_dict = Dict(:space => space(t), :data => Dict((f₁, f₂) => t[f₁, f₂] for (f₁, f₂) in fusiontrees(t)))
jldsave(filename; t_dict)

If you have already upgraded to TensorKit.jl v0.13, you can still install the old version in a separate environment, for example a temporary environment. To do this, run

]activate --temp
]add TensorKit@0.12.7

or

import Pkg
Pkg.activate(; temp = true)
Pkg.add("TensorKit@0.12.7")

Then, in the environment where you have TensorKit.jl v0.13 installed, you can read in the data and reconstruct the tensor as follows:

using JLD2
filename = "choose_some_filename.jld2"
t_dict = jldload(filename)
T = eltype(valtype(t_dict[:data]))
t = TensorMap{T}(undef, t_dict[:space])
for ((f₁, f₂), val) in t_dict[:data]
    t[f₁, f₂] .= val
end

Overview

TensorKit.jl is a package that provides types and methods to represent and manipulate tensors with symmetries. The emphasis is on the structure and functionality needed to build tensor network algorithms for the simulation of quantum many-body systems. Such tensors are typically invariant under a symmetry group which acts via specific representions on each of the indices of the tensor. TensorKit.jl provides the functionality for constructing such tensors and performing typical operations such as tensor contractions and decompositions, thereby preserving the symmetries and exploiting them for optimal performance.

While most common symmetries are already shipped with TensorKit.jl, there exist several extensions: SUNRepresentations.jl provides support for SU(N), while CategoryData.jl incorporates a large collection of small fusion categories. Additionally, for libraries that implement tensor network algorithms on top of TensorKit.jl, check out MPSKit.jl, MERAKit.jl and PEPSKit.jl.

Check out the tutorial and the full documentation.

Installation

TensorKit.jl can be installed with the Julia package manager. From the Julia REPL, type ] to enter the Pkg REPL mode and run:

pkg> add TensorKit

Or, equivalently, via the Pkg API:

julia> import Pkg; Pkg.add("TensorKit.jl")

Documentation

• STABLE - documentation of the most recently tagged version.
• DEV - documentation of the in-development version.

Project Status

The package is tested against Julia versions 1.10 and the latest 1.x release, as well as against the nightly builds of the Julia master branch on Linux, macOS, and Windows platforms with a 64-bit architecture.

Questions and Contributions

Contributions are very welcome, as are feature requests and suggestions. Please open an issue if you encounter any problems.