MultiTensorKit

TensorKit extension to multifusion categories

Package summary

MultiTensorKit.jl provides the user a package to work with multifusion categories, the extension of regular fusion categories where the unit is no longer simple and unique. Multifusion categories naturally embed the structure of module categories over fusion categories. Hence, MultiTensorKit.jl allows not only the fusion of objects within the same fusion category (as TensorKit.jl), but also the fusion with and between module categories over these fusion categories.

MultiTensorKit.jl is built to be compatible with TensorKit, thus allowing the construction of symmetric tensors with new symmetries due to the module structure. Through this, tensor network simulations of quantum many-body systems with aid of MPSKit.jl can be performed.

Table of contents

• Introduction
• Fusion category theory
• • Examples
• Extending to multifusion category theory
• • Module categories
  • Opposite module categories
  • Invertible bimodule categories and Morita equivalence
  • Multifusion categories
  • Examples of multifusion categories
• Library
• References

Installation

MultiTensorKit.jl is currently not registered to the Julia General Registry. You can install the package as

pkg> add https://github.com/QuantumKitHub/MultiTensorKit.jl.git

Usage

As the name suggests, MultiTensorKit is an extension of TensorKit.jl and TensorKitSectors.jl. Therefore, we recommend including TensorKit to your project. Additionally, MultiTensorKit was made to be functional with MPSKit.jl and MPSKitModels.jl for Matrix Product State (MPS) calculations, supporting symmetries which go beyond TensorKit. All these packages are registered in JuliaRegistries and can be added through the package manager.