Computing data for Levin-Wen with defects

TL;DR

This paper develops computational methods for analyzing non-chiral topological phases with defects, including domain walls and point defects, using algebraic techniques exemplified by Vec(S3).

Contribution

It introduces generalized tube algebra techniques to compute fusion, associators, and defect data in topological phases with defects, with detailed examples and code.

Findings

Computed domain wall fusion and associators for Vec(S3)

Enumerated and characterized point defects and their fusion data

Provided practical Mathematica tools for topological defect analysis

Abstract

We demonstrate how to do many computations for non-chiral topological phases with defects. These defects may be 1-dimensional domain walls or 0-dimensional point defects. Using $\operatorname{Vec}(S_3)$ as a guiding example, we demonstrate how domain wall fusion and associators can be computed using generalized tube algebra techniques. These domain walls can be both between distinct or identical phases. Additionally, we show how to compute all possible point defects, and the fusion and associator data of these. Worked examples, tabulated data and Mathematica code are provided.