On Enriching the Levin-Wen model with Symmetry

TL;DR

This paper extends the Levin-Wen model to include symmetry enriched topological phases, providing a rigorous framework for studying these phases in 2D systems with richer symmetry structures.

Contribution

The paper introduces an extension of the Levin-Wen model using unitary multi-fusion categories, enabling the study of symmetry protected and enriched topological phases.

Findings

Extended Levin-Wen model with multi-fusion categories

Framework for symmetry enriched topological phases

Potential for analyzing new topological materials

Abstract

Symmetry protected and symmetry enriched topological phases of matter are of great interest in condensed matter physics due to new materials such as topological insulators. The Levin-Wen model for spin/boson systems is an important rigorously solvable model for studying $2D$ topological phases. The input data for the Levin-Wen model is a unitary fusion category, but the same model also works for unitary multi-fusion categories. In this paper, we provide the details for this extension of the Levin-Wen model, and show that the extended Levin-Wen model is a natural playground for the theoretical study of symmetry protected and symmetry enriched topological phases of matter.