Classification of Gapped Domain Walls of Topological Orders in 2+1 dimensions: A Levin-Wen Model Realization

TL;DR

This paper develops a systematic method to classify gapped domain walls in 2+1D topological orders using Levin-Wen models, connecting domain wall and boundary classifications through bimodule and Frobenius algebra structures.

Contribution

It introduces a comprehensive construction and classification of gapped domain walls in Levin-Wen models, linking them to bimodule categories and Frobenius algebras.

Findings

Complete classification of gapped domain walls via bulk input data

Introduction of a generalized bimodule structure for domain-wall excitations

Folding along domain walls yields gapped boundaries described by Frobenius algebras

Abstract

This paper introduces a novel systematic construction of gapped domain walls (GDWs) within the Levin-Wen (LW) model. By gluing two LW models along their open sides in a compatible way, we achieve a complete GDW classification by subsets of bulk input data, which encompass the classifications in terms of bimodule categories. A generalized bimodule structure is introduced to capture domain-wall excitations. Furthermore, we demonstrate that folding along any GDW yields a gapped boundary (GB) described by a Frobenius algebra of the input UFC for the folded model, thus bridging our GDW classification and the GB classification in \cite{hu2018boundary}.