Domain walls from SPT-sewing

TL;DR

This paper presents a systematic method for constructing gapped domain walls in topologically ordered systems using gauged SPT phases, establishing a new correspondence and discovering exotic domain walls in the 3D toric code.

Contribution

It introduces a novel construction method for gapped domain walls via gauging SPT phases and establishes a correspondence between 1D SPT phases with complex symmetries and invertible domain walls.

Findings

Proves the correspondence for Abelian groups G.

Provides evidence for non-Abelian G, specifically G=S_3.

Constructs exotic anchoring domain walls in the 3D toric code.

Abstract

We introduce a systematic method for constructing gapped domain walls of topologically ordered systems by gauging a lower-dimensional symmetry-protected topological (SPT) order. Based on our construction, we propose a correspondence between 1d SPT phases with a non-invertible $G\times \text{Rep}(G)\times G$ symmetry and invertible domain walls in the quantum double associated with the group $G$. We prove this correspondence when $G$ is Abelian and provide evidence for the general case by studying the quantum double model for $G=S_3$. We also use our method to construct \emph{anchoring domain walls}, which are novel exotic domain walls in the 3d toric code that transform point-like excitations to semi-loop-like excitations anchored on these domain walls.