Domain walls from SPT-sewing

• URL: http://arxiv.org/abs/2411.11967v1
• Date: Mon, 18 Nov 2024 19:00:16 GMT
• Title: Domain walls from SPT-sewing
• Authors: Yabo Li, Zijian Song, Aleksander Kubica, Isaac H. Kim,
• Abstract summary: We propose a correspondence between 1d SPT phases with a non-invertible $Gtimes textRep(G)times G$ symmetry and invertible domain walls in the quantum double associated with the group $G$. We also use our method to construct emphanchoring 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.
• Score: 43.87233488320917
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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