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arXiv · 2411.11967

Domain walls from SPT-sewing

Yabo Li·Zijian Song·Aleksander Kubica·Isaac H. Kim
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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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Yabo Li, Zijian Song, Aleksander Kubica, Isaac H. Kim. 2024-11-18. Domain walls from SPT-sewing. https://arxiv.org/abs/2411.11967

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