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Categorical descriptions of 1+1D gapped phases with onsite symmetries

组织者

白岸斯 , 陈群皓 , 孔良 , 王亦龙 , 张智浩 , 郑浩

演讲者

张智浩

时间

2024年10月08日 13:30 至 15:00

地点

A3-2-301

线上

Zoom 230 432 7880 (BIMSA)

摘要

For a 1+1D gapped phase with onsite symmetries, there are two types of macroscopic observables: the topological defects and the symmetry operators. They form a mathematical structure called an enriched category. In this talk I will first review the general theory, and then analyze two concrete examples: the Ising chain with $\mathbb{Z}_2$ symmetry and the Haldane chain with $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry. I will also introduce the algebra of symmetry operators that act on the ground state invariantly, which also characterizes the 1+1D gapped phase. This algebra is also isomorphic to the ground state subspace on a circle. In particular, different SPTs can be distinguished by their ground state algebras. This talk is based on the work arXiv:2205.09656 joint with Rongge Xu.