BIMSA >
BIMSA TQFT and Higher Symmetries Seminar
Categorical descriptions of 1+1D gapped phases with onsite symmetries
Categorical descriptions of 1+1D gapped phases with onsite symmetries
Organizers
Speaker
Time
Tuesday, October 8, 2024 1:30 PM - 3:00 PM
Venue
A3-2-301
Online
Zoom 230 432 7880
(BIMSA)
Abstract
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.