1. An operator algebraic approach to symmetry defects and fractionalization
- Author
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Kawagoe, Kyle, Vadnerkar, Siddharth, and Wallick, Daniel
- Subjects
Mathematical Physics ,Condensed Matter - Strongly Correlated Electrons ,Mathematics - Operator Algebras - Abstract
We provide a superselection theory of symmetry defects in 2+1D symmetry enriched topological (SET) order in the infinite volume setting. For a finite symmetry group $G$ with a unitary on-site action, our formalism produces a $G$-crossed braided tensor category $G\mathsf{Sec}$. This superselection theory is a direct generalization of the usual superselection theory of anyons, and thus is consistent with this standard analysis in the trivially graded component $G\mathsf{Sec}_1$. This framework also gives us a completely rigorous understanding of symmetry fractionalization. To demonstrate the utility of our formalism, we compute $G\mathsf{Sec}$ explicitly in both short-range and long-range entangled spin systems with symmetry and recover the relevant skeletal data., Comment: 84 pages, 18 figures
- Published
- 2024