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arXiv · 2410.23380

An operator algebraic approach to symmetry defects and fractionalization

Kyle Kawagoe·Siddharth Vadnerkar·Daniel Wallick
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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.

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Kyle Kawagoe, Siddharth Vadnerkar, Daniel Wallick. 2024-10-30. An operator algebraic approach to symmetry defects and fractionalization. https://arxiv.org/abs/2410.23380

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