An operator algebraic approach to symmetry defects and fractionalization
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912292012032000 |
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| author | Kawagoe, Kyle Vadnerkar, Siddharth Wallick, Daniel |
| author_facet | Kawagoe, Kyle Vadnerkar, Siddharth Wallick, Daniel |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_23380 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An operator algebraic approach to symmetry defects and fractionalization Kawagoe, Kyle Vadnerkar, Siddharth Wallick, Daniel Mathematical Physics Strongly Correlated Electrons Operator Algebras 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. |
| title | An operator algebraic approach to symmetry defects and fractionalization |
| topic | Mathematical Physics Strongly Correlated Electrons Operator Algebras |
| url | https://arxiv.org/abs/2410.23380 |