Levin-Wen is a gauge theory: entanglement from topology
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929223363461120 |
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| author | Kawagoe, Kyle Jones, Corey Sanford, Sean Green, David Penneys, David |
| author_facet | Kawagoe, Kyle Jones, Corey Sanford, Sean Green, David Penneys, David |
| contents | We show that the Levin-Wen model of a unitary fusion category $\mathcal{C}$ is a gauge theory with gauge symmetry given by the tube algebra $\operatorname{Tube}(\mathcal{C})$. In particular, we define a model corresponding to a $\operatorname{Tube}(\mathcal{C})$ symmetry protected topological phase, and we provide a gauging procedure which results in the corresponding Levin-Wen model. In the case $\mathcal{C}=\mathsf{Hilb}(G,ω)$, we show how our procedure reduces to the twisted gauging of a trivial $G$-SPT to produce the Twisted Quantum Double. We further provide an example which is outside the bounds of the current literature, the trivial Fibonacci SPT, whose gauge theory results in the doubled Fibonacci string-net. Our formalism has a natural topological interpretation with string diagrams living on a punctured sphere. We provide diagrams to supplement our mathematical proofs and to give the reader an intuitive understanding of the subject matter. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_13838 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Levin-Wen is a gauge theory: entanglement from topology Kawagoe, Kyle Jones, Corey Sanford, Sean Green, David Penneys, David Strongly Correlated Electrons Mathematical Physics Category Theory Operator Algebras Quantum Algebra 81V27, 18M30 (primary) 18M20, 46L60, 57R56, 81T05, 81T25 (secondary) We show that the Levin-Wen model of a unitary fusion category $\mathcal{C}$ is a gauge theory with gauge symmetry given by the tube algebra $\operatorname{Tube}(\mathcal{C})$. In particular, we define a model corresponding to a $\operatorname{Tube}(\mathcal{C})$ symmetry protected topological phase, and we provide a gauging procedure which results in the corresponding Levin-Wen model. In the case $\mathcal{C}=\mathsf{Hilb}(G,ω)$, we show how our procedure reduces to the twisted gauging of a trivial $G$-SPT to produce the Twisted Quantum Double. We further provide an example which is outside the bounds of the current literature, the trivial Fibonacci SPT, whose gauge theory results in the doubled Fibonacci string-net. Our formalism has a natural topological interpretation with string diagrams living on a punctured sphere. We provide diagrams to supplement our mathematical proofs and to give the reader an intuitive understanding of the subject matter. |
| title | Levin-Wen is a gauge theory: entanglement from topology |
| topic | Strongly Correlated Electrons Mathematical Physics Category Theory Operator Algebras Quantum Algebra 81V27, 18M30 (primary) 18M20, 46L60, 57R56, 81T05, 81T25 (secondary) |
| url | https://arxiv.org/abs/2401.13838 |