Classification of connected étale algebras in multiplicity-free modular fusion categories at rank six
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917580284887040 |
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| author | Kikuchi, Ken Kam, Kah-Sen Huang, Fu-Hsiang |
| author_facet | Kikuchi, Ken Kam, Kah-Sen Huang, Fu-Hsiang |
| contents | We classify connected étale algebras $A$'s in multiplicity-free modular fusion categories (MFCs) $\mathcal{B}$'s at rank six, namely $\text{rank}(\mathcal{B})=6$. There are eight MFCs in total and the result indicates that only $so(5)_2$ has nontrivial connected étale algebra. We briefly mention anyon condensation as it is used to determine the category of right $A$-modules in $so(5)_2$. Finally, we discuss physical applications, specifically proving spontaneous $\mathcal{B}$-symmetry breaking (SSB) of these MFCs. The discussion also includes predicting ground state degeneracies and SSB in massive renormalization group flows from two non-unitary minimal models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00403 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of connected étale algebras in multiplicity-free modular fusion categories at rank six Kikuchi, Ken Kam, Kah-Sen Huang, Fu-Hsiang Quantum Algebra Strongly Correlated Electrons Category Theory We classify connected étale algebras $A$'s in multiplicity-free modular fusion categories (MFCs) $\mathcal{B}$'s at rank six, namely $\text{rank}(\mathcal{B})=6$. There are eight MFCs in total and the result indicates that only $so(5)_2$ has nontrivial connected étale algebra. We briefly mention anyon condensation as it is used to determine the category of right $A$-modules in $so(5)_2$. Finally, we discuss physical applications, specifically proving spontaneous $\mathcal{B}$-symmetry breaking (SSB) of these MFCs. The discussion also includes predicting ground state degeneracies and SSB in massive renormalization group flows from two non-unitary minimal models. |
| title | Classification of connected étale algebras in multiplicity-free modular fusion categories at rank six |
| topic | Quantum Algebra Strongly Correlated Electrons Category Theory |
| url | https://arxiv.org/abs/2402.00403 |