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| Auteurs principaux: | , |
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| Format: | Preprint |
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2026
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| Accès en ligne: | https://arxiv.org/abs/2603.01936 |
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| _version_ | 1866917305970065408 |
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| author | Bols, Alex Kjær, Boris |
| author_facet | Bols, Alex Kjær, Boris |
| contents | This is the continuation of our study of the Levin-Wen model based on an arbitrary unitary fusion category $\mathcal{C}$ on the infinite plane. The ground state of the Levin-Wen model hosts anyonic excitations whose fusion and braiding properties are captured by the associated braided $\rm C^*$-tensor category of superselection sectors $\mathsf{SSS}$. By constructing explicit isomorphisms between the fusion spaces of $\mathsf{SSS}$ and those of the Drinfeld center $Z(\mathcal{C})$, we show that these two categories have isomorphic $F$- and $R$-symbols. It follows that the full subcategory of finite sectors is unitarily braided monoidally equivalent to the Drinfeld center, $$\,\mathsf{SSS}_f \simeq Z(\mathcal{C}).$$ This provides the first complete characterisation of the category of superselection sectors for a class of two-dimensional lattice models supporting anyons with non-integer quantum dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01936 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sector Theory of Levin-Wen Models II : Fusion and Braiding Bols, Alex Kjær, Boris Mathematical Physics This is the continuation of our study of the Levin-Wen model based on an arbitrary unitary fusion category $\mathcal{C}$ on the infinite plane. The ground state of the Levin-Wen model hosts anyonic excitations whose fusion and braiding properties are captured by the associated braided $\rm C^*$-tensor category of superselection sectors $\mathsf{SSS}$. By constructing explicit isomorphisms between the fusion spaces of $\mathsf{SSS}$ and those of the Drinfeld center $Z(\mathcal{C})$, we show that these two categories have isomorphic $F$- and $R$-symbols. It follows that the full subcategory of finite sectors is unitarily braided monoidally equivalent to the Drinfeld center, $$\,\mathsf{SSS}_f \simeq Z(\mathcal{C}).$$ This provides the first complete characterisation of the category of superselection sectors for a class of two-dimensional lattice models supporting anyons with non-integer quantum dimensions. |
| title | Sector Theory of Levin-Wen Models II : Fusion and Braiding |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2603.01936 |