Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
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| Format: | Preprint |
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2023
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| _version_ | 1866914822286737408 |
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| author | Inamura, Kansei Ohmori, Kantaro |
| author_facet | Inamura, Kansei Ohmori, Kantaro |
| contents | We construct (2+1)-dimensional lattice systems, which we call fusion surface models. These models have finite non-invertible symmetries described by general fusion 2-categories. Our method can be applied to build microscopic models with, for example, anomalous or non-anomalous one-form symmetries, 2-group symmetries, or non-invertible one-form symmetries that capture non-abelian anyon statistics. The construction of these models generalizes the construction of the 1+1d anyon chains formalized by Aasen, Fendley, and Mong. Along with the fusion surface models, we also obtain the corresponding three-dimensional classical statistical models, which are 3d analogues of the 2d Aasen-Fendley-Mong height models. In the construction, the "symmetry TFTs" for fusion 2-category symmetries play an important role. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_05774 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories Inamura, Kansei Ohmori, Kantaro Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Quantum Algebra We construct (2+1)-dimensional lattice systems, which we call fusion surface models. These models have finite non-invertible symmetries described by general fusion 2-categories. Our method can be applied to build microscopic models with, for example, anomalous or non-anomalous one-form symmetries, 2-group symmetries, or non-invertible one-form symmetries that capture non-abelian anyon statistics. The construction of these models generalizes the construction of the 1+1d anyon chains formalized by Aasen, Fendley, and Mong. Along with the fusion surface models, we also obtain the corresponding three-dimensional classical statistical models, which are 3d analogues of the 2d Aasen-Fendley-Mong height models. In the construction, the "symmetry TFTs" for fusion 2-category symmetries play an important role. |
| title | Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Quantum Algebra |
| url | https://arxiv.org/abs/2305.05774 |