Dualities between 2+1d fusion surface models from braided fusion categories
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914204555935744 |
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| author | Eck, Luisa |
| author_facet | Eck, Luisa |
| contents | Fusion surface models generalize the concept of anyon chains to 2+1 dimensions, utilizing fusion 2-categories as their input. We investigate bond-algebraic dualities in these systems and show that distinct module tensor categories $\mathcal{M}$ over the same braided fusion category $\mathcal{B}$ give rise to dual lattice models. This extends the 1+1d result that dualities in anyon chains are classified by module categories over fusion categories. We analyze two concrete examples: (i) a $\text{Rep}(S_3)$ model with a constrained Hilbert space, dual to the spin-$\tfrac{1}{2}$ XXZ model on the honeycomb lattice, and (ii) a bilayer Kitaev honeycomb model, dual to a spin-$\tfrac{1}{2}$ model with XXZ and Ising interactions. Unlike regular $\mathcal{M}=\mathcal{B}$ fusion surface models, which conserve only 1-form symmetries, models constructed from $\mathcal{M} \neq \mathcal{B}$ can exhibit both 1-form and 0-form symmetries, including non-invertible ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_14722 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dualities between 2+1d fusion surface models from braided fusion categories Eck, Luisa Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics Fusion surface models generalize the concept of anyon chains to 2+1 dimensions, utilizing fusion 2-categories as their input. We investigate bond-algebraic dualities in these systems and show that distinct module tensor categories $\mathcal{M}$ over the same braided fusion category $\mathcal{B}$ give rise to dual lattice models. This extends the 1+1d result that dualities in anyon chains are classified by module categories over fusion categories. We analyze two concrete examples: (i) a $\text{Rep}(S_3)$ model with a constrained Hilbert space, dual to the spin-$\tfrac{1}{2}$ XXZ model on the honeycomb lattice, and (ii) a bilayer Kitaev honeycomb model, dual to a spin-$\tfrac{1}{2}$ model with XXZ and Ising interactions. Unlike regular $\mathcal{M}=\mathcal{B}$ fusion surface models, which conserve only 1-form symmetries, models constructed from $\mathcal{M} \neq \mathcal{B}$ can exhibit both 1-form and 0-form symmetries, including non-invertible ones. |
| title | Dualities between 2+1d fusion surface models from braided fusion categories |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2501.14722 |