Dualities between 2+1d fusion surface models from braided fusion categories

• URL: http://arxiv.org/abs/2501.14722v1
• Date: Fri, 24 Jan 2025 18:58:02 GMT
• Title: Dualities between 2+1d fusion surface models from braided fusion categories
• Authors: Luisa Eck,
• Abstract summary: We show that module tensor categories $mathcalM$ over the same braided fusion category $mathcalB$ give rise to dual lattice models. We analyze two concrete examples: (i) a $textRep(S_3)$ model with a constrained Hilbert space, dual to the spin-$tfrac12$ XXZ model on the honeycomb lattice, and (ii) a bilayer Kitaev honeycomb model, dual to a spin-$tfrac12$ model with XXZ and Ising interactions
• Score: 0.4662017507844857
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• Abstract: 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.

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