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Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories

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arxiv 2305.05774 v2 pith:QGIYBKBH submitted 2023-05-09 cond-mat.str-el cond-mat.stat-mechhep-thmath.QA

Kansei Inamura , Kantaro Ohmori This is my paper · ORCID
classification cond-mat.str-elcond-mat.stat-mechhep-thmath.QA
keywords modelsfusionsymmetriesconstructionsurfaceanyoncategorieslattice
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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.

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Cited by 4 Pith papers

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