“Generalizations of Kitaev’s honeycomb model from braided fusion categories”
Fusion surface models, as introduced by Inamura and Ohmori, extend the concept of anyon chains to 2+1 dimensions, taking fusion 2-categories as their input. In this talk, I will focus on fusion surface models constructed from fusion 1-categories, which preserve (possibly non-invertible) 1-form symmetries. I will discuss how Kitaev’s honeycomb model can be regarded as an Ising fusion surface model, and explore Z3 and Fibonacci generalizations, constructed from different input categories, that are likely to realize chiral topological order. Finally, I will describe how dualities between fusion surface models arise through different choices of module tensor categories over the underlying braided fusion category. This talk is based on arXiv:2408.04006 and upcoming work.
Host: Meng Cheng