TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.16.6.143
TI  - Fusion surface models: 2+1d lattice models from fusion 2-categories
PY  - 2024/06/03
UR  - https://scipost.org/SciPostPhys.16.6.143
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 16
IS  - 6
SP  - 143
A1  - Inamura, Kansei
AU  - Ohmori, Kantaro
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.16.6.143,
	title={{Fusion surface models: 2+1d lattice models from fusion 2-categories}},
	author={Kansei Inamura and Kantaro Ohmori},
	journal={SciPost Phys.},
	volume={16},
	pages={143},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.16.6.143},
	url={https://scipost.org/10.21468/SciPostPhys.16.6.143},
}