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

Autor:	Inamura, Kansei, Ohmori, Kantaro
Rok vydání:	2023
Předmět:	Condensed Matter - Strongly Correlated Electrons Condensed Matter - Statistical Mechanics High Energy Physics - Theory Mathematics - Quantum Algebra
Zdroj:	SciPost Phys. 16, 143 (2024)
Druh dokumentu:	Working Paper
DOI:	10.21468/SciPostPhys.16.6.143
Popis:	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. Comment: 61 pages. Minor changes, references updated
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2305.05774 Zobrazit plný text záznamu View this record from Arxiv