Topological aspects of the critical three-state Potts model
Abstract
We explore the topological defects of the critical three-state Potts spin system on the torus, Klein bottle and cylinder. A complete characterization is obtained by breaking down the Fuchs-Runkel-Schweigert construction of 2d rational CFT to the lattice setting. This is done by applying the strange correlator prescription to the recently obtained tensor network descriptions of string-net ground states in terms of bimodule categories [Lootens, Fuchs, Haegeman, Schweigert, Verstraete, SciPost Phys. 10, 053 (2021)]. The symmetries are represented by matrix product operators (MPO), as well as intertwiners between the diagonal tetracritical Ising model and the non-diagonal three-state Potts model. Our categorical construction lifts the global transfer matrix symmetries and intertwiners, previously obtained by solving Yang-Baxter equations, to MPO symmetries and intertwiners that can be locally deformed, fused and split. This enables the extraction of conformal characters from partition functions and yields a comprehensive picture of all boundary conditions.
Keywords
Cite
@article{arxiv.2107.11177,
title = {Topological aspects of the critical three-state Potts model},
author = {Robijn Vanhove and Laurens Lootens and Hong-Hao Tu and Frank Verstraete},
journal= {arXiv preprint arXiv:2107.11177},
year = {2023}
}
Comments
71 pages, many figures, includes supplementary material