Topological aspects of the critical three-state Potts model

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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 et al 2021 SciPost Phys. 10 053). 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.


Original languageEnglish
Article number235002
JournalJournal of Physics A: Mathematical and Theoretical
Issue number23
Publication statusPublished - 20 May 2022

External IDs

unpaywall 10.1088/1751-8121/ac68b1
WOS 000800920800001
Mendeley 50a20dc3-66df-36bf-bad3-d272abd12138
Scopus 85131329049


DFG Classification of Subject Areas according to Review Boards


  • conformal field theory, topological defects, tensor networks

Library keywords