Classification of connected étale algebras in multiplicity-free modular fusion categories at rank six

2024/02/01 by Kikuchi, Ken, Kam, Kah-Sen, Huang, Fu-Hsiang · 1 citation
#Category Theory (math.CT) #FOS: Mathematics #FOS: Physical sciences #Quantum Algebra (math.QA) #Strongly Correlated Electrons (cond-mat.str-el)

paper · doi:10.48550/arxiv.2402.00403

Abstract

We classify connected étale algebras A's in multiplicity-free modular fusion categories (MFCs) B's at rank six, namely rank(B)=6. There are eight MFCs in total and the result indicates that only so(5)₂ has nontrivial connected étale algebra. We briefly mention anyon condensation as it is used to determine the category of right A-modules in so(5)₂. Finally, we discuss physical applications, specifically proving spontaneous B-symmetry breaking (SSB) of these MFCs. The discussion also includes predicting ground state degeneracies and SSB in massive renormalization group flows from two non-unitary minimal models.

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