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Preprints, Working Papers, ... Year : 2020

Topological defects in periodic RSOS models and anyonic chains

Abstract

We provide a lattice regularization of all topological defects in minimal models CFTs using RSOS and anyonic spin chains. For defects of type $(1,s)$, we connect our result with the "topological symmetry" initially identified in Fibonacci anyons [Phys. Rev. Lett. 98, 160409 (2007)], and the center of the affine Temperley-Lieb algebra discussed in [1811.02551]. We show that the topological nature of the defects is exact on the lattice as well. Our defects of type $(r,1)$, in contrast, are only topological in the continuum limit. Identifications are obtained by a mix of algebraic and Bethe-ansatz techniques. Most of our discussion is framed in a Hamiltonian (or transfer matrix) formalism, and direct and crossed channel are both discussed in detail. For defects of type $(1,s)$, we also show how to implement their fusion, which turns out to reproduce the tensor product of the underlying monoidal category used to build the anyonic chain.

Dates and versions

hal-02542870 , version 1 (14-04-2020)

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J. Belletête, A.M. Gainutdinov, J.L. Jacobsen, H. Saleur, T.S. Tavares. Topological defects in periodic RSOS models and anyonic chains. 2020. ⟨hal-02542870⟩
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