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)(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)(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)(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

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    Last time updated on 14/05/2020