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 TemperleyLieb 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 Betheansatz 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2020
 DOI:
 10.48550/arXiv.2003.11293
 arXiv:
 arXiv:2003.11293
 Bibcode:
 2020arXiv200311293B
 Keywords:

 Mathematical Physics
 EPrint:
 42 pages, 4 figures