Ashkin–Teller universality in a quantum double model of Ising anyons

Abstract

We study a quantum double model whose degrees of freedom are Ising anyons. The termsof the Hamiltonian of this system give rise to a competition between single and doubletopologies. By studying the energy spectra of the Hamiltonian at different values ofthe coupling constants, we find extended gapless regions which include a largenumber of critical points described by conformal field theories with central chargec = 1. These theories are part of the orbifold of the bosonic theory compactified on a circle. We observe that the Hilbertspace of our anyonic model can be associated with extended Dynkin diagramsof affine Lie algebras, which yields exact solutions at some critical points. Incertain special regimes, our model corresponds to the Hamiltonian limit of theAshkin–Teller model, and hence integrability over a wide range of coupling parameters isestablished.