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.\nThe terms of the Hamiltonian of this system give rise to a competition between\nsingle and double topologies. By studying the energy spectra of the Hamiltonian\nat different values of the coupling constants, we find extended gapless regions\nwhich include a large number of critical points described by conformal field\ntheories with central charge c=1. These theories are part of the Z_2 orbifold\nof the bosonic theory compactified on a circle. We observe that the Hilbert\nspace of our anyonic model can be associated with extended Dynkin diagrams of\naffine Lie algebras which yields exact solutions at some critical points. In\ncertain special regimes, our model corresponds to the Hamiltonian limit of the\nAshkin-Teller model, and hence integrability over a wide range of coupling\nparameters is established.\n