Permutation-symmetric critical phases in disordered non-Abelian anyonic chains

Topological phases supporting non-Abelian anyonic excitations have been proposed as candidates for topological quantum computation. In this paper, we study disordered non-Abelian anyonic chains based on the quantum groups SU(2)ₖ, a hierarchy that includes the ν=5/2 fractional quantum Hall state and the proposed ν=12/5 Fibonacci state, among others. We find that for odd k these anyonic chains realize infinite-randomness critical phases in the same universality class as the Sₖ permutation symmetric multicritical points of Damle and Huse [Phys. Rev. Lett. 89, 277203 (2002)]. Indeed, we show that the pertinent subspace of these anyonic chains actually sits inside the Zₖ⊂Sₖ symmetric sector of the Damle-Huse model, and this Zₖ symmetry stabilizes the phase.