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 v = 5/2 fractional quantum Hall state and the proposed v = 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 S_k 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 Z_k ⊂ S_k symmetric sector of the Damle-Huse model, and this Z_k symmetry stabilizes the phase.