Permutation Symmetric Critical Phases in Disordered Non-Abelian Anyonic Chains

Abstract

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 $\nu =5/2$ FQH state and the proposed $\nu =12/5$ Fibonacci state, among others. We find that for odd $k$ these anyonic chains realize infinite randomness critical {\it phases} in the same universality class as the $S_k$ permutation symmetric multi-critical 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 ${\mathbb{Z}}_k\subset S_k$ symmetric sector of the Damle-Huse model, and this ${\mathbb{Z}}_k$ symmetry stabilizes the phase.

13 pages

References in corpus (3)

• Interacting anyons in topological quantum liquids: The golden chain
• Collective states of interacting Fibonacci anyons
• Infinite Randomness Phases and Entanglement Entropy of the Disordered Golden Chain

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