Strong-disorder renormalization for interacting non-Abelian anyon systems in two dimensions

TL;DR

This paper investigates the impact of quenched disorder on two-dimensional non-Abelian anyon systems, finding that they do not develop infinite randomness phases but tend to weaken disorder under strong-disorder renormalization.

Contribution

The study introduces a planar approximation for SDRG in 2D non-Abelian anyon systems and demonstrates its effectiveness through comparisons with known models.

Findings

Disordered Ising and Fibonacci anyon systems do not exhibit infinite randomness phases.

The planar approximation accurately reproduces known critical behavior in related models.

Disorder tends to weaken in 2D non-Abelian anyon systems under SDRG.

Abstract

We consider the effect of quenched spatial disorder on systems of interacting, pinned non-Abelian anyons as might arise in disordered Hall samples at filling fractions \nu=5/2 or \nu=12/5. In one spatial dimension, such disordered anyon models have previously been shown to exhibit a hierarchy of infinite randomness phases. Here, we address systems in two spatial dimensions and report on the behavior of Ising and Fibonacci anyons under the numerical strong-disorder renormalization group (SDRG). In order to manage the topology-dependent interactions generated during the flow, we introduce a planar approximation to the SDRG treatment. We characterize this planar approximation by studying the flow of disordered hard-core bosons and the transverse field Ising model, where it successfully reproduces the known infinite randomness critical point with exponent \psi ~ 0.43. Our main conclusion for disordered anyon models in two spatial dimensions is that systems of Ising anyons as well as systems of Fibonacci anyons do not realize infinite randomness phases, but flow back to weaker disorder under the numerical SDRG treatment.