Infinite-Randomness Fixed Points for Chains of Non-Abelian Quasiparticles

TL;DR

This paper explores the critical behavior and entanglement properties of one-dimensional chains of non-Abelian quasiparticles, revealing their connection to known models and characterizing their entanglement entropy scaling.

Contribution

It introduces a unified framework for understanding random singlet phases in chains of non-Abelian quasiparticles, linking them to known fixed points and quantifying entanglement entropy.

Findings

Chains of non-Abelian quasiparticles can exhibit random singlet phases similar to spin-1/2 chains.

For $k=2$, the phase describes the infinite randomness fixed point of the transverse field Ising model.

Entanglement entropy scales logarithmically with region size, proportional to the quantum dimension.

Abstract

One-dimensional chains of non-Abelian quasiparticles described by $SU(2)_k$ Chern-Simons-Witten theory can enter random singlet phases analogous to that of a random chain of ordinary spin-1/2 particles (corresponding to $k \to \infty$). For $k=2$ this phase provides a random singlet description of the infinite randomness fixed point of the critical transverse field Ising model. The entanglement entropy of a region of size $L$ in these phases scales as $S_L \simeq \frac{\ln d}{3} \log_2 L$ for large $L$, where $d$ is the quantum dimension of the particles.