Scaling and non-Abelian signature in fractional quantum Hall quasiparticle tunneling amplitude

TL;DR

This paper investigates the scaling behavior of quasiparticle tunneling amplitudes in fractional quantum Hall systems, revealing exact functional forms and nontrivial corrections for non-Abelian quasiparticles, advancing understanding of their properties.

Contribution

It provides a conjectured exact form of tunneling amplitudes in fractional quantum Hall states and analyzes the scaling of both Abelian and non-Abelian quasiparticles, including nontrivial corrections.

Findings

Exact functional form for tunneling amplitude in certain limits

Scaling behavior consistent with conformal dimensions for Abelian quasiparticles

Non-Abelian quasiparticles show nontrivial k-dependent scaling corrections

Abstract

We study the scaling behavior in the tunneling amplitude when quasiparticles tunnel along a straight path between the two edges of a fractional quantum Hall annulus. Such scaling behavior originates from the propagation and tunneling of charged quasielectrons and quasiholes in an effective field analysis. In the limit when the annulus deforms continuously into a quasi-one-dimensional ring, we conjecture the exact functional form of the tunneling amplitude for several cases, which reproduces the numerical results in finite systems exactly. The results for Abelian quasiparticle tunneling is consistent with the scaling anaysis; this allows for the extraction of the conformal dimensions of the quasiparticles. We analyze the scaling behavior of both Abelian and non-Abelian quasiparticles in the Read-Rezayi Z_k-parafermion states. Interestingly, the non-Abelian quasiparticle tunneling amplitudes exhibit nontrivial k-dependent corrections to the scaling exponent.