Conformal field theory description of mesoscopic phenomena in the fractional quantum Hall effect

TL;DR

This paper develops a universal conformal field theory framework to describe mesoscopic phenomena, like persistent currents, in fractional quantum Hall systems influenced by Aharonov-Bohm flux, applicable to various edge states.

Contribution

It introduces a novel CFT-based approach to analyze mesoscopic effects in fractional quantum Hall systems, including parafermion states, across temperature regimes.

Findings

Derived the asymptotic behavior of persistent currents at different temperatures.

Applied the framework specifically to parafermion Hall states.

Provided a universal description applicable to all known edge state CFTs.

Abstract

We give a universal description of the mesoscopic effects occurring in fractional quantum Hall disks due to the Aharonov-Bohm flux threading the system. The analysis is based on the exact treatment of the flux within the conformal field theory framework and is relevant for all fractional quantum Hall states whose edge states CFTs are known. As an example we apply this scheme for the parafermion Hall states and extract the main characteristics of the low- and high- temperature asymptotic behavior of the persistent currents.