A universal conformal field theory approach to the chiral persistent currents in the mesoscopic fractional quantum Hall states

TL;DR

This paper introduces a universal conformal field theory-based method to compute persistent currents and related magnetic properties in mesoscopic fractional quantum Hall systems, emphasizing the role of invariance conditions and applying it to Z_k parafermion states.

Contribution

It develops a general scheme using conformal field theory to analyze persistent currents in fractional quantum Hall states, including explicit formulas and invariance principles.

Findings

Z_k parafermion states exhibit universal non-Fermi liquid behavior.

Derived explicit formulas for partition functions with flux dependence.

Analyzed high-temperature asymptotics using modular S-matrices.

Abstract

We propose a general and compact scheme for the computation of the periods and amplitudes of the chiral persistent currents, magnetizations and magnetic susceptibilities in mesoscopic fractional quantum Hall disk samples threaded by Aharonov--Bohm magnetic field. This universal approach uses the effective conformal field theory for the edge states in the quantum Hall effect to derive explicit formulas for the corresponding partition functions in presence of flux. We point out the crucial role of a special invariance condition for the partition function, following from the Bloch-Byers-Yang theorem, which represents the Laughlin spectral flow. As an example we apply this procedure to the Z_k parafermion Hall states and show that they have universal non-Fermi liquid behavior without anomalous oscillations. For the analysis of the high-temperature asymptotics of the persistent currents in the parafermion states we derive the modular S-matrices constructed from the S matrices for the u(1) sector and that for the neutral parafermion sector which is realized as a diagonal affine coset.