Non-renormalization of the fractional quantum Hall conductivity by interactions

TL;DR

This paper demonstrates that in the fractional quantum Hall effect, interaction corrections do not alter the quantized conductivity, using a relativistic extension and a macroscopic motion approach to prove non-renormalization.

Contribution

It introduces a novel macroscopic motion framework and proves that interactions do not modify the fractional QHE conductivity to all orders in perturbation theory.

Findings

Interaction corrections do not change the mean field QHE conductivity.

A relativistic extension supports the non-renormalization proof.

Macroscopic motion approach offers an alternative perspective on fractional QHE.

Abstract

We investigate the theory of the fractional quantum Hall effect (QHE) proposed a long time ago by Lopez and Fradkin \cite{Fradkin1991chern} to describe the principal Jain series. The magnetic fluxes of the statistical gauge field attached to electrons remain at rest in the reference frame moving together with the electron liquid. In the laboratory reference frame the electric field of the statistical gauge field forms and screens the external electric field. The fractional QHE conductivity appears as a consequence of this screening already on the mean field theory level. We consider a relativistic extension of the model, and propose an alternative description of the fractional QHE based on macroscopic motion of the electron liquid within the Zubarev statistical operator approach. It is this macroscopic motion of electrons which in this pattern gives rise to the fractional QHE. Within this approach we propose the proof to all orders of perturbation theory that the interaction corrections cannot change the above mentioned mean field theory result for the QHE conductivity.