Exactness of linear response in the quantum Hall effect

TL;DR

This paper proves that in the quantum Hall effect, the linear response relation between current and electromotive force is exact, with no higher order corrections, even in fully interacting systems without flux averaging.

Contribution

It demonstrates that the linear response in the quantum Hall effect is exact, extending previous results to fully interacting systems without flux averaging.

Findings

Higher order corrections vanish in the quantum Hall effect

Linear response is exact in fully interacting systems

No flux averaging needed for exactness

Abstract

In general, linear response theory expresses the relation between a driving and a physical system's response only to first order in perturbation theory. In the context of charge transport, this is the linear relation between current and electromotive force expressed in Ohm's law. We show here that, in the case of the quantum Hall effect, all higher order corrections vanish. We prove this in a fully interacting setting and without flux averaging.