Exactness of linear response in the quantum Hall effect

Sven Bachmann, Wojciech De Roeck, Martin Fraas, Markus Lange

Published 2020-06-23Version 1

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.