Universal nonlinear responses of quantum Hall systems with Galilean invariance

TL;DR

This paper develops a comprehensive effective action framework for Galilean-invariant quantum Hall systems, revealing universal relations among nonlinear electromagnetic and thermal responses, including Hall conductivity and viscosity contributions.

Contribution

It constructs the most general symmetry-consistent effective action capturing nonlinear responses in Galilean-invariant quantum Hall systems.

Findings

Derived universal relations among nonlinear responses.

Connected Hall conductivity to longitudinal conductivity at finite frequency.

Linked Hall viscosity to nonlinear electrothermal conductivity.

Abstract

We study two-dimensional systems with Galilean invariance gapped under magnetic fields. When such quantum Hall systems are coupled with external sources for charge, energy, and momentum currents, they exhibit invariance under the Milne boost as well as under the gauge and general coordinate transformations. We construct the most general effective action consistent with all the symmetries in the derivative expansion, where an electric field is regarded as order of unity so as to allow for nonlinear responses. The resulting action is shown to consist of four terms proportional to the Hall conductivity and viscosity and the energy density and magnetization. We then compute the local currents induced by electromagnetic fields, revealing universal relations among distinct kinds of responses. In particular, we find the Hall conductivity determining the longitudinal conductivity at nonzero frequency and the Hall viscosity contributing to the nonlinear electrothermal conductivity at nonzero wave number.