Newton-Cartan Geometry and the Quantum Hall Effect

TL;DR

This paper develops an effective field theory for quantum Hall states using Newton-Cartan geometry, emphasizing nonrelativistic invariance and zero mass limit regularity, and discusses its universal predictions.

Contribution

It introduces Newton-Cartan geometry as a natural framework for modeling quantum Hall states, providing a novel geometric approach.

Findings

Universal predictions of the effective theory are discussed.

Newton-Cartan geometry effectively captures nonrelativistic invariance.

The theory ensures regularity in the zero mass limit.

Abstract

We construct an effective field theory for quantum Hall states, guided by the requirements of nonrelativistic general coordinate invariance and regularity of the zero mass limit. We propose Newton-Cartan geometry as the most natural formalism to construct such a theory. Universal predictions of the theory are discussed.