Magnetoelasticity theory of incompressible quantum Hall liquids

TL;DR

This paper introduces a magnetoelasticity theory for incompressible fractional quantum Hall states that satisfies key physical sum rules, predicts collective modes with roton minima, and connects to fermionic Chern-Simons theory.

Contribution

It proposes a new, transparent magnetoelasticity framework for quantum Hall liquids that aligns with known sum rules and reveals connections to existing theories.

Findings

Predicts a gapped intra-Landau level collective mode with roton minimum.

Recovers the correct static structure factor behavior as bare mass vanishes.

Establishes a link between magnetoelasticity theory and fermionic Chern-Simons theory.

Abstract

A simple and physically transparent magnetoelasticity theory is proposed to describe linear dynamics of incompressible fractional quantum Hall states. The theory manifestly satisfies the Kohn theorem and the $f$-sum rule, and predicts a gaped intra-Landau level collective mode with a roton minimum. In the limit of vanishing bare mass $m$ the correct form of the static structure factor, $s(q)\sim q^4$, is recovered. We establish a connection of the present approach to the fermionic Chern-Simons theory, and discuss further extensions and applications. We also make an interesting analogy of the present theory to the theory of visco-elastic fluids.