Field theory of the quantum Hall nematic transition

TL;DR

This paper develops a field theory describing the quantum phase transition from an isotropic to a nematic Laughlin liquid in quantum Hall systems, identifying critical modes and dynamic scaling behavior.

Contribution

It introduces a continuum field theory capturing the quantum Hall nematic transition, linking topological and geometric descriptions and identifying critical modes.

Findings

Identifies the intra-Landau level Girvin-MacDonald-Platzman mode as the soft mode at the transition.

Derives z=2 dynamic scaling at the critical point.

Provides a description of Goldstone and defect physics on the nematic side.

Abstract

The topological physics of quantum Hall states is efficiently encoded in purely topological quantum field theories of the Chern-Simons type. The reliable inclusion of low-energy dynamical properties in a continuum description however typically requires proximity to a quantum critical point. We construct a field theory that describes the quantum transition from an isotropic to a nematic Laughlin liquid. The soft mode associated with this transition approached from the isotropic side is identified as the familiar intra-Landau level Girvin-MacDonald-Platzman mode. We obtain z=2 dynamic scaling at the critical point and a description of Goldstone and defect physics on the nematic side. Despite the very different physical motivation, our field theory is essentially identical to a recent "geometric" field theory for a Laughlin liquid proposed by Haldane.