Field theory of the quantum Hall nematic transition

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.