Fluctuation-Induced First Order Transition between the Quantum Hall Liquid and Insulator

TL;DR

This paper investigates the phase transition between quantum Hall liquid and insulator states, demonstrating that gauge field fluctuations induce a first-order transition rather than a second-order one, within a Chern-Simons-Landau-Ginzburg framework.

Contribution

It reveals that gauge field fluctuations cause a first-order transition in the quantum Hall-insulator system, contrasting previous expectations of a second-order transition.

Findings

Transition is first order due to gauge fluctuations

Scaling exponent depends on statistical angle

Transition differs from conventional second-order behavior

Abstract

We study the phase transition between the quantum Hall liquid state and the insulating state within the framework of the Chern-Simons-Landau-Ginzburg theory of the quantum Hall effect. For the transition induced by a background periodic potential in the absence of disorder, the model is described by a relativistic scalar field coupled to the Chern-Simons gauge field. For this system, we show that the transition is of the first order, induced by the fluctuations of the gauge field, rather than second order, with statistical angle-dependent scaling exponent.