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

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.