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

We study the phase transition between the quantum Hall liquid and the insulator 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 single relativistic scalar field coupled to the Chern-Simons gauge field. Within the regime of parameters where perturbation expansion is valid, we show that the transition is first order, induced by the fluctuations of the gauge field, rather than second order, with statistical angle-dependent scaling exponent.