Gauge Invariance and the Critical Properties of Quantum Hall Plateaux Transitions
arXiv:cond-mat/9904414 · doi:10.1103/PhysRevB.61.10917
Abstract
A model consisting of a single massless scalar field with a topological coupling to a pure gauge field is defined and studied. It possesses an SL(2,Z) symmetry as a consequence of the gauge invariance. We propose that by adding impurities the model can be used to describe transitions between Quantum Hall plateaux. This leads to a correlation length exponent of 20/9, in excellent agreement with the most recent experimental measurements.
25 pages, minor changes in data discussion, Section V on connection with staircase model is expanded References added. Interpretive comments added in section 3 about the critical condition. with improved terminology