The Quantum hall Plateau Transition at Order 1/N

The localization behavior of non-interacting two-dimensional electrons in a random potential and strong magnetic field is a fundamental interest for the physics of the quantum Hall effect. In order to understand the emergence of powerlaw delocalization near the discrete extended-state energies E_n = hbar omega_c (n + 1/2), we study a generalization of the disorder-averaged Liouvillian framework for the lowest Landau level to N flavors of electron densities (N = 1 for the physical case). We find analytically the large-N limit and 1/N corrections for all disorder strengths: at N = inf this gives an estimate of the critical conductivity, and at order 1/N an estimate of the localization exponent nu. The localization properties of the analytically tractable N >> 1 theory seem to be continuously connected to those of the exact quantum Hall plateau transition at N = 1.