Quantum Hall plateau transition at order 1/N -: art. no. 046801

The localization behavior of noninteracting two-dimensional electrons in a random potential and strong magnetic field is of fundamental interest for the physics of the quantum Hall effect. In order to understand the emergence of power-law delocalization near the discrete extended-state energies E-n = (h) over barw(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 = infinity this gives an estimate of the critical conductivity, and at order 1/N an estimate of the localization exponent v.