The quantum Hall plateau transition at order 1/N

Abstract

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 $E_n=\hslash {\omega }_c(n+1/2)$, 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 $N=\infty$ 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 $N\gg 1$ theory seem to be continuously connected to those of the exact quantum Hall plateau transition at $N=1$.

4 pages, 4 figures; improved text, 1 corrected reference

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