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The quantum Hall plateau transition at order 1/N

Joel E. Moore·A. Zee·Jairo Sinova
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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 $E_n = \hbar ω_c (n+{1/2})$, 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 $ν$. 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 $N = 1$.

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Joel E. Moore, A. Zee, Jairo Sinova. 2001-05-11. The quantum Hall plateau transition at order 1/N. https://doi.org/10.1103/physrevlett.87.046801

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