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The Level Spacing Distribution Near the Anderson Transition

A. G. Aronov·V. E. Kravtsov·I. V. Lerner
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Abstract

For a disordered system near the Anderson transition we show that the nearest-level-spacing distribution has the asymptotics $P(s)\propto \exp(-A s^{2-γ})$ for $s\gg \av{s}\equiv 1$ which is universal and intermediate between the Gaussian asymptotics in a metal and the Poisson in an insulator. (Here the critical exponent $0<γ<1$ and the numerical coefficient $A$ depend only on the dimensionality $d>2$). It is obtained by mapping the energy level distribution to the Gibbs distribution for a classical one-dimensional gas with a pairwise interaction. The interaction, consistent with the universal asymptotics of the two-level correlation function found previously, is proved to be the power-law repulsion with the exponent $-γ$.

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A. G. Aronov, V. E. Kravtsov, I. V. Lerner. 1994-02-05. The Level Spacing Distribution Near the Anderson Transition. https://arxiv.org/abs/cond-mat/9402027

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