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Crossover of Level Statistics between Strong and Weak Localization in Two Dimensions

I. Kh. Zharekeshev·M. Batsch·B. Kramer
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Abstract

We investigate numerically the statistical properties of spectra of two-dimensional disordered systems by using the exact diagonalization and decimation method applied to the Anderson model. Statistics of spacings calculated for system sizes up to 1024 $\times$ 1024 lattice sites exhibits a crossover between Wigner and Poisson distributions. We perform a self-contained finite-size scaling analysis to find a single-valued one-parameter function $γ(L/ξ)$ which governs the crossover. The scaling parameter $ξ(W)$ is deduced and compared with the localization length. $γ( L/ξ)$ does {\em not} show critical behavior and has two asymptotic regimes corresponding to weakly and strongly localized states.

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I. Kh. Zharekeshev, M. Batsch, B. Kramer. 1996-06-06. Crossover of Level Statistics between Strong and Weak Localization in Two Dimensions. https://doi.org/10.1209/epl%2Fi1996-00499-9

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