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

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 $\gamma (L/\xi )$ which governs the crossover. The scaling parameter $\xi (W)$ is deduced and compared with the localization length. $\gamma (L/\xi )$ does {\em not} show critical behavior and has two asymptotic regimes corresponding to weakly and strongly localized states.

4 pages in revtex, 3 postscript figures

References in corpus (3)

• Relation between Energy Level Statistics and Phase Transition and its Application to the Anderson Model
• Scaling of Level Statistics at the Disorder-Induced Metal-Insulator Transition
• LEVEL CORRELATIONS DRIVEN BY WEAK LOCALIZATION IN 2-D SYSTEMS

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• Magnetization and Level Statistics at Quantum Hall Liquid-Insulator Transition in the Lattice Model
• Exact analytic solution for the generalized Lyapunov exponent of the 2-dimensional Anderson localization
• Scaling for level statistics from self-consistent theory of localization
• Localization of non-interacting electrons in thin layered disordered systems
• Level dynamics and avoided level crossings in driven disordered quantum dots
• A renormalization approach for the 2D Anderson model at the band edge: Scaling of the localization volume