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

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.Comment: 4 pages in revtex, 3 postscript figure

Energy-level statistics and localization of 2d electrons in random magnetic fields

Using the method of energy-level statistics, the localization properties of electrons moving in two dimensions in the presence of a perpendicular random magnetic field and additional random disorder potentials are investigated. For this model, extended states have recently been proposed to exist in the middle of the band. In contrast, from our calculations of the large-$s$ behavior of the nearest neighbor level spacing distribution $P(s)$ and from a finite size scaling analysis we find only localized states in the suggested energy and disorder range.Comment: 4 pages LaTeX, 4 eps-figures. to appear in Physica

Critical level spacing distribution of two-dimensional disordered systems with spin-orbit coupling

The energy level statistics of 2D electrons with spin-orbit scattering are considered near the disorder induced metal-insulator transition. Using the Ando model, the nearest-level-spacing distribution is calculated numerically at the critical point. It is shown that the critical spacing distribution is size independent and has a Poisson-like decay at large spacings as distinct from the Gaussian asymptotic form obtained by the random-matrix theory.Comment: 7 pages REVTeX, 2 uuencoded, gzipped figures; J. Phys. Condensed Matter, in prin

One-parameter superscaling in three dimensions

Numerical and analytical details are presented on the newly discovered superscaling property of the energy spacing distribution in the three dimensional Anderson model.Comment: 4 pages, 3 figure

Advanced Lanczos diagonalization for models of quantum disordered systems

An application of an effective numerical algorithm for solving eigenvalue problems which arise in modelling electronic properties of quantum disordered systems is considered. We study the electron states at the localization-delocalization transition induced by a random potential in the framework of the Anderson lattice model. The computation of the interior of the spectrum and corresponding wavefunctions for very sparse, hermitian matrices of sizes exceeding 10^6 x 10^6 is performed by the Lanczos-type method especially modified for investigating statistical properties of energy levels and eigenfunction amplitudes.Comment: 5 pages in pdf-forma

Asymptotics of Universal Probability of Neighboring Level Spacings at the Anderson Transition

The nearest-neighbor level spacing distribution is numerically investigated by directly diagonalizing disordered Anderson Hamiltonians for systems of sizes up to 100 x 100 x 100 lattice sites. The scaling behavior of the level statistics is examined for large spacings near the delocalization-localization transition and the correlation length exponent is found. By using high-precision calculations we conjecture a new interpolation of the critical cumulative probability, which has size-independent asymptotic form \ln I(s) \propto -s^{\alpha} with \alpha = 1.0 \pm 0.1.Comment: 5 pages, RevTex, 4 figures, to appear in Physical Review Letter

Finite-size scaling from self-consistent theory of localization

Accepting validity of self-consistent theory of localization by Vollhardt and Woelfle, we derive the finite-size scaling procedure used for studies of the critical behavior in d-dimensional case and based on the use of auxiliary quasi-1D systems. The obtained scaling functions for d=2 and d=3 are in good agreement with numerical results: it signifies the absence of essential contradictions with the Vollhardt and Woelfle theory on the level of raw data. The results \nu=1.3-1.6, usually obtained at d=3 for the critical exponent of the correlation length, are explained by the fact that dependence L+L_0 with L_0>0 (L is the transversal size of the system) is interpreted as L^{1/\nu} with \nu>1. For dimensions d\ge 4, the modified scaling relations are derived; it demonstrates incorrectness of the conventional treatment of data for d=4 and d=5, but establishes the constructive procedure for such a treatment. Consequences for other variants of finite-size scaling are discussed.Comment: Latex, 23 pages, figures included; additional Fig.8 is added with high precision data by Kramer et a