Numerical-Scaling Study of the Statistics of Energy Levels at the Anderson Transition

Abstract

The statistical properties of the energy spectra of the Anderson Hamiltonian for random systems are numerically investigated near the disorder-induced metal-insulator transition. The level spacing distribution, the level density correlation function and the spectral form-factor are shown to be size-invariant at the critical point. They exhibit a crossover from the critical orthogonal to the critical unitary ensembles, which is controlled by the magnetic flux. One-parameter finite size scaling of the level statistics is used to detect with high precision the critical parameters: the critical exponent and the disorder dependence of the correlation length.