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.