Numerical studies of the one-dimensional random Anderson model

Abstract

Results are reported of exact numerical calculations of the eigenvalues and eigenstates of a one-dimensional random Anderson model. The complete set of eigenstates is obtained for lattices containing up to 500 sites, and the degree of localization of the states is examined as a function of the eigenvalue of the state, the degree of randomness, and the number of lattice sites. Curves of degree of localization versus eigenvalue appear to show a central 'band' of extended states separated by a 'critical energy' from a 'tail' of localized states. However it is shown that the separation is only apparent, in that it is caused by the spatial extent of the eigenstates becoming comparable with the size of the finite lattice.