Monitoring the localization-delocalization transition within a one-dimensional model with nonrandom long-range interaction

Abstract

We consider a two-parameter one-dimensional Hamiltonian with uncorrelated diagonal disorder and non-random long-range intersite interaction Jmn = J/|m-n|μ.. The model is critical at 1 < μ < 3/2 and reveals the localization-delocalization transition with respect to the disorder magnitude. To detect the transition we analyze level and wave function statistics. It is demonstrated also that in the marginal case (μ = 3/2) all states are localized.