Monitoring the localization-delocalization transition within a 1D model with non-random long-range interaction

Abstract

We consider a two-parameter one-dimensional Hamiltonian with uncorrelated diagonal disorder and {\it non-random} long-range inter-site interaction $J_{mn}=J/|m-n{|}^{\mu }$. The model is critical at $1<\mu <3/2$ 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 ($\mu =3/2$) all states are localized.

4 pages, 5 figures