Localization properties of a one-dimensional tight-binding model with nonrandom long-range intersite interactions

Abstract

We perform both analytical and numerical studies of the one-dimensional tight-binding Hamiltonian with stochastic uncorrelated on-site energies and nonfluctuating long-range hopping integrals J(mn) = J/vertical bar m-n vertical bar(mu). It was argued recently [A. Rodriguez et al., J. Phys. A 33, L161 (2000)] that this model reveals a localization-delocalization transition with respect to the disorder magnitude provided 1 < mu < 3/2. The transition occurs at one of the band edges (the upper one for J > 0 and the lower one for J < 0). The states at the other band edge are always localized, which hints at the existence of a single mobility edge. We analyze the mobility edge and show that, although the number of delocalized states tends to infinity, they form a set of null measure in the thermodynamic limit, i.e., the mobility edge tends to the band edge. The critical magnitude of disorder for the band edge states is computed versus the interaction exponent mu by making use of the conjecture on the universality of the normalized participation number distribution at the transition.