Anderson transition in low-dimensional disordered systems driven by nonrandom long-range hopping

TL;DR

This paper demonstrates that nonrandom long-range hopping can induce delocalized states in low-dimensional disordered systems, challenging the traditional single-parameter scaling hypothesis.

Contribution

It provides analytical and numerical evidence that long-range hopping causes delocalization in 1D and 2D Anderson models, which was previously thought impossible.

Findings

Extended states occur at band edges due to long-range hopping.

Delocalization results from size scaling differences in level spacing and disorder.

Numerical and supersymmetric methods confirm delocalization phenomena.

Abstract

The single-parameter scaling hypothesis predicts the absence of delocalized states for noninteracting quasiparticles in low-dimensional disordered systems. We show analytically and numerically that extended states may occur in the one- and two-dimensional Anderson model with a nonrandom hopping falling off as some power of the distance between sites. The different size scaling of the bare level spacing and the renormalized magnitude of the disorder seen by the quasiparticles finally results in the delocalization of states at one of the band edges of the quasiparticle energy spectrum. The delocalized nature of those eigenstates is investigated by numerical diagonalization of the Hamiltonian and by the supersymmetric method for disorder averaging, combined with a renormalization group analysis.