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

TL;DR

This paper investigates a one-dimensional model with non-random long-range interactions and disorder, identifying a transition between localized and delocalized states depending on the interaction decay parameter.

Contribution

It introduces a model with non-random long-range interactions and analyzes the localization-delocalization transition using spectral statistics.

Findings

Transition occurs for 1<μ<3/2

All states localized at μ=3/2

Level and wave function statistics reveal the transition

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.