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

A. V. Malyshev·V. A. Malyshev·F. Dominguez-Adame
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Abstract

We consider a two-parameter one-dimensional Hamiltonian with uncorrelated diagonal disorder and {\it non-random} long-range inter-site interaction $J_{mn}=J/|m-n|^μ$. 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.

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A. V. Malyshev, V. A. Malyshev, F. Dominguez-Adame. 2004-12-01. Monitoring the localization-delocalization transition within a 1D model with non-random long-range interaction. https://doi.org/10.1103/physrevb.70.172202

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