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

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

2003-03-05

arxiv.org/abs/cond-mat/0303092v4

Phys. Rev. B 70, 172202 (2004)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 5 figures

Scientific paper

10.1103/PhysRevB.70.172202

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.

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