Information-Length Scaling in a Generalized One-Dimensional Lloyd’s Model

We perform a detailed numerical study of the localization properties of the eigenfunctions of one-dimensional (1D) tight-binding wires with on-site disorder characterized by long-tailed distributions: For large ϵ, P ( ϵ ) ∼ 1 / ϵ 1 + α with α ∈ ( 0, 2 ]; where ϵ are the on-site random energies. Our model serves as a generalization of 1D Lloyd’s model, which corresponds to α = 1. In particular, we demonstrate that the information length β of the eigenfunctions follows the scaling law β = γ x / ( 1 + γ x ), with x = ξ / L and γ ≡ γ ( α ). Here, ξ is the eigenfunction localization length (that we extract from the scaling of Landauer’s conductance) and L is the wire length. We also report that for α = 2 the properties of the 1D Anderson model are effectively reproduced.

Abstract licence: CC BY

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