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 [Formula: see text] , [Formula: see text] with [Formula: see text]; where [Formula: see text] are the on-site random energies. Our model serves as a generalization of 1D Lloyd’s model, which corresponds to [Formula: see text]. In particular, we demonstrate that the information length [Formula: see text] of the eigenfunctions follows the scaling law [Formula: see text] , with [Formula: see text] and [Formula: see text]. Here, [Formula: see text] 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 [Formula: see text] the properties of the 1D Anderson model are effectively reproduced.