Scaling Properties of Localization Length in 1D Paired Correlated Binary Alloys of Finite Size

TL;DR

This paper investigates how the localization length in a 1D disordered binary alloy model scales with system size, revealing a derived law that relates to known models like Anderson and Lloyd, using transfer matrix and diagonalization methods.

Contribution

It introduces a new scaling law for localization length in 1D correlated binary alloys, connecting it to established random matrix and Anderson models.

Findings

Derived a scaling law for localization length in finite systems.

Showed the scaling behavior is related to uncorrelated band random matrix models.

Validated results using transfer matrix and Hamiltonian diagonalization.

Abstract

We study scaling properties of the localized eigenstates of the random dimer model in which pairs of local site energies are assigned at random in a one dimensional disordered tight-binding model. We use both the transfer matrix method and the direct diagonalization of the Hamiltonian in order to find how the localization length of a finite sample scales to the localization length of the infinite system. We derive the scaling law for the localization length and show it to be related to scaling behavior typical of uncorrelated Band Random Matrix, Anderson and Lloyd models.