Localization-delocalization transition in a presence of correlated disorder: The random dimer model

TL;DR

This paper analyzes a one-dimensional dimer model with correlated disorder, confirming the existence of delocalized states at specific energies and deriving analytical expressions for the density of states and localization length.

Contribution

It provides an exact calculation of the localization length and density of states in the dimer model with correlated disorder, confirming delocalized states at critical energies.

Findings

Delocalized states exist at energies $E_c = \epsilon_{a,b}$ when $|\epsilon_a - \epsilon_b| \\leq 2$.

Analytic expressions for the density of states are derived and match numerical results.

Localization length indices are calculated at the critical energies.

Abstract

The one dimensional dimer model is investigated and the localization length calculated exactly. The presence of delocalized states at $E_c = \epsilon_{a,b}$ of two possible values of the chemical potential in case of $\mid\epsilon_a-\epsilon_b\mid \leq 2 $ is confirmed and the corresponding indices of the localization length were calculated. The singular integral equation connecting the density of states with the inverse localization length is solved and the analytic expression for the density of states compared with the numerical calculations.