Probing the Global Delocalization Transition in the de Moura-Lyra Model with the Kernel Polynomial Method

¹ Centro de Física das Universidades do Minho e Porto Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, 4169-007 Porto, Portugal

^* Corresponding author: nak@fc.up.pt
^** Corresponding author: up201201453@fc.up.pt

Published online: 16 April 2020

Abstract

In this paper, we report numerical calculations of the localization length in a non-interacting one-dimensional tight-binding model at zero tem¬perature, holding a correlated disorder model with an algebraic power-spectrum (de Moura-Lyra model). Our calculations were based on a Kernel Polynomial implementation of the Thouless formula for the inverse localization length of a general nearest-neighbor 1D tight-binding model with open boundaries. Our results confirm the delocalization of all eigenstates in de Moura-Lyra model for α > 1 and a localization length which diverges as ξ ∝ (1 – α)^–1 for α → 1^–, at all energies in the weak disorder limit (as previously seen in [12]).