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]).
Highlights
The kernel polynomial method (KPM) [1] is recognized as a valuable tool for calculating the physical properties of quantum systems and has been extensively studied in computational condensed-matter physics [2]
By devising a way to control finite size effects, and suitably take the thermodynamic limit, a delocalization transition of all eigenstates was proved to happen at α = 1 in the thermodynamic limit [12]
In order to validate our KPM estimates of ξ−1, we first addressed the numerical convergence of the localization length for the well-known uncorrelated Anderson model
Summary
The kernel polynomial method (KPM) [1] is recognized as a valuable tool for calculating the physical properties of quantum systems and has been extensively studied in computational condensed-matter physics [2]. In 1998, de Moura and Lyra [10] analyzed an 1D tightbinding model with spatially correlated on-site disorder having an algebraic power-spectrum, S (k) ∝ k−α, uncovering an unexpected insulator-to-metal transition as α = 2 is crossed from below, accompanied by the appearance of a mobility edge which separates extended states (near the band center) from localized ones. This model was revisited recently [12], having been shown to suffer from rather strong and tricky to handle finite-size effects over the entire parameter region α ∈ [0, ∞[.
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