Spectral Functions of One-Dimensional Systems with Correlated Disorder

TL;DR

This paper studies how correlated disorder affects the spectral functions of one-dimensional tight-binding systems, using numerical and analytical methods to reveal non-perturbative effects and non-self-averaging behavior at certain disorder correlations.

Contribution

It provides the first combined numerical and analytical analysis of spectral functions in 1D systems with correlated disorder, highlighting non-perturbative effects and non-self-averaging phenomena.

Findings

Spectral functions mirror the probability distribution of on-site energies.

Spatial correlations induce non-perturbative spectral features.

Spectral functions are not self-averaging for power-spectrum exponent $\geq1$.

Abstract

We investigate the spectral function of Bloch states in an one-dimensional tight-binding non-interacting chain with two different models of static correlated disorder, at zero temperature. We report numerical calculations of the single-particle spectral function based on the Kernel Polynomial Method, which has an $\mathcal{O}(N)$ computational complexity. These results are then confirmed by analytical calculations, where precise conditions were obtained for the appearance of a classical limit in a single-band lattice system. Spatial correlations in the disordered potential give rise to non-perturbative spectral functions shaped as the probability distribution of the random on-site energies, even at low disorder strengths. In the case of disordered potentials with an algebraic power-spectrum, $\propto\left|k\right|^{-\alpha}$, we show that the spectral function is not self-averaging for $\alpha\geq1$.