Spectral Functions of One-Dimensional Systems with Correlated Disorder

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 $\alpha \ge 1$.

arXiv comment27 Pages with 10 Figures

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Cited by in corpus (5)

• Anomalous correlation-induced dynamical phase transitions
• Global Delocalization Transition in the de Moura-Lyra Model
• Probing Band-center Anomaly with the Kernel Polynomial Method
• Bound states in one-dimensional systems with colored noise
• Single impurity-induced localization transitions in electronic systems