3 years ago

# Spectral Functions of One-Dimensional Systems with Correlated Disorder.

N. A. Khan, J. M. Viana Parente Lopes, J. P. Santos Pires, J. M. B. Lopes Dos Santos

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 disorder potential give rise to non-perturbative and universal spectral functions, 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 $\alpha\geq1$.

Publisher URL: http://arxiv.org/abs/1806.06584

DOI: arXiv:1806.06584v3

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