2018/06/30 by Niaz Ali Khan, N. A. Khan, J. M. Viana Parente Lopes +2 · 10 citations
Mathematics · Physics and Astronomy · #Algebraic number #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Function (biology) #Kernel (algebra) #Lattice (music) #Limit (mathematics) #Mathematical analysis #Mathematics #Physics #Physics of Superconductivity and Magnetism #Polynomial #Pure mathematics #Quantum and electron transport phenomena #Quantum mechanics #Spectral density #Spectral function #Statistical physics #cond-mat.dis-nn
paper · pdf · doi:10.1088/1361-648x/ab03ad
published in Journal of Physics Condensed Matter 31(17), 175501 (IOP Publishing) · 27 Pages with 10 Figures
arxiv created 2019/01/31 · openalex publication_date 2019/01/31 · arxiv updated 2019/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the spectral function of Bloch states in a 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 [Formula: see text] 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, [Formula: see text] [Formula: see text], we show that the spectral function is not self-averaging for [Formula: see text].