paper

A fractional Anderson model

arXiv:2205.01268 · doi:10.1016/j.physleta.2022.128190

Abstract

We examine the interplay between disorder and fractionality in a one-dimensional tight-binding Anderson model. In the absence of disorder, we observe that the two lowest energy eigenvalues detach themselves from the bottom of the band, as fractionality is decreased, becoming completely degenerate at , with a common energy equal to a half bandwidth, . The remaining states become completely degenerate forming a flat band with energy equal to a bandwidth, . Thus, a gap is formed between the ground state and the band. In the presence of disorder and for a fixed disorder width, a decrease in reduces the width of the point spectrum while for a fixed , an increase in disorder increases the width of the spectrum. For all disorder widths, the average participation ratio decreases with showing a tendency towards localization. However, the average mean square displacement (MSD) shows a hump at low values, signaling the presence of a population of extended states, in agreement with what is found in long-range hopping models.

arXiv comment6 pages, 5 figures

References in corpus (14)