Interplay of off-diagonal random disorder and quasiperiodic potential in a one-dimensional Aubry-André model

Abstract

We study the interplay of a random off-diagonal (hopping) disorder with the on-site quasiperiodic potential in a one-dimensional Aubry-André (AA) chain. There is evidence for the absence of delocalized states, at least for a finite lattice, in presence of a weak disorder, thereby removing the possibility of a sharp transition from extended to localized regime. This renders testimony for the presence of a weakly localized phase which we denote as the "critical" phase. We also evaluate whether the random disorder helps or hinders the quasiperiodic term on either side of the "duality" point in inducing a complete localization phenomenon via computing a few relevant quantities, such as the inverse participation ratio (IPR), which estimates the extent of localization, and an extensive multifractal analysis to assess the nature of the disordered states. We observe that a weak random disorder corresponding to the strength of the quasiperiodic term above the critical value (λc = 2) is more efficient in inducing the localization phenomenon as compared to a large disorder below the critical value. We also find that a large disorder is found to compete with the quasiperiodic term beyond its critical value in localizing the eigenstates, while it aids at strengths below the critical value, both of which are intuitively conceivable. Such a differential behavior of the random off-diagonal disorder and its interplay with the quasiperiodic potential albeit expected, have not been reported earlier in the literature. With regard to the multifractal analysis, we ascertain the nature of the critical phase and comment on the fractal dimension, the critical exponents and occurrence of rare events.