Comparison of higher-order level spacing ratios signatures localization-delocalization transitions in one-dimensional single-electron lattice systems

How to distinguish localized and delocalized states is a challenging and important problem in the theory of Anderson localization. For this reason, we explore energy-resolved average relative level spacing ratios < R-(k)> for a single electron in the one-dimensional uniform potential model, Anderson model, Aubry-Andre-Harper model and slowly varying potential model, respectively. The orders k = 1, 2 and 3 are considered. Numerical results show that < R-(1)> < < R-(2)> < < R-(3)> for delocalized states, while < R-(1)> is maximal for localized states. Therefore, level spacing ratios can be used as a fruitful index to monitor localization-delocalization transitions. (C) 2020 Elsevier B.V. All rights reserved.