Universal role of quantum uncertainty in Anderson metal–insulator transition

Abstract

We explore quantum uncertainty, based on Wigner–Yanase skew information, in various one-dimensional single-electron wave functions. For the power-law function and eigenfunctions in the Aubry–André model, the electronic localization properties are well-defined. For them, we find that quantum uncertainty is relatively small and large for delocalized and localized states, respectively. And around the transition points, the first-order derivative of the quantum uncertainty exhibits singular behavior. All these characters can be used as signatures of the transition from a delocalized phase to a localized one. With this criterion, we also study the quantum uncertainty in one-dimensional disorder system with long-range correlated potential. The results show that the first-order derivative of spectrum-averaged quantum uncertainty is minimal at a certain correlation exponent αm for a finite system, and has perfect finite-size scaling behaviors around αm. By extrapolating αm, the threshold value αc≃1.56±0.02 is obtained for the infinite system. Thus we give another perspective and propose a consistent interpretation for the discrepancies about localization property in the long-range correlated potential model. These results suggest that the quantum uncertainty can provide us with a new physical intuition to the localization transition in these models.