Abstract
Connecting electron localization properties with energy spectra statistics is a fundamental issue in condensed matter physics. Inspired by the circular data analysis and the Kuramoto order parameter developed in classical systems, the sequence of the ratio of consecutive level spacing {rm} is mapped to a set of unit vectors {eˆm} distributed on a unit circle. A quantity Ir=Z2M is proposed to measure the randomness of eigenvalue spectra of quantum systems, where M is the sequence length and Z=1M|∑m=1Meˆm|. For the other sequence {Rm} related to {rm}, a similar quantity IR is also defined. It is found that 〈Ir〉>〈IR〉 for localized phases and 〈Ir〉<〈IR〉 for delocalized ones, which can serve as a fruitful index to monitor Anderson transition.
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