Critical Level Statistics of the Fibonacci Model

Abstract

We numerically analyze spectral properties of the Fibonacci model which is a one-dimensional quasiperiodic system. We find that the energy levels of this model have the distribution of the band widths $w$ obeys $P_B(w)\sim w^α$ $(w\to 0)$ and $P_B(w) \sim e^{-βw}$ $(w\to\infty)$, the gap distribution $P_G(s)\sim s^{-δ}$ $(s\to 0)$ ($α,β,δ>0$) . We also compare the results with those of multi-scale Cantor sets. We find qualitative differences between the spectra of the Fibonacci model and the multi-scale Cantor sets.