Critical Quantum Chaos and the One-Dimensional Harper Model

We obtain numerically a scale-invariant distribution of the bandwidths $S$ for the critical Harper model, which is closely described by a semi-Poisson $P\left(S\right)=4S\exp (-2S)$ curve. After a suitable unfolding of spectra, derived from different boundary conditions, a semi-Poisson level spacing distribution and a sub-Poisson linear number variance are deduced from the bandwidth distribution. The obtained results support possible universality of the critical spectral statistics and suggest its connection to spectral multifractality.