Fractal analysis of wave functions at the localization-delocalization transition in a disordered quantum small-world-network model

Localization-delocalization transition in disordered quantum small-world network model is confirmed by using the numerical multifractal analysis of the wave functions at the critical point. A linear relation between the numerator and the denominator of the parametric representation for the singularity spectrum of the wave functions near the transition point is obtained, serving as a criterion of the critical behavior. The singularity spectrum $f\left(\alpha \right)$ at the critical point is size independent. The variation of the fractal intensity ${\alpha }_q$ at $q=0\mathrm{}$ and $q=1\mathrm{}$ in changing the rewiring probability p reveals the phase transition as shown in the level statistics on the same model.