Localization-delocalization transition of electron states in a disordered quantum small-world network

We investigate the localization behavior of electrons in a random lattice that is constructed from a quasi-one-dimensional chain with a large coordinate number Z and rewired bonds, resembling the small-world network proposed recently, but with site-energy disorder and quantum links instead of classical ones. The random rewiring of bonds in the chain with large Z enhances both the topological disorder and the effective dimensionality. From the competition between disorder and dimensionality enhancement a transition from localization to delocalization is found by using the level statistics method. The critical value of the rewiring rate for this transition is determined numerically. We obtain a universal critical integrated distribution of level spacing s in the form $I_{p_c}\mathrm{}\left(s\right)\mathrm{}\propto \exp \left(-A_c{s}^{\alpha }\right),$ with $A_c\simeq 1.50$ and $\alpha \simeq \mathrm{1.0.}$ This reveals the possible existence of metal-insulator transition in materials with chains as the backbones.