Multifractal properties of the wave functions of the square-lattice tight-binding model with next-nearest-neighbor hopping in a magnetic field

We have used multifractal analysis for the wave functions to study the universality of the scaling properties of Harper's equation, the equation for a particle moving on a tight-binding square lattice in the presence of a gauge field, when coupling to next-nearest sites are added. We find that the properties of the wave functions are consistent with those of the spectra obtained by Han et al. [Phys. Rev. B 50, 11 365 (1994)]. The phase diagram consists of the three regions where the wave functions are localized, extended and critical, respectively.