Critical properties of Harper's equation on a triangular lattice

We numerically study a one-dimensional quasiperiodic system obtained from two-dimensional electrons on the triangular lattice in a uniform magnetic field aided by the multifractal method. The phase diagram consists of three phases: two metallic phases and one insulating phase separated by critical lines with one bicritical point. Novel transitions between the two metallic phases exist. We examine the spectra and wave functions along the critical lines. Several types of level statistics are obtained. Distributions of the bandwidths P-B(w) near the origin (in the tail) have the form P-B(w)similar to w(beta) [P-B(w)similar to e(-gamma w)] (beta,gamma > 0), while at the bicritical point P-B(w)similar to w(-beta') (beta(')>0). Also distributions of the level spacings follow an inverse power law P-G(s)similar to s(-delta) (delta > 0). For the wave functions at the centers of spectra, scaling exponents and their distribution in terms of the alpha-f(alpha) curve are obtained. The results in the vicinity of critical points are consistent with the phase diagram.