Renormalization approach to quasiperiodic tight binding models

Tight binding models such as the Harper equation exhibiting the localization transition are studied using a nonperturbative renormalization method. The self-similarity underlying the fractal wave function is described by an infinite set of universal scaling ratios. Our studies confirm the existence of a fat critical phase in perturbed Harper models describing quantum spin chains and shows the existence of two new universality classes. Furthermore, the decimation scheme proposed here provides a new method for finding the minimum and the maximum energy eigenvalues up to machine precision.