Unusual scaling of the spectrum in a deterministic aperiodic tight-binding model

Local and global scaling properties of the integrated density of states of the tight-binding Rudin-Shapiro model are numerically derived by investigating the dependence of the bandwidths of its periodic approximants on the size of the unit cells. Scaling relations intermediate between the power and exponential laws are found for various values of the energy and amplitude of the on-site potential V. An analysis of the global properties of the spectrum performed in the case when V is equal to the hopping integral t points out its multifractal structure. Multifractal arguments together with earlier results concerning the nature of the wave functions indicate a pure point spectrum for V≥t, while for smaller values of the amplitude V the spectrum reveals a mixed character.