We report a new approach to the study of electron spectral clustering and wave-function scaling in several one-dimensional quasiperiodic systems. The approach is based on renormalization-group ideas. We introduce a novel decimation technique which generates a simple physical picture of the electron spectral behavior and the nature of the wave functions. Our renormalization-group scheme is verified by the numerical computation of the probability density summed over the states belonging to the clusters and subclusters of the spectrum.

• Received 20 May 1986

DOI:https://doi.org/10.1103/PhysRevLett.57.2057