Multifractal Properties of Wave Functions for One-Dimensional Systems with an Incommensurate Potential

Abstract

One-dimensional (tight-binding) Hamiltonians with an incommensurate potential give rise to extended, localized and critical wave functions depending on the amplitude of the potential. We have performed a multifractal analysis of these wave functions that shows: a) exactly at the critical point all wave functions show multifractal fluctuations extending to all length scales, b) localized states manifest multifractality up to the localization length, c) extended states also manifest multifractality up to the correlation length. These results manifest strict analogies with the scaling and crossover properties of percolation.