Multifractal wave functions on a Fibonacci lattice

Abstract

Wave functions on a Fibonacci lattice are analyzed from the multifractal point of view. An entropy function [f(\ensuremath{\alpha})] which represents the distribution of a particle probability density is obtained exactly for the state at the center of the spectrum. Numerical calculations for other states are also presented. A finite-size scaling analysis shows that the ordered critical wave functions are multifractals.