On the multifractal spectrum of the Fibonacci chain

We consider the multifractal properties of a quasiperiodic tight binding Hamiltonian where the hopping elements are arranged according to the Fibonacci chain. By using the trace map approach and an assumption relating the cycles of the trace map to the integrated density of states, it is shown that the maximal scaling of the spectrum does not always occur at the edges or the centre of the spectrum, which is confirmed by numerical simulations. A good description of the multifractal spectrum is obtained by applying the 3z -model which was recently developed for the Harper model.