Rényi entropy and the multifractal spectra of systems near the localization transition

Abstract

We show that the R\'enyi entropies of single particle, critical wave functions for disordered systems contain information about the multifractal spectrum. It is shown for moments of the R\'enyi entropy, ${S}_{n}$, where $|n|<1$, it is possible to extract universal information about the multifractility of such systems. This is shown through a generic calculation and then illustrated through two example models. We find good agreement between our analytic formula and numerical simulations of the two test models. Our formalism is easily extendable to generic noninteracting fermion models. It is also suggested that recent experimental advances in measuring the multifractal spectrum might allow some moments of the R\'enyi entropy to be measured.