Temporal density fluctuations and Renyi entropy through the many-body localization crossover

We investigate the effects of electron-electron interactions in disordered one dimensional Anderson insulators. Our observables are the exponents characterizing the temporal fluctuations of the density, as well as the second Renyi entropy, with a focus on their dependency on the disorder strength W . As it turns out, these observables lend themselves to computational (and experimental) studies, because the corresponding power laws can be extrapolated into the thermodynamic limit even within the range of numerically accessible system sizes. We find a characteristic behavior where both the exponents grow as logarithm of the single particle localization length. We interpret our finding as evidence that the dynamically active Hilbert space volume exhibits a multifractal substructure.