Detecting delocalization-localization transitions from full density distributions

Characterizing the delocalization transition in closed quantum systems with a many-body localized phase is key open question field of nonequilibrium physics. We exploit that localization particles as realized Anderson and standard (MBL) implies Fock-space single-particle basis sets characterized by real-space index. Using recently introduced quantitative measure for computed from density distributions, occupation distance, we systematically study its scaling behavior across delocalozation transitions identify critical points collapses numerical data. Excellent agreement literature results found disorder strengths noninteracting fermions, such one-dimensional Aubry-Andr\'e three-dimensional model. observe distinctively different case interacting fermions random consistent Kosterlitz-Thouless transition. Finally, use our to extract point function filling fermions.