  We study many-body localization (MBL) for interacting one-dimensional lattice
fermions in random (Anderson) and quasiperiodic (Aubry-Andre) models, focusing
on the role of interaction range. We obtain the MBL quantum phase diagrams by
calculating the experimentally relevant inverse participation ratio (IPR) at
half-filling using exact diagonalization methods and extrapolating to the
infinite system size. For short-range interactions, our results produce in the
phase diagram a qualitative symmetry between weak and strong interaction
limits. For long-range interactions, no such symmetry exists as the strongly
interacting system is always many-body localized, independent of the effective
disorder strength, and the system is analogous to a pinned Wigner crystal. We
obtain various scaling exponents for the IPR, suggesting conditions for
different MBL regimes arising from interaction effects.
