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Real materials always contain, to some extent, randomness in the form ofdefects or irregularities. It is known since the seminal work of Anderson thatrandomness can drive a metallic phase to an insulating one, and the mechanismresponsible for this transition is intrinsically different from the one of theinteraction-induced transitions discovered by Mott. Lattice Hamiltonians, withtheir conceptual and computational advantages, permitted to investigate broadlythe interplay of both mechanisms. However, a clear understanding of thedifferences (or not) with their real-space counterparts is lacking, especiallyin the presence of long-range Coulomb interactions. This work aims at sheddinglight on this challenging question by investigating a real-spaceone-dimensional model of interacting electrons in the presence of a disorderedpotential. The transition between delocalized and localized phases arecharacterized using two different indicators, namely the single-particleoccupation entropy and the position-space information entropy. In addition, theperformance of density functional approximations to reproduce the exactground-state densities of this many-body localization model are gauged.

Real space Mott-Anderson electron localization with long-range interactions: exact and approximate descriptions