Solving lattice density functionals close to the Mott regime

We study a lattice version of the local density approximation (LDA) based on Bethe ansatz (BALDA). Contrary to what happens in density functional theory in the continuum and despite its name, BALDA displays some very nonlocal features and it has a discontinuous functional derivative. The same features prevent the convergence of the self-consistent Kohn-Sham cycle thus hindering the study of BALDA solutions close to a Mott phase or in the Coulomb blockade regime. Here, we propose a numerical approach which, differently from previous works, does not introduce ad hoc parameters to smear out the singularity. Our results are relevant for all lattice models where BALDA is applied ranging from Kondo systems to harmonically trapped Hubbard fermions. As an example, we apply the method to the study of a one-dimensional lattice model with Hubbard interaction and a staggered potential which can be driven from an ionic to a Mott-insulating state. In the Mott regime, the presence of a vacuum allows us to calculate the different contribution to the gap and to highlight an ultranonlocality of BALDA. © 2014 American Physical Society.