# Density functional theory ...

The basic ideas and major conceptual breakthroughs of density functional theory (DFT) are applicable to the many-body problem in general, regardless of the detailed form of the interactions or the specific physical context. For instance, DFT with an appropriate kinetic and interaction-energy functional would be applicable to the physics of strongly correlated Fermi systems that are usually described in the framework of parametrized lattice models (e.g., Hubbard, Anderson, etc.). It is our goal to apply the concepts of DFT to the lattice models describing strongly correlated fermions. Such a lattice density functional theory (LDFT) is a valuable many-body approach to many-body models and can also provide useful new insights relevant to ab initio calculations.

The interaction energy W[?] of the Hubbard model is investigated as a functional of the single-particle density matrix ?. W[?], which plays the central role in LDFT, can be determined exactly for some relevant reference systems in the framework of Levy’s constrained-search formulation by using sparse-matrix diagonalization or renormalization group numerical methods. Analyzing the functional dependence of W[?], and introducing an appropriate scaling within the domain of representability of ?, it is shown that W has a pseudo-universal behavior as a function of g_{ij }= (?ij - ??ij) / (?0ij - ??ij), where ?ij refers to the bond order between nearest neighbors, and ?0ij (??ij) to the corresponding limit of weak (strong) correlations. Simple and accurate approximations to W[?] have been inferred that allowed a variety of applications including 1D, 2D and 3D Hubbard models, dimerized chains, attractive interactions and spin polarized systems.