Density-matrix functional study of the Hubbard model on one- and two-dimensional bipartite lattices

The inhomogeneous Hubbard model is investigated in one and two dimensions by using lattice density-functional theory (LDFT). The ground-state energy $E=T+W$ is regarded as a functional of the single-particle density matrix γ, where T[γ] represents the kinetic and crystal-field energy, and W[γ] the interaction energy. Besides the known functional T[γ] we propose a simple scaling approximation to the interaction energy W[γ], which is based on exact results for the Hubbard dimer and on a scaling hypothesis within the domain of representability of γ. As applications we consider the Hubbard model on one- and two-dimensional bipartite lattices. Several ground-state properties are determined including the kinetic and Coulomb energy, density distribution, nearest-neighbor bond order, and charge gap. Comparison with exact Lanczos diagonalizations shows that LDFT with the scaled dimer approximation to W[γ] yields a quite accurate description of the interplay between correlations and charge redistributions, from weak to strong coupling regimes, and for all band fillings. Goals and limitations of the present approach are discussed.