Interaction-energy functional of the Hubbard model: Local formulation and application to low-dimensional lattices

The interaction energy $W[\ensuremath{\gamma}]$ of the Hubbard model is regarded as a functional of the single-particle density matrix $\ensuremath{\gamma}$ in the framework of lattice density-functional theory. The local character of the Hubbard interaction is exploited to express $W$ as a sum of local contributions ${\ensuremath{\omega}}_i[\ensuremath{\gamma}]$, for which a simple semilocal scaling approximation is proposed. The method is applied to the ionic Hubbard model on one- and two-dimensional lattices with homogeneous and inhomogeneous Coulomb repulsions. Results are given for the kinetic and Coulomb energies, interatomic charge transfers, local magnetic moments, and charge gaps. Goals and limitations of the functional are discussed by comparison with exact results.