A density-functional theory (DFT) of lattice fermion models is presented, which uses the single-particle density matrix ${\gamma }_{\mathrm{ij}}$ as basic variable. A simple, explicit approximation to the interaction-energy functional $W\left[\gamma \right]$ of the Hubbard model is derived from exact dimer results, scaling properties of $W\left[\gamma \right]$ and known limits. Systematic tests on the one-dimensional chain show a remarkable agreement with the Bethe-ansatz exact solution for all interaction regimes and band fillings. New results are obtained for the ground-state energy and charge-excitation gap in two dimensions. A successful description of strong electron correlations within DFT is achieved.

• Received 1 May 2002

DOI:https://doi.org/10.1103/PhysRevB.66.155118