The Hubbard model is investigated in the framework of lattice density functional theory (LDFT). The single-particle density matrix ${\gamma }_{\mathrm{ij}}$ with respect to the lattice sites is considered as the basic variable of the many-body problem. A new approximation to the interaction-energy functional $W\left[\gamma \right]$ is proposed which is based on its scaling properties and which recovers exactly the limit of strong electron correlations at half-band filling. In this way, a more accurate description of W is obtained throughout the domain of representability of ${\gamma }_{\mathrm{ij}},$ including the crossover from weak to strong correlations. As examples of applications results are given for the ground-state energy, charge-excitation gap, and charge susceptibility of the Hubbard model in one-, two-, and three-dimensional lattices. The performance of the method is demonstrated by comparison with available exact solutions, with numerical calculations, and with LDFT using a simpler dimer ansatz for W. Goals and limitations of the different approximations are discussed.

• Received 9 September 2003

DOI:https://doi.org/10.1103/PhysRevB.69.085101