Interaction-energy functional for lattice density functional theory: Applications to one-, two-, and three-dimensional Hubbard models

摘要

The Hubbard model is investigated in the framework of lattice density functional theory (LDFT). The single-particle density matrix γ_(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[γ] 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 γ_(ij), including the crossover from weak to strong correlations. As examples of applications results are given for the ground-state euetgy, 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.