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 densityfunctional theory (LDFT). The single-particle density matrix $\gamma_{ij}$ withrespect the lattice sites is considered as the basic variable of the many-bodyproblem. A new approximation to the interaction-energy functional $W[\gamma]$is proposed which is based on its scaling properties and which recovers exactlythe limit of strong electron correlations at half-band filling. In this way, amore accurate description of $W$ is obtained throughout the domain ofrepresentability of $\gamma_{ij}$, including the crossover from weak to strongcorrelations. As examples of applications results are given for theground-state energy, charge-excitation gap, and charge susceptibility of theHubbard model in one-, two-, and three-dimensional lattices. The performance ofthe method is demonstrated by comparison with available exact solutions, withnumerical calculations, and with LDFT using a simpler dimer ansatz for $W$.Goals and limitations of the different approximations are discussed.