Abstract
The attractive Hubbard model is investigated in the framework of lattice density-functional theory (LDFT).The ground-state energy E = T + W is regarded as a functional of the single-particle density matrix γij withrespect to the lattice sites, where T [γ ] represents the kinetic and crystal-field energies and W[γ ] the interactionenergy. Aside from the exactly known functional T [γ ], we propose a simple scaling approximation to W[γ ],which is based on exact analytic results for the attractive Hubbard dimer and on a scaling hypothesis withinthe domain of representability of γ . As applications, we consider one-, two-, and three-dimensional finite andextended bipartite lattices having homogeneous or alternating onsite energy levels. In addition, the Bethe lattice isinvestigated as a function of coordination number. Results are given for the kinetic, Coulomb, and total energies,as well as for the density distribution γii , nearest-neighbor bond order γij , and pairing energy �Ep, as a functionof the interaction strength |U|/t, onsite potential ε/t , and band filling n = Ne/Na . Remarkable even-odd andsuper-even oscillations of �Ep are observed in finite rings as a function of band filling. Comparison with exactLanczos diagonalizations and density-matrix renormalization-group calculations shows that LDFT yields a verygood quantitative description of the properties of the model in the complete parameter range, thus providing asignificant improvement over the mean-field approaches. Goals and limitations of the method are discussed.