Abstract
The interaction energy of the Hubbard model W[γ ] is investigated as a functional of the single-particle density matrix γ. W[γ ] plays a central role in the lattice density-functional theory of strongly correlated electrons. It is determined exactly in the framework of Levy's constrained-search formulation by using sparse-matrix diagonalization or renormalization-group numerical methods. Results for representative examples of one-dimensional chains, small clusters, spin-polarized systems, and attractive interactions are presented. The functional dependence of W[γ ] is analysed. Introducing an appropriate scaling it is shown that W has pseudo-universal behaviour as a function of , where γ ij refers to the bond order between nearest neighbours and () refers to the corresponding limit of weak (strong) correlations. Simple and accurate approximations to W can be inferred for general applications.
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