DENSITY-FUNCTIONAL THEORY ON A LATTICE - COMPARISON WITH EXACT NUMERICAL RESULTS FOR A MODEL WITH STRONGLY CORRELATED ELECTRONS

Most of the basic ideas of the density-functional theory (DFT) are sho wn to be unrelated to the fact that the particle density is used as th e basic variable. After presenting the general formalism and a simple example unrelated to densities, we discuss various approaches to densi ty-functional theory on a lattice. One has proven useful for the under standing of various fundamental issues of the DFT. The exact Kohn-Sham band gap and the band gap in the local-density approximation (LDA) ar e compared to the exact result for a one-dimensional model. As the int eracting homogeneous system can be solved exactly no further approxima tion is needed to formulate the LDA.