Schonhammer K., Gunnarsson O., Noack R. M.
Most of the basic ideas of the density-functional theory (DFT) are shown to be unrelated to the fact that the particle density is used as the basic variable. After presenting the general formalism and a simple example unrelated to densities, we discuss various approaches to density-functional theory on a lattice. One has proven useful for the understanding of various fundamental issues of the DFT. The exact Kohn-Sham band gap and the band gap in the local-density approximation (LDA) are compared to the exact result for a one-dimensional model. As the interacting homogeneous system can be solved exactly no further approximation is needed to formulate the LDA.
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