Density Functional Theory for Strongly-Interacting Electrons

Although Kohn-Sham (KS) density functional theory (DFT) is an exact theory, able in principle to describe any interacting N-electron system in terms of the non-interacting Kohn-Sham model, in practice only approximate expressions for the exchange-correlation term are available. For decades, a large number of such approximations have been developed, proving enormously successful and accurate for applications in many different fields. However, there still remain important sit- uations, of both fundamental and practical interest, for which all the commonly employed exchange-correlation functionals fail to provide an accurate description. The paradigm of such scenarios are those systems in which the electronic correla- tion plays the most important role. In this chapter, we show how the knowledge on the strong-interaction limit of DFT, recently formulated within the so-called strictly-correlated-electrons (SCE) formalism, can be imported into the Kohn-Sham approach and used to build approximations for the exchange-correlation energy that are able to reproduce key features of the strongly-correlated regime. We report results of the first applications of this "KS SCE'' DFT approach on quasi-one-dimensional systems, showing its very good accuracy in the limits of both vanishing and infinite correlation. In the last part of the chapter, we propose a generalization of the approach for its application to more general systems.