The exact strong-interaction limit of the Hohenberg-Kohn energy density functional can be used to construct an approximation for the exchange-correlation term of the Kohn-Sham approach that is able to capture the features of the strongly-correlated regime without breaking the spin or other symmetry. The resulting exchange-correlation potential has ``bumps'' (or barriers) that give rise to charge localization in the low-density limit and that are a well-known key feature of the exact Kohn-Sham potential for strongly-correlated systems. I will discuss the general features of this approach, with an illustration for the study of strongly correlated quantum wires and quantum dots, as well as negative ions. The generalization to open systems will be also presented, paying particular attention to the derivative discontinuity of the exchange-correlation energy at integer particle numbers. Perspectives on how to extend the approach to more general chemical and physical systems will be also discussed, highlighting the formal connection with optimal transport (or mass transportation theory) problems.
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