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Kohn-Sham density functional theory for quantum wires in arbitrary correlation regimes

We use the exact strong-interaction limit of the Hohenberg-Kohn energy density functional to construct an approximation for the exchange-correlation term of the Kohn-Sham approach. The resulting exchange-correlation potential is able to capture the features of the strongly-correlated regime without breaking the spin or any other symmetry. In particular, it shows "bumps" (or barriers) that give rise to charge localization at low densities and that are a well-known key feature of the exact Kohn-Sham potential for strongly-correlated systems. Here we illustrate this approach for the study of both weakly and strongly correlated model quantum wires, comparing our results with those obtained with the configuration interaction method and with the usual Kohn-Sham local density approximation.