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Benavides-Riveros, Carlos L.; Wolff, Jakob; Marques, Miguel A. L.; Schilling, Christian (2020): Reduced Density Matrix Functional Theory for Bosons. In: Physical Review Letters, Vol. 124, No. 18, 180603
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Based on a generalization of Hohenberg-Kohn's theorem, we propose a ground state theory for bosonic quantum systems. Since it involves the one-particle reduced density matrix gamma as a variable but still recovers quantum correlations in an exact way it is particularly well suited for the accurate description of Bose-Einstein condensates. As a proof of principle we study the building block of optical lattices. The solution of the underlying v-representability problem is found and its peculiar form identifies the constrained search formalism as the ideal starting point for constructing accurate functional approximations: The exact functionals F[gamma] for this N-boson Hubbard dimer and general Bogoliubov-approximated systems are determined. For Bose-Einstein condensates with N-BEC approximate to N condensed bosons, the respective gradient forces are found to diverge, del F-gamma proportional to 1/root 1-N-BEC/N providing a comprehensive explanation for the absence of complete condensation in nature.