BenavidesRiveros, 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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Abstract
Based on a generalization of HohenbergKohn's theorem, we propose a ground state theory for bosonic quantum systems. Since it involves the oneparticle 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 BoseEinstein condensates. As a proof of principle we study the building block of optical lattices. The solution of the underlying vrepresentability 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 Nboson Hubbard dimer and general Bogoliubovapproximated systems are determined. For BoseEinstein condensates with NBEC approximate to N condensed bosons, the respective gradient forces are found to diverge, del Fgamma proportional to 1/root 1NBEC/N providing a comprehensive explanation for the absence of complete condensation in nature.