Reduced Density Matrix Functional Theory for Bosons

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 γ 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[γ] for this N-boson Hubbard dimer and general Bogoliubov-approximated systems are determined. For Bose-Einstein condensates, the respective gradient forces are found to diverge, providing a comprehensive explanation for the absence of complete condensation in nature.

CL Benavides-Riveros, J Wolff, MAL Marques, and C Schilling, Phys. Rev. Lett. 124, 180603 (2020).