title: N-density representability and the optimal transport limit of the Hohenberg-Kohn functional.
abstract: We derive and analyze a hierarchy of approximations to the strongly correlated limit of the Hohenberg-Kohn functional. These "density representability approximations" are obtained by first noting that in the strongly correlated limit, N-representability of the pair density reduces to the requirement that the pair density must come from a symmetric N-point density. One then relaxes this requirement to the existence of a representing symmetric k-point density with k < N. The approximate energy can be computed by simulating a fictitious k-electron system. We investigate the approximations by deriving analytically exact results for a 2-site model problem, and by incorporating them into a self-consistent Kohn-Sham calculation for small atoms. We find that the low order representability conditions already capture the main part of the correlations.
authors.affiliation: Mathematics Department, Technische Universität München, Garching bei München, Garching, 85748, Germany.
authors.forename: Gero
authors.initials: G
authors.lastname: Friesecke
authors.forename: Christian B
authors.initials: CB
authors.lastname: Mendl
authors.forename: Brendan
authors.initials: B
authors.lastname: Pass
authors.forename: Codina
authors.initials: C
authors.lastname: Cotar
authors.forename: Claudia
authors.initials: C
authors.lastname: Klüppelberg
mesh_terms: D011789:Quantum Theory