Three strongly correlated charged bosons in a one-dimensional harmonic trap: natural orbital occupancies

We study a one-dimensional system composed of three charged bosons confined in an external harmonic potential. More precisely, we investigate the ground-state correlation properties of the system, paying particular attention to the strong-interaction limit. We explain for the first time the nature of the degeneracies appearing in this limit in the spectrum of the reduced density matrix. An explicit representation of the asymptotic natural orbitals and their occupancies is given in terms of some integral equations.Comment: 6 pages, 4 figures, To appear in European Physical Journal

Single-particle-exact density functional theory

We introduce 'single-particle-exact density functional theory' (1pEx-DFT), a novel density functional approach that represents all single-particle contributions to the energy with exact functionals. Here, we parameterize interaction energy functionals by utilizing two new schemes for constructing density matrices from 'participation numbers' of the single-particle states of quantum many-body systems. These participation numbers play the role of the variational variables akin to the particle densities in standard orbital-free density functional theory. We minimize the total energies with the help of evolutionary algorithms and obtain ground-state energies that are typically accurate at the one-percent level for our proof-of-principle simulations that comprise interacting Fermi gases as well as the electronic structure of atoms and ions, with and without relativistic corrections. We thereby illustrate the ingredients and practical features of 1pEx-DFT and reveal its potential of becoming an accurate, scalable, and transferable technology for simulating mesoscopic quantum many-body systems.Comment: 32 pages, 6 figures, 4 table