Some new routes to density functional theory

We showcase two alternative DFT formulations: Orbital-free density-potential functional theory (DPFT) and single-particle-exact density functional theory (1pEx-DFT). In DPFT the variational variables are both the density and an effective potential, with approximations built on the Wigner function formalism and a split-operator approach. For the purpose of this presentation, we focus on DPFT applications to 1D systems. In 1pEx-DFT we parameterize approximate interaction energy functionals by utilizing two new schemes for constructing density matrices from occupation numbers of the single-particle part of quantum many-body systems. These occupation numbers play the role of the variational variables akin to the particle densities in standard orbital-free DFT. We minimize the total energies with the help of evolutionary algorithms and obtain ground-state energies that are accurate at the one-percent level for our proof-of-principle 1pEx-simulations that comprise interacting Fermi gases in 1D as well as the electronic structure of atoms and ions.