Density-potential functional theory for fermions in one dimension

We showcase the advantages of orbital-free density-potential functional theory (DPFT), a more flexible variant of Hohenberg-Kohn density functional theory. DPFT resolves the usual trouble with the gradient-expanded kinetic energy functional by facilitating systematic semiclassical approximations in terms of an effective potential energy that incorporates all interactions. With the aid of two systematic approximation schemes we demonstrate that DPFT is not only scalable, universally applicable in both position and momentum space, and allows kinetic and interaction energy to be approximated consistently, but can also compete with highly accurate, yet restricted, methods. As two- and three-dimensional geometries are extensively covered elsewhere, our focus here is on one-dimensional settings, with semiclassical observables systematically derived from both the Wigner function formalism and a split-operator approach. The high quality of our results for Fermi gases in Morse potentials invites the use of DPFT for describing more exotic systems, such as trapped large-spin fermion mixtures with contact or dipole-dipole interactions.