Density functional theory in one-dimension for contact-interacting fermions

TL;DR

This paper develops a density functional theory for one-dimensional contact-interacting fermions, demonstrating that local approximations work well and accurately calculating ground-state energies for model systems.

Contribution

It introduces a local density approximation for correlation in 1D contact-interacting fermions using perturbation theory and Bethe-Ansatz, with applications to finite systems.

Findings

Local exchange energy is a functional of density

Local density approximation for correlation is highly accurate

Ground-state energies for model systems match expected results

Abstract

A density functional theory is developed for fermions in one dimension, interacting via a delta-function. Such systems provide a natural testing ground for questions of principle, as the local density approximation should work well for short-ranged interactions. The exact-exchange contribution to the total energy is a local functional of the density. A local density approximation for correlation is obtained using perturbation theory and Bethe-Ansatz results for the one-dimensional contact-interacting uniform Fermi gas. The ground-state energies are calculated for two finite systems, the analogs of Helium and of Hooke's atom. The local approximation is shown to be excellent, as expected.