Abstract
A density-functional theory is developed for fermions in one dimension, interacting via a function. Such systems provide a natural testing ground for questions of principle, as the local-density approximation should be highly accurate since for this interaction type the exchange contribution to the local-density approximation is intrinsically self-interaction-free. 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-density approximation is shown to be excellent as expected.
- Received 4 February 2004
DOI:https://doi.org/10.1103/PhysRevA.70.032508
©2004 American Physical Society