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

R. J. Magyar and K. Burke
Phys. Rev. A 70, 032508 – Published 21 September 2004; Erratum Phys. Rev. A 72, 029901 (2005)

Abstract

A density-functional theory is developed for fermions in one dimension, interacting via a δ 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.

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  • Received 4 February 2004

DOI:https://doi.org/10.1103/PhysRevA.70.032508

©2004 American Physical Society

Erratum

Authors & Affiliations

R. J. Magyar

  • Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, New Jersey 08854-8019, USA

K. Burke

  • Department of Chemistry and Chemical Biology, Rutgers University, 610 Taylor Road, Piscataway, New Jersey 08854-8019, USA

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Issue

Vol. 70, Iss. 3 — September 2004

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