  Within density-functional theory, the local-density approximation (LDA)
correlation functional is typically built by fitting the difference between the
near-exact and Hartree-Fock (HF) energies of the uniform electron gas (UEG),
together with analytic perturbative results from the high- and low-density
regimes. Near-exact energies are obtained by performing accurate diffusion
Monte Carlo calculations, while HF energies are usually assumed to be the Fermi
fluid HF energy. However, it has been known since the seminal work of
Overhauser that one can obtain lower, symmetry-broken (SB) HF energies at any
density. Here, we have computed the SBHF energies of the one-dimensional UEG
and constructed a SB version of the LDA (SBLDA) from the results. We compare
the performance of the LDA and SBLDA functionals when applied to
one-dimensional systems, including atoms and molecules. Generalization to
higher dimensions is also discussed.
