Symmetry-broken local-density approximation for one-dimensional systems

TL;DR

This paper introduces a symmetry-broken local-density approximation (SBLDA) for one-dimensional systems, leveraging symmetry-broken Hartree-Fock energies to improve density-functional theory calculations.

Contribution

The authors develop a new SBLDA functional based on symmetry-broken Hartree-Fock energies for 1D systems, extending the traditional LDA approach.

Findings

SBLDA outperforms LDA in 1D atom and molecule calculations.

Symmetry breaking lowers Hartree-Fock energies at all densities.

Discussion on extending the approach to higher dimensions.

Abstract

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.