The Hartree-Fock ground state of high-density jellium

The usual textbook paramagnetic solution is not the Hartree-Fock (HF) ground state of the uniform electron gas (jellium). Overhauser\footnote{A. W. Overhauser, Phys. Rev. 128, 1437 (1962).} showed that, for example, a spin-density-wave state would have lower energy, even at the high density limit. We obtain numerically the unrestricted Hartree-Fock (uHF) ground state of 3-D jellium, using a projection technique starting from random initial states. Supercells with around 1000 electrons are studied, with a range of $r_s$ values at high densities. We study the energetics of the uHF ground state, and discuss its real- and ${\mathbf k}$-space structures.