Existence of a metallic phase and upper bounds of the Hartree-Fock   energy in the homogeneous electron gas
  We consider the ground state of the homogeneous electron gas and we prove that a Hartree-Fock solution, motivated by previous simulations, has lower energy than the Fermi gas in the large density limit. This solution is a metallic phase : the density modulation corresponds to a partially occupied crystal (the number of sites is larger than the number of electrons). 
F. Delyon, M. Duneau, B. Bernu, M. Holzmann