Existence of a metallic phase and upper bounds of the Hartree-Fock energy in the homogeneous electron gas

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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).
12 pages, 2 figures

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