@article{6649,
  abstract     = {While Hartree–Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In this paper we start from the Hartree–Fock state given by plane waves and introduce collective particle–hole pair excitations. These pairs can be approximately described by a bosonic quadratic Hamiltonian. We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann–Brueckner–type upper bound to the ground state energy. Our result justifies the random-phase approximation in the mean-field scaling regime, for repulsive, regular interaction potentials.
},
  author       = {Benedikter, Niels P and Nam, Phan Thành and Porta, Marcello and Schlein, Benjamin and Seiringer, Robert},
  issn         = {1432-0916},
  journal      = {Communications in Mathematical Physics},
  pages        = {2097–2150},
  publisher    = {Springer Nature},
  title        = {{Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime}},
  doi          = {10.1007/s00220-019-03505-5},
  volume       = {374},
  year         = {2020},
}