article published yes Niels P Benedikter author 3DE6C32A-F248-11E8-B48F-1D18A9856A870000-0002-1071-6091 Phan Thành Nam author Marcello Porta author Benjamin Schlein author Robert Seiringer author 4AFD0470-F248-11E8-B48F-1D18A9856A870000-0002-6781-0521 RoSe department FWF Open Access Fund project Structure of the Excitation Spectrum for Many-Body Quantum Systems project Analysis of quantum many-body systems project 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. https://research-explorer.ista.ac.at/download/6649/6668/2019_CommMathPhysics_Benedikter.pdf application/pdfno https://creativecommons.org/licenses/by/4.0/ Springer Nature2020 eng 0010-3616 1432-0916 1809.01902 00052791070001910.1007/s00220-019-03505-5 3742097–2150 N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Communications in Mathematical Physics 374 (2020) 2097–2150. Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. <i>Communications in Mathematical Physics</i>. 2020;374:2097–2150. doi:<a href="https://doi.org/10.1007/s00220-019-03505-5">10.1007/s00220-019-03505-5</a> Benedikter, Niels P., et al. “Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime.” <i>Communications in Mathematical Physics</i>, vol. 374, Springer Nature, 2020, pp. 2097–2150, doi:<a href="https://doi.org/10.1007/s00220-019-03505-5">10.1007/s00220-019-03505-5</a>. Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., &#38; Seiringer, R. (2020). Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href="https://doi.org/10.1007/s00220-019-03505-5">https://doi.org/10.1007/s00220-019-03505-5</a> Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2020. Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. Communications in Mathematical Physics. 374, 2097–2150. Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2020. <a href="https://doi.org/10.1007/s00220-019-03505-5">https://doi.org/10.1007/s00220-019-03505-5</a>. N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime,” <i>Communications in Mathematical Physics</i>, vol. 374. Springer Nature, pp. 2097–2150, 2020. 66492019-07-18T13:30:04Z2025-04-14T07:27:00Z