{"ec_funded":1,"quality_controlled":"1","day":"01","status":"public","abstract":[{"text":"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.\r\n","lang":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"date_updated":"2023-08-17T13:51:50Z","intvolume":"       374","article_type":"original","external_id":{"arxiv":["1809.01902"],"isi":["000527910700019"]},"has_accepted_license":"1","isi":1,"volume":374,"project":[{"call_identifier":"FWF","_id":"3AC91DDA-15DF-11EA-824D-93A3E7B544D1","name":"FWF Open Access Fund"},{"grant_number":"P27533_N27","call_identifier":"FWF","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","_id":"25C878CE-B435-11E9-9278-68D0E5697425"},{"name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227"}],"department":[{"_id":"RoSe"}],"page":"2097–2150","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"first_name":"Niels P","orcid":"0000-0002-1071-6091","full_name":"Benedikter, Niels P","id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","last_name":"Benedikter"},{"last_name":"Nam","first_name":"Phan Thành","full_name":"Nam, Phan Thành"},{"first_name":"Marcello","full_name":"Porta, Marcello","last_name":"Porta"},{"last_name":"Schlein","first_name":"Benjamin","full_name":"Schlein, Benjamin"},{"full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"language":[{"iso":"eng"}],"file_date_updated":"2020-07-14T12:47:35Z","date_published":"2020-03-01T00:00:00Z","article_processing_charge":"No","year":"2020","file":[{"checksum":"f9dd6dd615a698f1d3636c4a092fed23","creator":"dernst","file_id":"6668","access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_updated":"2020-07-14T12:47:35Z","file_size":853289,"date_created":"2019-07-24T07:19:10Z","file_name":"2019_CommMathPhysics_Benedikter.pdf"}],"ddc":["530"],"date_created":"2019-07-18T13:30:04Z","publication":"Communications in Mathematical Physics","citation":{"ista":"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.","ama":"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>","chicago":"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>.","mla":"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>.","ieee":"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.","short":"N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Communications in Mathematical Physics 374 (2020) 2097–2150.","apa":"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>"},"type":"journal_article","oa_version":"Published Version","month":"03","title":"Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"doi":"10.1007/s00220-019-03505-5","_id":"6649","publication_status":"published","scopus_import":"1","oa":1,"publisher":"Springer Nature"}