{"abstract":[{"lang":"eng","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"}],"publisher":"Springer Nature","status":"public","citation":{"short":"N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Communications in Mathematical Physics 374 (2020) 2097–2150.","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.","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>","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>.","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>","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."},"volume":374,"article_type":"original","quality_controlled":"1","ddc":["530"],"scopus_import":"1","day":"01","has_accepted_license":"1","date_created":"2019-07-18T13:30:04Z","oa":1,"file_date_updated":"2020-07-14T12:47:35Z","date_published":"2020-03-01T00:00:00Z","page":"2097–2150","oa_version":"Published Version","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime","corr_author":"1","year":"2020","external_id":{"isi":["000527910700019"],"arxiv":["1809.01902"]},"_id":"6649","file":[{"file_id":"6668","creator":"dernst","checksum":"f9dd6dd615a698f1d3636c4a092fed23","file_name":"2019_CommMathPhysics_Benedikter.pdf","relation":"main_file","access_level":"open_access","date_created":"2019-07-24T07:19:10Z","content_type":"application/pdf","date_updated":"2020-07-14T12:47:35Z","file_size":853289}],"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"ec_funded":1,"publication":"Communications in Mathematical Physics","article_processing_charge":"No","intvolume":"       374","publication_status":"published","isi":1,"month":"03","department":[{"_id":"RoSe"}],"language":[{"iso":"eng"}],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","author":[{"id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","full_name":"Benedikter, Niels P","last_name":"Benedikter","first_name":"Niels P","orcid":"0000-0002-1071-6091"},{"full_name":"Nam, Phan Thành","last_name":"Nam","first_name":"Phan Thành"},{"first_name":"Marcello","full_name":"Porta, Marcello","last_name":"Porta"},{"first_name":"Benjamin","last_name":"Schlein","full_name":"Schlein, Benjamin"},{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","last_name":"Seiringer","orcid":"0000-0002-6781-0521"}],"date_updated":"2025-04-14T07:27:00Z","doi":"10.1007/s00220-019-03505-5","arxiv":1,"project":[{"_id":"3AC91DDA-15DF-11EA-824D-93A3E7B544D1","name":"FWF Open Access Fund","call_identifier":"FWF"},{"grant_number":"P27533_N27","call_identifier":"FWF","_id":"25C878CE-B435-11E9-9278-68D0E5697425","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems"},{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227","call_identifier":"H2020"}]}