[{"day":"01","file_date_updated":"2019-07-24T07:19:10Z","department":[{"_id":"RoSe"}],"quality_controlled":"1","page":"2097–2150","publication_status":"published","date_created":"2019-07-18T13:30:04Z","doi":"10.1007/s00220-019-03505-5","title":"Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime","article_type":"original","oa_version":"Published Version","month":"03","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"intvolume":" 374","publisher":"Springer Nature","type":"journal_article","publication":"Communications in Mathematical Physics","_id":"6649","date_published":"2020-03-01T00:00:00Z","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"}],"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"date_updated":"2020-05-12T12:52:29Z","project":[{"_id":"3AC91DDA-15DF-11EA-824D-93A3E7B544D1","call_identifier":"FWF","name":"FWF Open Access Fund"},{"grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","call_identifier":"FWF"},{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","call_identifier":"H2020","name":"Analysis of quantum many-body systems"}],"volume":374,"language":[{"iso":"eng"}],"status":"public","author":[{"full_name":"Benedikter, Niels P","orcid":"0000-0002-1071-6091","first_name":"Niels P","last_name":"Benedikter","id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Phan Thành","last_name":"Nam","full_name":"Nam, Phan Thành"},{"first_name":"Marcello","last_name":"Porta","full_name":"Porta, Marcello"},{"first_name":"Benjamin","last_name":"Schlein","full_name":"Schlein, Benjamin"},{"full_name":"Seiringer, Robert","first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","cc_license":"'https://creativecommons.org/licenses/by/4.0/'","file":[{"date_created":"2019-07-24T07:19:10Z","date_updated":"2019-07-24T07:19:10Z","file_size":853289,"open_access":1,"file_id":"6668","relation":"main_file","access_level":"open_access","success":1,"content_type":"application/pdf","creator":"dernst","file_name":"2019_CommMathPhysics_Benedikter.pdf"}],"external_id":{"arxiv":["1809.01902"]},"accept":"1","year":"2020","ddc":["530"],"citation":{"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,” *Communications in Mathematical Physics*, vol. 374, pp. 2097–2150, 2020.","mla":"Benedikter, Niels P., et al. “Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime.” *Communications in Mathematical Physics*, vol. 374, Springer Nature, 2020, pp. 2097–2150, doi:10.1007/s00220-019-03505-5.","apa":"Benedikter, N. P., Nam, P. T., 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. https://doi.org/10.1007/s00220-019-03505-5","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.” *Communications in Mathematical Physics* 374 (2020): 2097–2150. https://doi.org/10.1007/s00220-019-03505-5.","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.","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. *Communications in Mathematical Physics*. 2020;374:2097–2150. doi:10.1007/s00220-019-03505-5"}}]