# Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime

N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Communications in Mathematical Physics 374 (2020) 2097–2150.

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*Journal Article*|

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*English*

Author

Benedikter, Niels P

^{IST Austria}^{}; Nam, Phan Thành ; Porta, Marcello ; Schlein, Benjamin ; Seiringer, Robert^{IST Austria}Department

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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.

Publishing Year

Date Published

2020-03-01

Journal Title

Communications in Mathematical Physics

Volume

374

Page

2097–2150

ISSN

eISSN

IST-REx-ID

### Cite this

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/s00220-019-03505-5Benedikter, 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/s00220-019-03505-5Benedikter, 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.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.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., 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.**Main File(s)**

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arXiv 1809.01902