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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Author
Benedikter, Niels PIST Austria ; Nam, Phan Thành; Porta, Marcello; Schlein, Benjamin; Seiringer, RobertIST Austria
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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

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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
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. Springer Nature. https://doi.org/10.1007/s00220-019-03505-5
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. Springer Nature, 2020. 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. Springer Nature, 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.
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