10.1007/s00220-019-03505-5
Benedikter, Niels P
Niels P
Benedikter0000-0002-1071-6091
Nam, Phan Thành
Phan Thành
Nam
Porta, Marcello
Marcello
Porta
Schlein, Benjamin
Benjamin
Schlein
Seiringer, Robert
Robert
Seiringer
Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime
Springer
2019
2019-07-18T13:30:04Z
2019-08-02T12:39:24Z
journal_article
https://research-explorer.app.ist.ac.at/record/6649
https://research-explorer.app.ist.ac.at/record/6649.json
0010-3616
1809.01902
853289 bytes
application/pdf
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.