Correlation energy of a weakly interacting Fermi gas

@article{Benedikter2021CorrelationEO,
  title={Correlation energy of a weakly interacting Fermi gas},
  author={Niels Benedikter and Phan Th{\`a}nh Nam and Marcello Porta and Benjamin Schlein and Robert Seiringer},
  journal={Inventiones mathematicae},
  year={2021},
  volume={225},
  pages={885-979}
}
We derive rigorously the leading order of the correlation energy of a Fermi gas in a scaling regime of high density and weak interaction. The result verifies the prediction of the random-phase approximation. Our proof refines the method of collective bosonization in three dimensions. We approximately diagonalize an effective Hamiltonian describing approximately bosonic collective excitations around the Hartree–Fock state, while showing that gapless and non-collective excitations have only a… 
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