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 negligible effect on the ground state energy.

Correlation energy of a weakly interacting Fermi gas / Benedikter, N.; Nam, P. T.; Porta, M.; Schlein, B.; Seiringer, R.. - In: INVENTIONES MATHEMATICAE. - ISSN 0020-9910. - 225:3(2021), pp. 885-979. [10.1007/s00222-021-01041-5]

Correlation energy of a weakly interacting Fermi gas

Benedikter, N.;Porta, M.;Schlein, B.;
2021-01-01

Abstract

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 negligible effect on the ground state energy.
2021
225
3
885
979
https://doi.org/10.1007/s00222-021-01041-5
https://arxiv.org/abs/2005.08933
Benedikter, N.; Nam, P. T.; Porta, M.; Schlein, B.; Seiringer, R.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/126049
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