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arXiv:2610.25262

Upper Bound on the Correlation Energy of a Dense Fermi Gas in the Thermodynamic Limit

Niels Benedikter, Sascha Lill, Marcello Porta, Benjamin Schlein

math-phcond-mat.str-elmath.SPquant-phSubmitted Oct 18, 2026• Announced Oct 20, 2026• 0 citations
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Abstract

We prove that the random phase approximation provides an upper bound on the correlation energy of a three-dimensional, weakly interacting, Fermi gas in the thermodynamic limit at high density. More precisely, we consider a mean-field scaling regime where the kinetic and interaction Hamiltonian are scaled by $ρ^{-2/3}$ and $ρ^{-1}$, respectively. We use a correlated trial state constructed through a quasi-bosonic Bogoliubov transformation of collective particle--hole excitations associated to patches on the Fermi surface. Key of the proof is to control the position-space localization of the collective excitations. Combined with an iterated Duhamel expansion of the expectation values of (localized) particle number operators we obtain extensive estimates, which justify the reduction to an effective quadratic Hamiltonian and its approximate diagonalization.

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72 pages

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