Correlation Energy of a Weakly Interacting Fermi Gas

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.

69 pages, 2 figures; v2: additional references on lattice point counting; v3: expanded introduction and list of references

References in corpus (3)

• The BCS Functional for General Pair Interactions
• Spin Hall insulators beyond the Helical Luttinger model
• The Free Energy of the Quantum Heisenberg Ferromagnet at Large Spin

Cited by in corpus (14)

• Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential
• The Gell-Mann$-$Brueckner Formula for the Correlation Energy of the Electron Gas: A Rigorous Upper Bound in the Mean-Field Regime
• On the Effective Quasi-Bosonic Hamiltonian of the Electron Gas: Collective Excitations and Plasmon Modes
• Effective Dynamics of Extended Fermi Gases in the High-Density Regime
• Lower bounds on the energy of the Bose gas
• Bosonization of Fermionic Many-Body Dynamics
• Friedrichs Diagrams -- Bosonic and Fermionic
• Bosonized Momentum Distribution of a Fermi Gas via Friedrichs Diagrams
• Dynamics of mean-field Fermi systems with nonzero pairing
• The Huang-Yang formula for the low-density Fermi gas: upper bound
• Effective Polaron Dynamics of an Impurity Particle Interacting with a Fermi Gas
• Effective quantum dynamics for magnetic fermions
• Differential Equations of Quantum Mechanics
• Effective Dynamics of Interacting Fermions from Semiclassical Theory to the Random Phase Approximation