Bosonic Collective Excitations in Fermi Gases

TL;DR

This paper reviews the bosonic approximation for fermionic systems, deriving an effective Hamiltonian that predicts collective excitations like plasmons, aligning with established theories and experimental results.

Contribution

It provides a rigorous justification of bosonization as an upper bound on correlation energy and demonstrates its effectiveness in predicting collective excitations in Fermi gases.

Findings

Bosonization offers a valid approximation for many-body correlations.

The effective Hamiltonian predicts plasmons consistent with RPA.

The theory aligns with experimental observations.

Abstract

Hartree-Fock theory has been justified as a mean-field approximation for fermionic systems. However, it suffers from some defects in predicting physical properties, making necessary a theory of quantum correlations. Recently, bosonization of many-body correlations has been rigorously justified as an upper bound on the correlation energy at high density with weak interactions. We review the bosonic approximation, deriving an effective Hamiltonian. We then show that for systems with Coulomb interaction this effective theory predicts collective excitations (plasmons) in accordance with the random phase approximation of Bohm and Pines, and with experimental observation.