Particle-Hole Pair Localization on the Fermi Surface and its Impact on the Correlation Energy

TL;DR

This paper investigates how the localization or delocalization of particle-hole pairs on the Fermi surface affects the accuracy of correlation energy calculations in interacting fermion systems.

Contribution

It demonstrates that a simplified collective bosonic approach captures about 92% of the optimal correlation energy, highlighting the impact of particle-hole pair localization.

Findings

A collective bosonic model yields an upper bound of about 92% of the optimal correlation energy.

Both localized and delocalized approaches achieve similar precision for regular interactions.

Simple collective models can approximate the correlation energy remarkably closely.

Abstract

In recent years it has been shown how approximate bosonization can be used to justify the random phase approximation for the correlation energy of interacting fermions in a mean-field scaling limit. At the core is the interpretation of particle-hole excitations close to the Fermi surface at bosons. The main two approaches however differ in emphasizing collective degrees of freedom (particle-hole pairs delocalized over patches on the Fermi surface) or particle-hole pairs exactly localized in momentum space. Both methods lead to equal precision for the correlation energy with regular interaction potentials. This poses the question how big the influence of delocalizing particle-hole pairs really is. In the present note we show that a description with few, completely collective bosonic degrees of freedom only yields an upper bound of about 92% of the optimal value. Nevertheless it is remarkable that such a simple approach comes that close to the optimal bound.