Self-Consistent Random Phase Approximation - Application to the Hubbard Model for finite number of sites

TL;DR

This paper applies the Self-Consistent Random Phase Approximation (SCRPA) to the 1D Hubbard model on finite chains, demonstrating high accuracy for certain site numbers and highlighting areas needing further investigation.

Contribution

The study extends SCRPA application to finite 1D Hubbard chains, confirming its effectiveness for 2+4n sites and analyzing its limitations for 4n sites.

Findings

SCRPA yields excellent results for 2+4n sites with minimal effort.

SCRPA exactly solves the two sites problem.

The method correctly captures high-density Fermi gas limits.

Abstract

Within the 1D Hubbard model linear closed chains with various numbers of sites are considered in Self Consistent Random Phase Approximation (SCRPA). Excellent results with a minimal numerical effort are obtained for 2+4n sites cases, confirming earlier results with this theory for other models. However, the 4n sites cases need further considerations. SCRPA solves the two sites problem exactly. It therefore contains the two electrons and high density Fermi gas limits correctly.