Energy functional for the three-level Lipkin model

TL;DR

This paper derives and analyzes the energy functional of a three-level Lipkin model, comparing exact numerical results with RPA approximations, and explores effects of non-degenerate levels and symmetry-breaking potentials.

Contribution

It provides a novel analytical derivation of the energy functional for the three-level Lipkin model and assesses the accuracy of RPA in different regimes.

Findings

RPA solutions match exact results well outside phase transition regions

Analytical insights into energy functional with symmetry-breaking potentials

Good agreement between RPA and exact results for non-degenerate levels

Abstract

We compute the energy functional of a three-level Lipkin model via a Legrendre transform and compare exact numerical results with analytical solutions obtained from the random phase approximation (RPA). Except for the region of the phase transition, the RPA solutions perform very well. We also study the case of three non-degenerate levels and again find that the RPA solution agrees well with the exact numerical result. For this case, the analytical results give us insight into the form of the energy functional in the presence of symmetry-breaking one-body potentials.