Density Matrix Functional Theory for the Lipkin model

TL;DR

This paper develops a semi-empirical Density Matrix Functional theory for the Lipkin model, effectively describing ground state energies and suggesting potential for systems with shape phase-transitions like nuclei.

Contribution

It introduces a new Density Matrix Functional approach based on natural orbitals for the Lipkin model, demonstrating its accuracy and potential applications.

Findings

Accurately reproduces ground state energies across interaction strengths

Improves description of one-body observables

Highlights relevance for systems with shape phase-transitions

Abstract

A Density Matrix Functional theory is constructed semi-empirically for the two-level Lipkin model. This theory, based on natural orbitals and occupation numbers, is shown to provide a good description for the ground state energy of the system as the two-body interaction and particle number vary. The application of Density Matrix Functional theory to the Lipkin model illustrates that it could be a valuable tool for systems presenting a shape phase-transition such as nuclei. The improvement of one-body observables description as well as the interest for Energy Density Functional theory are discussed.