Ground state energy of a homogeneous Bose-Einstein condensate beyond Bogoliubov

TL;DR

This paper discusses the accuracy of the ground-state energy calculations for a homogeneous Bose-Einstein condensate, providing evidence that beyond-Bogoliubov methods yield more complete results, especially for the next-to-leading order terms.

Contribution

It offers strong indications that the next-to-leading order term in the ground state energy is correct and highlights contributions missed by the Bogoliubov approximation.

Findings

Leading order energy term confirmed by rigorous proof

Next-to-leading order contributions are accurately captured beyond Bogoliubov

Perturbative methods reveal additional energy contributions

Abstract

The standard calculations of the ground-state energy of a homogeneous Bose gas rely on approximations which are physically reasonable but difficult to control. Lieb and Yngvason [Phys. Rev. Lett. 80, 2504 (1998)] have proved rigorously that the commonly accepted leading order term of the ground state energy is correct in the zero-density-limit. Here, strong indications are given that also the next to leading term is correct. It is shown that the first terms obtained in a perturbative treatment provide contributions which are lost in the Bogoliubov approach.