Ground state energy of the two-dimensional weakly interacting Bose gas: First correction beyond Bogoliubov theory

TL;DR

This paper calculates the first correction beyond Bogoliubov theory for the ground state energy of a two-dimensional weakly interacting Bose gas, using a systematic expansion and confirming results with Monte Carlo simulations.

Contribution

It introduces a systematic method to compute the next order correction to the ground state energy beyond Bogoliubov theory for 2D Bose gases.

Findings

Good agreement with recent Monte Carlo results

First correction improves accuracy over Bogoliubov prediction

Systematic expansion in interaction strength parameter

Abstract

We consider the grand potential $\Omega$ of a two-dimensional weakly interacting homogeneous Bose gas at zero temperature. Building on a number-conserving Bogoliubov method for a lattice model in the grand canonical ensemble, we calculate the next order term as compared to the Bogoliubov prediction, in a systematic expansion of $\Omega$ in powers of the parameter measuring the weakness of the interaction. Our prediction is in very good agreement with recent Monte Carlo calculations.