Two-dimensional weakly interacting Bose gas: equation of state

TL;DR

This study uses quantum Monte Carlo simulations to accurately determine the equation of state of a two-dimensional weakly interacting Bose gas at extremely low densities, confirming theoretical predictions and proposing experimental tests.

Contribution

First direct numerical verification of the beyond mean-field equation of state for a 2D dilute Bose gas at ultra-low densities.

Findings

Agreement between perturbative methods and simulations at very low densities

Identification of the universal regime described solely by the gas parameter na^2

Proposal to test the equation of state via collective oscillation frequencies

Abstract

The equation of state of a weakly interacting two-dimensional Bose gas is studied at zero temperature by means of quantum Monte Carlo methods. Going down to as low densities as na^2 ~ 10^{-100} permits us for the first time to obtain agreement on beyond mean-field level between predictions of perturbative methods and direct many-body numerical simulation, thus providing an answer to the fundamental question of the equation of state of a two-dimensional dilute Bose gas in the universal regime (i.e. entirely described by the gas parameter na^2). We also show that the measure of the frequency of a breathing collective oscillation in a trap at very low densities can be used to test the universal equation of state of a two-dimensional Bose gas.