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 $n{a}^{2}\ensuremath{\propto}{10}^{\ensuremath{-}100}$ permits us 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 $n{a}^{2}$). 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.

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