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.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.

Physical Review AMay 12, 200942 citations

Quantum Monte Carlo simulation of a two-dimensional Bose gas

Sebastiano Pilati, Jordi Boronat, J. Casulleras +1 more

The equation of state of a homogeneous two-dimensional Bose gas is calculated using quantum Monte Carlo methods. The low-density universal behavior is investigated using different interatomic model potentials, both finite ranged and strictly repulsive and zero ranged, supporting a bound state. The condensate fraction and the pair distribution function are calculated as a function of the gas parameter, ranging from the dilute to the strongly correlated regime. In the case of the zero-range pseudopotential we discuss the stability of the gaslike state for large values of the two-dimensional scattering length, and we calculate the critical density where the system becomes unstable against cluster formation.The equation of state of a homogeneous two-dimensional Bose gas is calculated using quantum Monte Carlo methods. The low-density universal behavior is investigated using different interatomic model potentials, both finite ranged and strictly repulsive and zero ranged, supporting a bound state. The condensate fraction and the pair distribution function are calculated as a function of the gas parameter, ranging from the dilute to the strongly correlated regime. In the case of the zero-range pseudopotential we discuss the stability of the gaslike state for large values of the two-dimensional scattering length, and we calculate the critical density where the system becomes unstable against cluster formation.

arXiv:cond-mat/0411049Physical Review AFeb 11, 200551 citations

Monte Carlo simulations for two-dimensional quantum systems

I. Morgenstern, Diethelm W�rtz

The European Physical Journal BMar 1, 198810 citations

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.