Variational Monte Carlo analysis of Bose--Einstein condensation in a two-dimensional trap

The ground-state properties of a system with a small number of interacting bosons over a wide range of densities are investigated. The system is confined in a two-dimensional isotropic harmonic trap, where the interaction between bosons is treated as a hard-core potential. By using variational Monte Carlo method, we diagonalize the one-body density matrix of the system to obtain the ground-state energy, condensate wavefunction and the condensate fraction. We find that in the dilute limit the depletion of central condensate in the 2D system is larger than in a 3D system for the same interaction strength; however as the density increases, the depletion at the centre of 2D trap will be equal to or even lower than that at the centre of 3D trap, which is in agreement with the anticipated in Thomas--Fermi approximation. In addition, in the 2D system the total condensate depletion is still larger than in a 3D system for the same scattering length.