Semiclassical approach to ground-state properties of hard-core bosons in two dimensions
Résumé
Motivated by some inconsistencies in the way quantum fluctuations are included beyond the classical treatment of hard-core bosons on a lattice in the recent literature, we revisit the large-S semiclassical approach to hard-core bosons on the square lattice at T=0. First of all, we show that, if one stays at the purely harmonic level, the only correct way to get the 1/S correction to the density is to extract it from the derivative of the ground-state energy with respect to the chemical potential, and that to extract it from a calculation of the ground-state expectation value of the particle number operator, it is necessary to include 1/√S corrections to the harmonic ground state. Building on this alternative approach to get 1/S corrections, we provide the first semiclassical derivation of the momentum distribution, and we revisit the calculation of the condensate density. The results of these as well as other physically relevant quantities such as the superfluid density are systematically compared to quantum Monte Carlo simulations. This comparison shows that the logarithmic corrections in the dilute Bose gas limit are only captured by the semiclassical approach if the 1/S corrections are properly calculated, and that the semiclassical approach is able to reproduce the 1/k divergence of the momentum distribution at k=0. Finally, the effect of 1/S2 corrections is briefly discussed.