We calculate the superfluid stiffness of two-dimensional (2D) lattice hard-core bosons at half filling (equivalent to the $S=1/2\mathrm{}$ $\mathrm{XY}$ model) using the squared winding number quantum Monte Carlo estimator. For $L_x\times L_y$ lattices with aspect ratio $L_x{/L}_y=R$ and $L_x{,L}_y\to \infty ,$ we confirm the recent prediction [N. Prokof’ev and B.V. Svistunov, Phys. Rev. B 61, 11 282 (2000)] that the finite-temperature stiffness parameters ${\rho }_x^W$ and ${\rho }_y^W$ determined from the winding number differ from each other and from the true superfluid density ${\rho }_s.$ Formally, ${\rho }_y^W\to {\rho }_s$ in the limit in which $L_x\to \infty$ first and then $L_y\to \infty .$ In practice we find that ${\rho }_y^W$ converges exponentially to ${\rho }_s$ for $R>\mathrm{}1.\mathrm{}$ We also confirm that for 3D systems, ${\rho }_x^W={\rho }_y^W={\rho }_z^W={\rho }_s$ for any R. In addition, we determine the Kosterlitz-Thouless transition temperature to be $T_{\mathrm{KT}}/J=0.343\mathrm{}03\left(8\right)\mathrm{}$ for the 2D model.

• Received 19 June 2003

DOI:https://doi.org/10.1103/PhysRevB.69.014509