Aspect-ratio dependence of the spin stiffness of a two-dimensional XY model

Abstract

We calculate the superfluid stiffness of 2D lattice hard-core bosons at half-filling (equivalent to the S=1/2 XY-model) using the squared winding number quantum Monte Carlo estimator. For L_x x L_y lattices with aspect ratio L_x/L_y=R, and L_x,L_y -> infinity, we confirm the recent prediction [N. Prokof'ev and B.V. Svistunov, Phys. Rev. B 61, 11282 (1999)] that the finite-temperature stiffness parameters ρ^W_x and ρ^W_y determined from the winding number differ from each other and from the true superfluid density ρ_s. Formally, ρ^W_y -> ρ_s in the limit in which L_x -> infinity first and then L_y -> infinity. In practice we find that ρ^W_y converges exponentially to ρ_s for R>1. We also confirm that for 3D systems, ρ^W_x = ρ^W_y = ρ^W_z = ρ_s for any R. In addition, we determine the Kosterlitz-Thouless transition temperature to be T_KT/J=0.34303(8) for the 2D model.