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

TL;DR

This study uses quantum Monte Carlo simulations to analyze how the aspect ratio of a 2D XY model affects the measurement of superfluid stiffness, revealing anisotropic effects and confirming theoretical predictions.

Contribution

It provides a detailed numerical analysis of aspect-ratio dependence on superfluid stiffness in 2D XY models, confirming theoretical predictions and exploring convergence behavior.

Findings

W_y converges exponentially to _s for R>1

_x = _y = _z = _s in 3D systems for any R

Kosterlitz-Thouless transition temperature is 0.34303(8) J

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 \rho^W_x and \rho^W_y determined from the winding number differ from each other and from the true superfluid density \rho_s. Formally, \rho^W_y -> \rho_s in the limit in which L_x -> infinity first and then L_y -> infinity. In practice we find that \rho^W_y converges exponentially to \rho_s for R>1. We also confirm that for 3D systems, \rho^W_x = \rho^W_y = \rho^W_z = \rho_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.