Method of calculating the spin-wave velocity of spin-1/2 antiferromagnets with O(N) symmetry in a Monte Carlo simulation

Motivated by the so-called cubical regime in magnon chiral perturbation theory, we propose a method to calculate the low-energy constant, namely, the spin-wave velocity c of spin-1/2 antiferromagnets with O(N) symmetry in a Monte Carlo simulation. Specifically, we suggest that c can be determined by c = L/beta when the squares of the spatial and temporal winding numbers are tuned to be the same in the Monte Carlo calculations. Here, beta and L are the inverse temperature and the box size used in the simulations when this condition is met. We verify the validity of this idea by simulating the quantum spin-1/2 XY model. The c obtained by using the squares of winding numbers is given by c = 1.1348(5)Ja, which is consistent with the known values of c in the literature. Unlike other conventional approaches, our idea provides a direct method to measure c. Further, by simultaneously fitting our Monte Carlo data of susceptibilities chi(11) and spin susceptibilities chi to their theoretical predictions from magnon chiral perturbation theory, we find c is given by c = 1.1347(2)Ja, which agrees with the one we obtain by the method of using the squares of winding numbers. The low-energy constant magnetization density M and spin stiffness rho of the quantum spin-1/2 XY model are determined as well, and are given by M= 0.435 61(1)/a(2) and rho = 0.269 74(5) J, respectively. Thanks to the prediction power of magnon chiral perturbation theory, which places a very restricted constraint among the low-energy constants for the model considered here, the accuracy of M we present in this study is much more precise than previous Monte Carlo results.