Method of calculating the spin-wave velocity of spin-12 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-12 antiferromagnets with O(N) symmetry in a Monte Carlo simulation. Specifically, we suggest that c can be determined by c=L/β when the squares of the spatial and temporal winding numbers are tuned to be the same in the Monte Carlo calculations. Here, β 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-12 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 χ₁₁ and spin susceptibilities χ 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 ρ of the quantum spin-12 XY model are determined as well, and are given by M=0.43561(1)/a2 and ρ=0.26974(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.