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Motivated by the so-called cubical regime in magnon chiral perturbationtheory, we propose a new method to calculate the low-energy constant, namelythe spin-wave velocity $c$ of spin-1/2 antiferromagnets with $O(N)$ symmetry ina 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 aretuned to be the same in the Monte Carlo calculations. Here $\beta$ and $L$ arethe inverse temperature and the box size used in the simulations when thiscondition is met. We verify the validity of this idea by simulating the quantumspin-1/2 XY model. The $c$ obtained by using the squares of winding numbers isgiven by $c = 1.1348(5)Ja$ which is consistent with the known values of $c$ inthe literature. Unlike other conventional approaches, our new idea provides adirect method to measure $c$. Further, by simultaneously fitting our MonteCarlo data of susceptibilities $\chi_{11}$ and spin susceptibilities $\chi$ totheir 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 thenew method of using the squares of winding numbers. The low-energy constantsmagnetization density ${\cal M}$ and spin stiffenss $\rho$ of quantum spin-1/2XY model are determined as well and are given by ${\cal M} = 0.43561(1)/a^2$and $\rho = 0.26974(5)J$, respectively. Thanks to the prediction power ofmagnon chiral perturbation theory which puts a very restricted constraint amongthe low-energy constants for the model considered here, the accuracy of ${\calM}$ we present in this study is much precise than previous Monte Carlo result.

A New Method of Calculating the Spin-Wave Velocity $c$ of Spin-1/2 Antiferromagnets With $O(N)$ Symmetry in a Monte Carlo Simulation