  Motivated by the so-called cubical regime in magnon chiral perturbation
theory, we propose a new 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 new 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
new method of using the squares of winding numbers. The low-energy constants
magnetization density ${\cal M}$ and spin stiffenss $\rho$ of quantum spin-1/2
XY 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 of
magnon chiral perturbation theory which puts a very restricted constraint among
the low-energy constants for the model considered here, the accuracy of ${\cal
M}$ we present in this study is much precise than previous Monte Carlo result.
