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

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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/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-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 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 new method of using the squares of winding numbers. The low-energy constants magnetization density M and spin stiffenss ρ of quantum spin-1/2 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 puts 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 precise than previous Monte Carlo result.