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

TL;DR

This paper introduces a novel Monte Carlo method to accurately determine the spin-wave velocity in spin-1/2 antiferromagnets with $O(N)$ symmetry by tuning winding numbers, validated through simulations of the XY model.

Contribution

The paper proposes a direct Monte Carlo approach to calculate the spin-wave velocity using winding number ratios, validated by consistency with theoretical predictions and previous results.

Findings

The new method yields $c = 1.1348(5)Ja$, consistent with literature.

Fitting susceptibilities confirms $c = 1.1347(2)Ja$, matching the winding number method.

Precise determination of magnetization density and spin stiffness.

Abstract

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.