### Abstract

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 χ_{11} 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.

Original language | English |
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Article number | 024419 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 83 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2011 Jan 31 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

**Method of calculating the spin-wave velocity of spin-12 antiferromagnets with O(N) symmetry in a Monte Carlo simulation.** / Jiang, F. -J.

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TY - JOUR

T1 - Method of calculating the spin-wave velocity of spin-12 antiferromagnets with O(N) symmetry in a Monte Carlo simulation

AU - Jiang, F. -J.

PY - 2011/1/31

Y1 - 2011/1/31

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevB.83.024419

DO - 10.1103/PhysRevB.83.024419

M3 - Article

VL - 83

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 2

M1 - 024419

ER -