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

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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 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.

Original languageEnglish
Article number024419
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume83
Issue number2
DOIs
Publication statusPublished - 2011 Jan 31

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Spin waves
magnons
symmetry
perturbation theory
simulation
Magnetization
magnetic permeability
Stiffness
predictions
boxes
energy
stiffness
Monte Carlo simulation
magnetization
Temperature

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

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title = "Method of calculating the spin-wave velocity of spin-12 antiferromagnets with O(N) symmetry in a Monte Carlo simulation",
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 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.",
author = "Jiang, {F. -J.}",
year = "2011",
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doi = "10.1103/PhysRevB.83.024419",
language = "English",
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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.

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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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