Monte Carlo determination of the low-energy constants for a two-dimensional spin-1 Heisenberg model with spatial anisotropy

Research output: Contribution to journalArticle

Abstract

The low-energy constants, namely the spin stiffness ρs, the staggered magnetization density ℳs per area, and the spinwave velocity c of the two-dimensional (2D) spin-1 Heisenberg model on the square and rectangular lattices are determined using the first principles Monte Carlo method. In particular, the studied models have different antiferromagnetic couplings J1 and J2 in the spatial 1- and 2-directions, respectively. For each considered J2∕J1, the aspect ratio of the corresponding linear box sizes L2∕L1 used in the simulations is adjusted so that the squares of the two spatial winding numbers take the same values. In addition, the relevant finite-volume and -temperature predictions from magnon chiral perturbation theory are employed in extracting the numerical values of these low-energy constants. Our results of ρs1 are in quantitative agreement with those obtained by the series expansion method over a broad range of J2∕J1. This in turn provides convincing numerical evidence for the quantitative correctness of our approach. The ℳs and c presented here for the spatially anisotropic models are new and can be used as benchmarks for future related studies.

Original languageEnglish
Article number242
JournalEuropean Physical Journal B
Volume90
Issue number12
DOIs
Publication statusPublished - 2017 Dec 1

Fingerprint

Anisotropy
anisotropy
series expansion
Monte Carlo method
boxes
energy
aspect ratio
Aspect ratio
Magnetization
stiffness
Monte Carlo methods
perturbation theory
Stiffness
magnetization
predictions
simulation
Temperature
temperature
Direction compound

Keywords

  • Solid State and Materials

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

@article{45090bda05e341dc9312d62dfd894bd7,
title = "Monte Carlo determination of the low-energy constants for a two-dimensional spin-1 Heisenberg model with spatial anisotropy",
abstract = "The low-energy constants, namely the spin stiffness ρs, the staggered magnetization density ℳs per area, and the spinwave velocity c of the two-dimensional (2D) spin-1 Heisenberg model on the square and rectangular lattices are determined using the first principles Monte Carlo method. In particular, the studied models have different antiferromagnetic couplings J1 and J2 in the spatial 1- and 2-directions, respectively. For each considered J2∕J1, the aspect ratio of the corresponding linear box sizes L2∕L1 used in the simulations is adjusted so that the squares of the two spatial winding numbers take the same values. In addition, the relevant finite-volume and -temperature predictions from magnon chiral perturbation theory are employed in extracting the numerical values of these low-energy constants. Our results of ρs1 are in quantitative agreement with those obtained by the series expansion method over a broad range of J2∕J1. This in turn provides convincing numerical evidence for the quantitative correctness of our approach. The ℳs and c presented here for the spatially anisotropic models are new and can be used as benchmarks for future related studies.",
keywords = "Solid State and Materials",
author = "Jiang, {Fu Jiun}",
year = "2017",
month = "12",
day = "1",
doi = "10.1140/epjb/e2017-80459-x",
language = "English",
volume = "90",
journal = "European Physical Journal B",
issn = "1434-6028",
publisher = "Springer New York",
number = "12",

}

TY - JOUR

T1 - Monte Carlo determination of the low-energy constants for a two-dimensional spin-1 Heisenberg model with spatial anisotropy

AU - Jiang, Fu Jiun

PY - 2017/12/1

Y1 - 2017/12/1

N2 - The low-energy constants, namely the spin stiffness ρs, the staggered magnetization density ℳs per area, and the spinwave velocity c of the two-dimensional (2D) spin-1 Heisenberg model on the square and rectangular lattices are determined using the first principles Monte Carlo method. In particular, the studied models have different antiferromagnetic couplings J1 and J2 in the spatial 1- and 2-directions, respectively. For each considered J2∕J1, the aspect ratio of the corresponding linear box sizes L2∕L1 used in the simulations is adjusted so that the squares of the two spatial winding numbers take the same values. In addition, the relevant finite-volume and -temperature predictions from magnon chiral perturbation theory are employed in extracting the numerical values of these low-energy constants. Our results of ρs1 are in quantitative agreement with those obtained by the series expansion method over a broad range of J2∕J1. This in turn provides convincing numerical evidence for the quantitative correctness of our approach. The ℳs and c presented here for the spatially anisotropic models are new and can be used as benchmarks for future related studies.

AB - The low-energy constants, namely the spin stiffness ρs, the staggered magnetization density ℳs per area, and the spinwave velocity c of the two-dimensional (2D) spin-1 Heisenberg model on the square and rectangular lattices are determined using the first principles Monte Carlo method. In particular, the studied models have different antiferromagnetic couplings J1 and J2 in the spatial 1- and 2-directions, respectively. For each considered J2∕J1, the aspect ratio of the corresponding linear box sizes L2∕L1 used in the simulations is adjusted so that the squares of the two spatial winding numbers take the same values. In addition, the relevant finite-volume and -temperature predictions from magnon chiral perturbation theory are employed in extracting the numerical values of these low-energy constants. Our results of ρs1 are in quantitative agreement with those obtained by the series expansion method over a broad range of J2∕J1. This in turn provides convincing numerical evidence for the quantitative correctness of our approach. The ℳs and c presented here for the spatially anisotropic models are new and can be used as benchmarks for future related studies.

KW - Solid State and Materials

UR - http://www.scopus.com/inward/record.url?scp=85037535737&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85037535737&partnerID=8YFLogxK

U2 - 10.1140/epjb/e2017-80459-x

DO - 10.1140/epjb/e2017-80459-x

M3 - Article

AN - SCOPUS:85037535737

VL - 90

JO - European Physical Journal B

JF - European Physical Journal B

SN - 1434-6028

IS - 12

M1 - 242

ER -