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

Fu-Jiun Jiang

doi:10.1140/epjb/e2017-80459-x

paper

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

arXiv:1702.02436 · doi:10.1140/epjb/e2017-80459-x

Abstract

The low-energy constants, namely the spin stiffness $ρ_{s}$ , the staggered magnetization density $M_{s}$ 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 antiferromagnetic couplings $J_{1}$ and $J_{2}$ in the spatial 1- and 2-directions, respectively. For each considered $J_{2} / J_{1}$ , the aspect ratio of the corresponding linear box sizes $L_{2} / L_{1}$ 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 $ρ_{s 1}$ are in quantitative agreement with those obtained by the series expansion method over a broad range of $J_{2} / J_{1}$ . This in turn provides convincing numerical evidence for the quantitative correctness of our approach. The $M_{s}$ and $c$ presented here for the spatially anisotropic models are new and can be used as benchmarks for future related studies.

8 pages, 11 figures

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

Abstract

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