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arXiv · 0902.4861

Monte Carlo Determination of the Low-Energy Constants of a Spin 1/2 Heisenberg Model with Spatial Anisotropy

F. J. Jiang·F. Kämpfer·M. Nyfeler
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Abstract

Motivated by the possible mechanism for the pinning of the electronic liquid crystal direction in YBCO as proposed in \cite{Pardini08}, we use the first principles Monte Carlo method to study the spin 1/2 Heisenberg model with antiferromagnetic couplings $J_{1}$ and $J_{2}$ on the square lattice. The corresponding low-energy constants, namely the spin stiffness $\rho_s$, the staggered magnetization density ${\cal M}_s$, the spin wave velocity $c$, as well as the ground state energy density $e_0$ are determined by fitting the Monte Carlo data to the predictions of magnon chiral perturbation theory. In particular, the spin stiffnesses $\rho_{s1}$ and $\rho_{s2}$ are investigated as a function of the ratio $J_{2}/J_{1}$ of the couplings. Although we find a good agreement between our results with those obtained by the series expansion method in the weakly anisotropic regime, for strong anisotropy we observe discrepancies.

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F. J. Jiang, F. Kämpfer, M. Nyfeler. 2009-02-27. Monte Carlo Determination of the Low-Energy Constants of a Spin 1/2 Heisenberg Model with Spatial Anisotropy. https://doi.org/10.1103/physrevb.80.033104

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