Monte Carlo determination of the low-energy constants of a spin- 1 2 Heisenberg model with spatial anisotropy

Motivated by the possible mechanism for the pinning of the electronic liquid crystal direction in YBa2 Cu3 O6.45 as proposed by Pardini [Phys. Rev. B 78, 024439 (2008)], we use the first-principles Monte Carlo method to study the spin- 1 2 Heisenberg model with antiferromagnetic couplings J1 and J2 on the square lattice. In particular, the low-energy constants spin stiffness ρs, staggered magnetization Ms, and spin wave velocity c are determined by fitting the Monte Carlo data to the predictions of magnon chiral perturbation theory. Further, the spin stiffnesses ρs1 and ρs2 as a function of the ratio J2 / J1 of the couplings are investigated in detail. 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.