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

Abstract

Motivated by the possible mechanism for the pinning of the electronic liquid crystal direction in YBa2Cu3O6.45 [YBa subscript 2 Cu supscript 3 O subscript 6.45] as proposed by Pardini et al. [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 [J subscript 1] and J2 [J subscript 2] on the square lattice. In particular, the low-energy constants spin stiffness ρs [p subscrit s], staggered magnetization Ms [M subscript s], 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 [p subscript s1] and ρs2 [p subscript s2] as a function of the ratio J2/J1 [J subscript 2 / J subscript 1] 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.