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.
Categories: cond-mat.str-el hep-lat hep-ph