We use projector quantum Monte Carlo methods to study the doublet ground states of two-dimensional $S=1/2$ antiferromagnets on $L\times L$ square lattices with $L$ odd. We compute the ground-state spin texture ${\Phi }^z\left(\vec{r}\right)={\langle S^z\left(\vec{r}\right)\rangle }_{\uparrow }$ in the ground state ${|G\rangle }_{\uparrow }$ with $S_{\mathrm{tot}}^z=1/2$, and relate $n^z$, the thermodynamic limit of the staggered component of ${\Phi }^z\left(\vec{r}\right)$, to $m$, the thermodynamic limit of the magnitude of the staggered magnetization vector in the singlet ground state of the same system with $L$ even. If the direction of the staggered magnetization in ${|G\rangle }_{\uparrow }$ were fully pinned along the $\widehat{z}$ axis in the thermodynamic limit, then we would expect $n^z/m=1$. By studying several different deformations of the square lattice Heisenberg antiferromagnet, we find instead that $n^z/m$ is a universal function of $m$, independent of the microscopic details of the Hamiltonian, and well approximated by $n^z/m\approx 0.266+0.288m-0.306m^2$ for $S=1/2$ antiferromagnets. We define $n^z$ and $m$ analogously for spin-$S$ antiferromagnets, and explore this universal relationship using spin-wave theory, a simple mean-field theory written in terms of the total spin of each sublattice, and a rotor model for the dynamics of the staggered magnetization vector. We find that spin-wave theory predicts $n^z/m\approx (0.987-1.003/S)+0.013m/S$ to leading order in $1/S$, while the sublattice-spin mean-field theory and the rotor model both give $n^z/m=S/(S+1)$ for spin-$S$ antiferromagnets. We argue that this latter relationship becomes asymptotically exact in the limit of infinitely long-range unfrustrated exchange interactions.

• Received 8 February 2012

DOI:https://doi.org/10.1103/PhysRevB.86.064418