Ground-state staggered magnetization of two-dimensional quantum Heisenberg antiferromagnets

Abstract

The ground-state staggered magnetization of spin-S quantum Heisenberg antiferromagnets may be estimated in spin-wave theory (effectively a 1/S expansion) or by perturbation in ${J}_{\ensuremath{\perp}}$=${J}_{x}$=${J}_{y}$ away from the Ising (${J}_{\ensuremath{\perp}}$=0, ${J}_{z}$>0) limit. The latter series in ${J}_{\ensuremath{\perp}}^{2}$ is poorly convergent for the square lattice and a naive summation of the available terms yields overestimates of the staggered magnetization. A new way of analyzing the perturbation series that should remove the slow convergence is proposed. The resulting ground-state staggered magnetization per spin for spin-1/2 is 0.313, while spin-wave theory yields 0.303, in units where the full, classical staggered magnetization is 0.500.