Antiferromagnetic order in systems with doublet S_tot=1/2 ground states

Abstract

We use projector quantum Monte Carlo methods to study the doublet ground states of two-dimensional S=1/2 antiferromagnets on L×L square lattices with L odd. We compute the ground-state spin texture Φ^z(⃗r)=⟨S^z(⃗r)⟩↑ in the ground state |G⟩↑ with S^z_tot=1/2, and relate n^z, the thermodynamic limit of the staggered component of Φ^z(⃗r), 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⟩↑ were fully pinned along the ˆz 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≈0.266+0.288m−0.306m² 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≈(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.