Antiferromagnetic Order in Systems With Doublet S-tot=1/2 Ground States

Department of Physics, Boston University, 02215, Boston, Massachussetts, USA
Physical review. B, Condensed matter (Impact Factor: 3.66). 08/2012; 86(6). DOI: 10.1103/PhysRevB.86.064418
Source: arXiv


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 Φz(r⃗)=〈Sz(r⃗)〉↑ in the ground state |G〉↑ with Stotz=1/2, and relate nz, the thermodynamic limit of the staggered component of Φz(r⃗), 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 ẑ axis in the thermodynamic limit, then we would expect nz/m=1. By studying several different deformations of the square lattice Heisenberg antiferromagnet, we find instead that nz/m is a universal function of m, independent of the microscopic details of the Hamiltonian, and well approximated by nz/m≈0.266+0.288m−0.306m2 for S=1/2 antiferromagnets. We define nz 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 nz/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 nz/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.

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