Antiferromagnetic order in systems with doublet S[sub tot] = 12 ground states

Abstract

We use projector quantum Monte Carlo(QMC) methods to study the doublet ground states of two dimensional S = 1/2 Heisenberg antiferromagnets on L × L square lattices with an odd number of sites Ntot = L2. We compute the ground-state spin texture Φz(r) = 〈Sz(r〉↑ in the Stotz = 1/2 component (|G〉↑) of this doublet. We investigate the relationship between nz, the thermodynamic limit of the staggered component of Φz(r), and m, the thermodynamic limit of the magnitude of staggered magnetization vector in the singlet ground state of the same system with Ntot (or 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. 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 reproduces the universality 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 relationship becomes asymptotically exact in the limit of infinitely long-range unfrustrated exchange interactions.