General solution for the antiferromagnetic Heisenberg model with exchange anisotropy toward the Ising limit

Abstract

The Heisenberg antiferromagnetic model for spin S and no external field is approximately solved for anisotropy, dimension, or spin size, assuring high antiferromagnetic order. Explicit closed-form expressions for the ground state, ground state energy, excitations and correlation functions are obtained. The approximate solution converges rapidly to the exact one as S or the lattice dimensionality increases, or when the anisotropy approaches the Ising limit. In particular, for two and three dimensional lattices it remains very accurate all the way from the Ising to the isotropic Heisenberg models. The proposed new solution gives more accuracy than linear spin waves theory and is expressed in terms of a set of excitations carrying no spin, in opposition to the spin-one excitations of spin waves theory.