Haldane conjecture and elementary excitations in the XXZ spin-1 linear chain: A novel variational approach

Abstract

A physically motivated approach is used to study the linear chain XXZ spin‐1 Hamiltonian in the antiferromagnetic regime. A variational Hamiltonian is obtained restricting the basis set to states with local antiferromagnetic environments separated by sites with S^z=0 acting as domain walls. Ground‐state properties of this variational Hamiltonian are obtained and, in particular, an order–disorder transition is found with critical behavior corresponding to the two‐dimensional Ising model universality class, in agreement with Haldane conjecture. Excellent agreement with finite chain data concerning the position of Haldane’s point, ground‐state energy, and elementary excitations is found.