Role of domain walls in the ground-state properties of the spin-1/2XXZHamiltonian in the linear chain

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Abstract
The XXZ spin-1/2 Hamiltonian in the linear chain is exactly transformed into a model where the local degrees of freedom are domain walls between opposite antiferromagnetic domains. The ground state of the new Hamiltonian is studied with the Hartree-Fock approximation. This approximation is shown to become exact in the XY and extreme antiferromagnetic limits, with excellent results in between. Known results concerning the existence or nonexistence of long-range order and gap in the excitation spectrum are reproduced by our solution. Good quantitative agreement with representative properties of the exact solution is obtained. The domain-wall Hamiltonian is shown to be the natural framework for the understanding of the ground state and low-lying excited states of the XXZ system in the antiferromagnetic regime.