Surface excitations and surface energy of the antiferromagnetic XXZ chain by the Bethe ansatz approach

Abstract

We study boundary bound states using the Bethe ansatz formalism for the open XXZ (Δ > 1) chain in a boundary magnetic field h. Boundary bound states are represented by the 'boundary strings' similar to those described in Skorik and Saleur. We find that for certain values of h the ground-state wavefunction contains boundary strings and from this infer the existence of two 'critical' fields in agreement with Jimbo et al. An expression for the vacuum surface energy in the thermodynamic limit is derived and found to be an analytic function of h. We argue that boundary excitations appear only in pairs with `bulk' excitations or with boundary excitations at the other end of the chain. We mainly discuss the case where the magnetic fields at the left and the right boundaries are antiparallel, but we also comment on the case of parallel fields. In the Ising (Δ = ∞) and isotropic (Δ = 0) limits our results agree with those previously known.

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