Generic boundary scattering in the open XXZ chain

The open critical XXZ spin chain with a general right boundary and a trivial diagonal left boundary is considered. Within this framework we propose a simple computation of the exact generic boundary S-matrix (with diagonal and non-diagonal entries), starting from the `bare’ Bethe ansatz equations. Our results coincide with the ones obtained by Ghoshal and Zamolodchikov, after assuming suitable identifications of the bulk and boundary parameters.

💡 Research Summary

The paper investigates the open critical XXZ spin‑½ chain with a trivial diagonal left boundary (K⁺∝I) and a fully non‑diagonal right boundary described by the most general 2×2 K‑matrix depending on three parameters (ξ, κ, θ). By fixing the left boundary to the identity, the authors reduce the problem to a single non‑trivial boundary while retaining the full richness of the reflection equation.

The bulk R‑matrix is the standard six‑vertex solution of the Yang‑Baxter equation, and the transfer matrix is built in the usual Sklyanin formalism. The right‑hand K‑matrix is parametrized following Ghoshal‑Zamolodchikov’s conventions, with θ removable by a gauge transformation, leaving ξ and κ as the essential physical boundary couplings. The eigenvalues of K⁻(λ) are expressed as ε₁,₂(λ)=−2iκ sinh