Abstract
The spectral problem of the Heisenberg XXZ spin- chain on the segment is investigated within a modified algebraic Bethe ansatz framework. We consider in this work the most general boundaries allowed by integrability. The eigenvalues and the eigenvectors are obtained. They are characterised by a set of Bethe roots with cardinality equal to , the length of the chain, and which satisfies a set of Bethe equations with an additional term.
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