Jordan blocks and the Bethe ansatz I: The eclectic spin chain as a limit

Abstract

We present a procedure to extract the generalised eigenvectors of a non-diagonalisable matrix by considering a diagonalisable perturbation of it and computing the non-diagonalisable limit of its eigenvectors. As an example of this process, we compute a subset of the spectrum of the eclectic spin chain by means of the Nested Coordinate Bethe Ansatz. This allows us to show that the Bethe Ansatz of the finitely twisted spin chain contains enough information to reconstruct the generalised eigenvectors of the eclectic spin chain.

42 pages; v2: title and abstract modified, typos corrected, discussion improved, additional results in sections 5 and 6; v3: typos corrected, discussion improved

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Cited by in corpus (3)

• Form-factors and complete basis of observables via separation of variables for higher rank spin chains
• Jordan blocks and the Bethe ansatz II: The eclectic spin chain beyond $K=1$
• An integrable deformed Landau-Lifshitz model with particle production?