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arXiv:1606.00978 · Physics of Particles and Nuclei Letters

On the structure of Bethe vectors

Jan Fuksa

Published Jun 30, 2017• 1 citation
arXivHTMLPDF

Abstract

The structure of Bethe vectors for generalised models associated with the rational and trigonometric R-matrix is investigated. The Bethe vectors in terms of two-component and multi-component models are described. Consequently, their structure in terms of local variables and operators is provided. This, as a consequence, proves the equivalence of coordinate and algebraic Bethe ansatzes for the Heisenberg spin chains. Hermitian conjugation of the elements of the monodromy matrix for the spin chains is studied.

DOI
10.1134/s1547477117040094

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The structure of Bethe vectors for generalised models associated with the rational and trigonometric R-matrix is investigated. The Bethe vectors in terms of two-component and multi-component models are described. Consequently, their structure in terms of local variables and operators is provided. This, as a consequence, proves the equivalence of coordinate and algebraic Bethe ansatzes for the Heisenberg spin chains. Hermitian conjugation of the elements of the monodromy matrix for the spin chains is studied.
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We consider an XYZXYZXYZ spin chain within the framework of the generalized algebraic Bethe ansatz. We calculate the actions of monodromy matrix elements on Bethe vectors as a linear combination of new Bethe vectors. We also compute the multiple action of the gauge transformed monodromy matrix elements on the pre-Bethe vector and conceive the result in terms of a partition function of the 8-vertex model.
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