Abstract
The critical limit of the eight-vertex model eigenvectors obtained by means of the generalized Bethe Ansatz is shown to give the six-vertex eigenvectors as constructed in a previous paper by two of the authors. Furthermore, an explicit mapping is established between these eigenvectors and the usual Bethe Ansatz eigenvectors of the six-vertex model. This allows one to show that the indexv labeling the eight-vertex eigenstates becomes exactly the third component of the total spin in the critical limit.
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Destri, C., de Vega, H.J. & Giacomini, H.J. The six-vertex model eigenvectors as critical limit of the eight-vertex model bethe ansatz. J Stat Phys 56, 291–308 (1989). https://doi.org/10.1007/BF01044438
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DOI: https://doi.org/10.1007/BF01044438