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Algebraic Bethe Ansatz for a seven-vertex model

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Abstract

The paper is devoted to construction of algebraic Bethe Ansatz for a seven-vertex model. R-matrix of the system is obtained by means of twist from the six-vertex model considered by us earlier. The presence of the seventh nonzero element in the R-matrix complicates the situation. In particular, commutation relations of elements of the monodromy matrix become more complicated in comparison with the six-vertex model. We construct algebraic Bethe Ansatz by introducing a new operator that is the difference of two operators on the main diagonal of the monodromy matrix. The eigenstates and spectrum of the system are found. This is the first step on the way of comparison of systems with six-and seven-vertex R-matrices, respectively. Bibliography: 8 titles.

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  1. St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg, Russia

    P. P. Kulish & P. D. Ryasichenko

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  1. P. P. Kulish
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  2. P. D. Ryasichenko
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 347, 2007, pp. 178–186.

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Kulish, P.P., Ryasichenko, P.D. Algebraic Bethe Ansatz for a seven-vertex model. J Math Sci 151, 2901–2906 (2008). https://doi.org/10.1007/s10958-008-9012-8

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  • DOI: https://doi.org/10.1007/s10958-008-9012-8

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