The spectrum of an open vertex model based on the U_q[SU(2)] at roots of unity

Details The spectrum of an open vertex model based on the U_q[SU(2)] at roots of unity The spectrum of an open vertex model based on the U_q[SU(2)] at roots of unity

2009-11-20

arxiv.org/abs/0911.4069v1

Physics

Mathematical Physics

21 pages

Scientific paper

We study the exact solution of an $N$-state vertex model based on the representation of the $U_q[SU(2)]$ algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class of diagonal $K$-matrices having one free-parameter. We determine the eigenvalues of the double-row transfer matrix and the respective Bethe ansatz equation within the algebraic Bethe ansatz framework. The structure of the Bethe ansatz equation combine a pseudomomenta function depending on a free-parameter with scattering phase-shifts that are fixed by the roots of unity and boundary variables.

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