Regular XXZ Bethe states at roots of unity as highest weight vectors of the sl2 loop algebra
نویسنده
چکیده
Abstract. We show that every regular Bethe ansatz eigenvector of the XXZ spin chain at roots of unity is a highest weight vector of the sl2 loop algebra, for some restricted sectors with respect to eigenvalues of the total spin operator S , and evaluate explicitly the highest weight in terms of the Bethe roots. We also discuss whether a given regular Bethe state in the sectors generates an irreducible representation or not. In fact, we present such a regular Bethe state in the inhomogeneous case that generates a reducible Weyl module. Here, we call a solution of the Bethe ansatz equations which is given by a set of distinct and finite rapidities regular Bethe roots. We call a nonzero Bethe ansatz eigenvector with regular Bethe roots a regular Bethe state.
منابع مشابه
XXZ Bethe states as highest weight vectors of the sl2 loop algebra at roots of unity
We show that regular Bethe ansatz eigenvectors of the XXZ spin chain at roots of unity are highest weight vectors and generate irreducible representations of the sl2 loop algebra. We show it in some sectors with respect to eigenvalues of the total spin operator SZ . Here the parameter q, which is related to the XXZ anisotropy ∆ through ∆ = (q + q−1)/2, is given by a root of unity, q2N = 1, for ...
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We show that regular Bethe ansatz eigenvectors of the XXZ spin chain at roots of unityare highest weight vectors and generate irreducible representations of the sl2 loop algebra.Here the parameter q, which is related to the XXZ anisotropy ∆ through ∆ = (q+q−1)/2,is given by a root of unity, q2N = 1, for an integer N . First, for a regular Bethe stateat a root of unity, we sh...
متن کاملBethe states as the highest weight vector of the sl 2 loop algebra at roots of unity
We prove that the regular Bethe ansatz eigenvectors of the XXZ spin chain at roots of unity are the highest weight vectors of the sl2 loop algebra. Here the variable q is related to the XXZ coupling parameter ∆ by ∆ = (q + q−1)/2, and it is given by a root of unity: q2N = 1. It follows that the regular Bethe state gives the highest weights of the Drinfeld generators of Uq(L(sl2)). Thus, we can ...
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We show that every regular Bethe ansatz eigenstate of the XXZ spin chain at roots of unity is a highest weight vector of the sl2 loop algebra and discuss whether it generates an irreducible representation or not. We show it in some sectors with respect to eigenvalues of the total spin operator SZ . The parameter q is given by a root of unity, q2N 0 = 1, for an integer N . Here, q is related to ...
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We review the main result of cond-mat/0503564. The Hamiltonian of the XXZ spin chain and the transfer matrix of the six-vertex model has the sl2 loop algebra symmetry if the q parameter is given by a root of unity, q 0 = 1, for an integer N . We discuss the dimensions of the degenerate eigenspace generated by a regular Bethe state in some sectors, rigorously as follows: We show that every regul...
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