1 2 Ju l 2 00 1 Non - regular eigenstate of the XXX model as some limit of the Bethe state Tetsuo
نویسنده
چکیده
For the one-dimensional XXX model under the periodic boundary conditions, we discuss two types of eigenvectors, regular eigenvectors which have finite-valued rapidities satisfying the Bethe ansatz equations, and non-regular eigenvectors which are descendants of some regular eigenvectors under the action of the SU(2) spin-lowering operator. It was pointed out by many authors that the non-regular eigenvectors should correspond to the Bethe ansatz wavefunctions which have multiple infinite rapidities. However, it has not been explicitly shown whether such a delicate limiting procedure should be possible. In this paper, we discuss it explicitly in the level of wavefunctions: we prove that any non-regular eigenvector of the XXX model is derived from the Bethe ansatz wavefunctions through some limit of infinite rapidities. We formulate the regularization also in terms of the algebraic Bethe ansatz method. As an application of infinite rapidity, we discuss the period of the spectral flow under the twisted periodic boundary conditions. [email protected] . 1
منابع مشابه
1 9 Ju l 2 00 1 Non - regular eigenstate of the XXX model as some limit of the Bethe state
For the one-dimensional XXX model under the periodic boundary conditions, we discuss two types of eigenvectors, regular eigenvectors which have finite-valued rapidities satisfying the Bethe ansatz equations, and non-regular eigenvectors which are descendants of some regular eigenvectors under the action of the SU(2) spin-lowering operator. It was pointed out by many authors that the non-regular...
متن کامل2 00 1 Non - regular eigenstate of the XXX model as some limit of the Bethe state
For the one-dimensional XXX model under the periodic boundary conditions, we discuss two types of eigenvectors, regular eigenvectors which have finite-valued rapidities satisfying the Bethe ansatz equations, and non-regular eigenvectors which are descendants of some regular eigenvectors under the action of the SU(2) spin-lowering operator. It was pointed out by many authors that the non-regular...
متن کاملRegular XXZ Bethe states at roots of unity – as highest weight vectors of the sl 2 loop
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 ...
متن کاملXXZ 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 ...
متن کاملBethe states as highest weight vectors of the sl 2 loop algebra at roots of unity
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 کامل