Algebraic Bethe Ansatz for spinor R-matrices

Abstract

We present a supermatrix realisation of q-deformed spinor-spinor and spinor-vector R-matrices. These R-matrices are then used to construct transfer matrices for U q 2 (so 2n+1 )-and Uq(so 2n+2 )-symmetric closed spin chains. Their eigenvectors and eigenvalues are computed. Contents1. Introduction 1 2. Spinor R-matrices 2 3. Algebraic Bethe Ansatz for U q 2 (so 2n+1 )-symmetric spin chains 15 4. Algebraic Bethe Ansatz for U q (so 2n+2 )-symmetric spin chains 21 5. Conclusions and Outlook 29 Appendix A. The semi-classical limit 29 References 31

Bethe vectors and recurrence relations for twisted Yangian based models

“…The exchange relations between these matrix operators turn out to be reminiscent of those of the six-vertex model. Such techniques have been used to study one-dimensional so 2n -and sp 2n -symmetric spin chains in [Rsh91,GP16,GR20,Rg22].…”