Algebraic Bethe Ansatz for SO(N)-invariant transfer matrices

Rafael I. Nepomechie, Ana L. Retore

Integrable open quantum spin-chain transfer matrices constructed from trigonometric R-matrices associated to affine Lie algebras g ˆ , and from certain K-matrices (reflection matrices) depending on a discrete parameter p , were recently considered in arXiv:1802.04864 and arXiv:1805.10144 . It was shown there that these transfer matrices have quantum group symmetry corresponding to removing the p th node from the g ˆ Dynkin diagram. Here we determine the spectrum of these transfer matrices by using analytical Bethe ansatz, and we determine the dependence of the corresponding Bethe equations on p . We propose formulas for the Dynkin labels of the Bethe states in terms of the numbers of Bethe roots of each type. We also briefly study how duality transformations are implemented on the Bethe ansatz solutions.

C.S. Melo, Marcio Jose Martins

Simone Artz, Luca Mezincescu, Rafael I. Nepomechie

We determine the eigenvalues of the transfer matrices for integrable open quantum spin chains which are associated with the affine Lie algebras A 2n-1 (2) , B n (1) , C n (1) , D n (1) , and which have the quantum-algebra invariance U q (C n ), U q (B n ), U q (C n ), U q (D n ), respectively.

Marcio Jose Martins

P. P. Kulish, Nicolai Reshetikhin

The algebraic Bethe ansatz is constructed for the GL(N) invariant transfer matrices with arbitrary GL(N) spin. For this purpose the notion of vacuum subspace is introduced. It is shown that the GL(N) magnet can be interpreted as an integrable discrete approximation of vector or matrix nonlinear Schrodinger models or of the quantum N-wave system.

Marcio Jose Martins, C.S. Melo