Boundary Algebraic Bethe Ansatz for a nineteen vertex model with $U_q[\mathrm{osp}(2|2{)}^{(2)}]$ symmetry

Abstract

The boundary algebraic Bethe Ansatz for a supersymmetric nineteen vertex-model constructed from a three-dimensional representation of the twisted quantum affine Lie superalgebra $U_q[\mathrm{osp}(2|2{)}^{(2)}]$ is presented. The eigenvalues and eigenvectors of Sklyanin's transfer matrix, with diagonal reflection $K$-matrices, are calculated and the corresponding Bethe Ansatz equations are obtained.

Keywords: Algebraic Bethe Ansatz, Open boundary conditions, Lie superalgebras, twisted Lie algebras, nineteen vertex-models