Algebraic Bethe Ansatz solutions for the $sl(2|1)^{(2)}$ and $osp(2|1)$ models with boundary terms

Abstract

This work is concerned with the formulation of the graded quantum inverse scattering method for a class oflattice models with reflecting boundary conditions. The $sl(2|1)^{(2)}$ and $osp(2|1)$ models are considered with their diagonal reflections in BFB grading. This allowed us to derive the eigenvalues and eigenvectors for the corresponding transfer matrices as well as explicit expressions for the Bethe Ansatz equations.