Quasi-classical descendants of disordered vertex models with boundaries

We study descendants of inhomogeneous vertex models with boundary reflections when the spin–spin scattering is assumed to be quasi-classical. This corresponds to consider certain power expansion of the boundary-Yang–Baxter equation (or reflection equation). As final product, integrable su(2)-spin chains interacting with a long range with XXZ anisotropy are obtained. The spin–spin coupling constants are non-uniform, and a non-uniform tunable external magnetic field is applied; the latter can be obtained when the boundary conditions are assumed to be quasi-classical as well. The exact spectrum is achieved by algebraic Bethe ansatz. Having realized the su(2) operators in terms of fermions, the class of models we found turns out to describe confined fermions with pairing force interactions. The class of models presented in this paper is a one-parameter extension of certain Hamiltonians constructed previously. Extensions to su(n)-spin open chains are discussed.