Exactly solvable quantum spin ladders associated with the orthogonal and symplectic Lie algebras

Abstract

We extend the results of spin ladder models associated with the Lie algebras su(2n) to the case of the orthogonal and symplectic algebras o(2n), sp(2n) where n is the number of legs for the system. Two classes of models are found whose symmetry, either orthogonal or symplectic, has an explicit n dependence. Integrability of these models is shown for an arbitrary coupling of X X-type rung interactions and applied magnetic field term.