Nested algebraic Bethe ansaetze for orthogonal and symplectic spin chains

In this thesis the nested algebraic Bethe ansatz technique is applied to various orthogonal and symplectic closed and open spin chain models. Each spin chain considered is regarded as a representation of an underlying quantum group algebra, and expressions for eigenvectors of transfer matrices associated to these models are constructed using the algebra relations, reducing the problem to a set of Bethe equations. The specific models considered are the Ol'shanskii twisted Yangian spin chain, where gl_n bulk symmetry is broken to orthogonal or symplectic symmetry; the MacKay twisted Yangian spin chain, an open spin chain with bulk orthogonal or symplectic symmetry and various boundary types; and the q-deformed orthogonal or symplectic closed spin chain. For the first and third cases, a closed 'trace formula' expression for the eigenvector is also provided.