Integrable models of quantum one-dimensional magnets with $O(n)$ and $Sp(2k)$ symmetry

A new family of quantum one-dimensional magnets with $O(n)$ and $Sp(2k)$ symmetry is found. The eigenvalues of the corresponding transfer matrices on a finite lattice are calculated. A generalization of the matrix Bethe ansatz to systems with complicated pseudovacuum is proposed.