Abstract
We describe here the extension of the density matrix renormalization group algorithm to the case where the Hamiltonian has a non-Abelian global symmetry group. The block states transform as irreducible representations of the non-Abelian group. Since the representations are multi-dimensional, a single block state in the new representation corresponds to multiple states of the original density matrix renormalization group basis. We demonstrate the usefulness of the construction via the one-dimensional Hubbard model as the symmetry group is enlarged from U(1)×U(1), up to SU(2)×SU(2).