  To begin with, we introduce several exact models for SU(3) spin chains: (1) a
translationally invariant parent Hamiltonian involving four-site interactions
for the trimer chain, with a three-fold degenerate ground state. We provide
numerical evidence that the elementary excitations of this model transform
under representation 3bar of SU(3) if the original spins of the model transform
under rep. 3. (2) a family of parent Hamiltonians for valence bond solids of
SU(3) chains with spin reps. 6, 10, and 8 on each lattice site. We argue that
of these three models, only the latter two exhibit spinon confinement and hence
a Haldane gap in the excitation spectrum. We generalize some of our models to
SU(n). Finally, we use the emerging rules for the construction of VBS states to
argue that models of antiferromagnetic chains of SU(n) spins in general possess
a Haldane gap if the spins transform under a representation corresponding to a
Young tableau consisting of a number of boxes \lambda which is divisible by n.
If \lambda and n have no common divisor, the spin chain will support deconfined
spinons and not exhibit a Haldane gap. If \lambda and n have a common divisor
different from n, it will depend on the specifics of the model including the
range of the interaction.
