Abstract
To begin with, we introduce several exact models for SU(3) spin chains: First is a translationally invariant parent Hamiltonian involving four-site interactions for the trimer chain, with a threefold degenerate ground state. We provide numerical evidence that the elementary excitations of this model transform under representation of SU(3) if the original spins of the model transform under representation 3. Second is a family of parent Hamiltonians for valence bond solids of SU(3) chains with spin representations 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 . Finally, we use the emerging rules for the construction of valence bond solid states to argue that models of antiferromagnetic chains of 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 which is divisible by . If and have no common divisor, the spin chain will support deconfined spinons and not exhibit a Haldane gap. If and have a common divisor different from , it will depend on the specifics of the model including the range of the interaction.
8 More- Received 19 January 2007
DOI:https://doi.org/10.1103/PhysRevB.75.184441
©2007 American Physical Society