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We study the zero temperature phase diagram of a class of two-dimensionalSU(N) antiferromagnets. These models are characterized by having the same typeof SU(N) spin placed at each site of the lattice, and share the property that,in general, more than two spins must be combined to form a singlet. Animportant motivation to study these systems is that they may be realizednaturally in Mott insulators of alkaline earth atoms placed on opticallattices; indeed, such Mott insulators have already been obtainedexperimentally, although the temperatures are still high compared to themagnetic exchange energy. We study these antiferromagnets in a large-N limit,finding a variety of ground states. Some of the models studied here have avalence bond solid ground state, as was found in prior studies, yet we findthat many others have a richer variety of ground states. Focusing on thetwo-dimensional square lattice, in addition to valence cluster states (whichare analogous to valence bond states), we find both Abelian and non-Abelianchiral spin liquid ground states, which are magnetic counterparts of thefractional quantum Hall effect. We also find a "doubled" chiral spin liquidground state that preserves time reversal symmetry. These results are based ona combination of rigorous lower bounds on the large-N ground state energy, anda systematic numerical ground state search. We conclude by discussing whetherexperimentally relevant SU(N) antiferromagnets -- away from the large-N limit-- may be chiral spin liquids.

Topological liquids and valence cluster states in two-dimensional SU(N) magnets