| Summary: | SU(N) Mott insulators have been proposed and/or realized in solid-state materials and with ultracold atoms on optical lattices. We study the two-dimensional SU(N) antiferromagnets on the triangular lattice. Starting from an SU(N) Heisenberg model with the fundamental representation on each site in the large-N limit, we perform a self-consistent calculation and find a variety of ground states including the valence cluster states, stripe ordered states with a doubled unit cell, and topological chiral spin liquids. The system favors a cluster or ordered ground state when the number of flavors N is less than 6. It is shown that increasing the number of flavors enhances quantum fluctuations and eventually transfers the clusterized ground states into topological chiral spin liquids. This chiral spin liquid ground state has an equivalent for the square lattice SU(N) magnets. We further identify the corresponding lowest competing states that represent another distinct type of chiral spin liquid state. We conclude with a discussion of the relevant systems and the experimental probes.
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