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SU($N$) Mott insulators have been proposed and/or realized in solid-statematerials and with ultracold atoms on optical lattices. We study thetwo-dimensional SU($N$) antiferromagnets on the triangular lattice. Startingfrom an SU($N$) Heisenberg model with the fundamental representation on eachsite in the large-$N$ limit, we perform a self-consistent calculation and finda variety of ground states including the valence cluster states, stripe orderedstates with a doubled unit-cell and topological chiral spin liquids. The systemfavors a cluster or ordered ground state when the number of flavors $N$ is lessthan 6. It is shown that, increasing the number of flavors enhances quantumfluctuations and eventually transfer the clusterized ground states into atopological chiral spin liquids. This chiral spin liquid ground state has anequivalent for the square lattice SU($N$) magnets. We further identify thecorresponding lowest competing states that represent another distinct type ofchiral spin liquid states. We conclude with a discussion about the relevantsystems and the experimental probes.

Topological chiral spin liquids and competing states in triangular lattice SU($N$) Mott insulators