Guided by the recent discovery of chiral spin liquids on the square lattice for SU(2) and SU(3) models, we propose a family of generic time-reversal symmetry breaking SU(N)-symmetric models of arbitrary N (in the fundamental representation). By using a combination of state-of-the-art numerical methodes (exact diagonalization, DMRG and PEPS), we provide strong evidence for the existence of a chiral spin liquid ground-state.
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