Abstract
We study N-component interacting particles (hardcore bosons and fermions) loaded in topological lattice models with SU(N)-invariant interactions based on density matrix renormalization group method. By tuning the interplay of interspecies and intraspecies interactions, we demonstrate that a class of SU(N) fractional quantum Hall states can emerge at fractional filling factors ν=N/(N+1) for bosons (ν=N/(2N+1) for fermions) in the lowest Chern band, characterized by the nontrivial fractional Hall responses and the fractional charge pumping. Moreover, we establish a topological characterization based on the K matrix, and discuss the close relationship to the fractional quantum Hall physics in topological flat bands with Chern number N.