We study $N$-component interacting particles (hardcore bosons and fermions)loaded in topological lattice models with SU$(N)$-invariant interactions basedon density matrix renormalization group method. By tuning the interplay ofinterspecies and intraspecies interactions, we demonstrate that a class ofSU$(N)$ fractional quantum Hall states can emerge at fractional filling factors$\nu=N/(N+1)$ for bosons ($\nu=N/(2N+1)$ for fermions) in the lowest Chernband, characterized by the nontrivial fractional Hall responses and thefractional charge pumping. Moreover, we establish a topologicalcharacterization based on the $\mathbf{K}$ matrix, and discuss the closerelationship to the fractional quantum Hall physics in topological flat bandswith Chern number $N$.
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机译：我们基于密度矩阵重归一化群方法，利用SU $（N）$不变相互作用研究了拓扑格子模型中加载的$ N $组分相互作用粒子（核玻色子和费米子）。通过调整种间相互作用和种间相互作用，我们证明了一类SU $（N）$分数量子霍尔态可以在玻色子的分数填充因子$ \ nu = N /（N + 1）$处出现（$ \ nu = N /（2N + 1）$（对于费米子而言）在最低的Chernband中，其特征在于非平凡的分数霍耳响应和分数电荷泵浦。此外，我们建立基于$ \ mathbf {K} $矩阵的拓扑特征，并讨论与Chern数为$ N $的拓扑平坦带中分数量子霍尔物理学的紧密关系。
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