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The integer quantum Hall state occurs when the Landau levels are fullyoccupied by the fermions, while the fractional quantum Hall state usuallyemerges when the Landau level is partially filled by the strongly correlatedfermions or bosons. Here, we report two fractional Chern insulating states ofthe hard-core bosons in a multi-band lattice model hosting topological flatbands with high Chern number. The previously proposed $\nu=1/3$ fractionalChern insulating state inherited from the high Chern number $C=2$ of the lowesttopological flat band is revisited by the infinite density matrixrenormalization group algorithm. In particular, we numerically identify abosonic $1/2$-Laughlin-like fractional Chern insulating state at the integerfillings. We show two lower topological flat bands jointly generate aneffective $C=1$ Chern band with half-filling. Furthermore, we find a strictlyparticle-hole-like symmetry between the $\nu$ and $3-\nu$ filling in our model.These findings extend our understanding of quantum Hall states and offer a newroute to realize the novel fractional states in the system with multi-bands andhigh-Chern numbers.

Bosonic fractional Chern insulating state at integer fillings in multi-band system