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Flat-band Ferromagnetism of SU$(N)$ Hubbard Model on the Kagome Lattices

The kagome lattice, a well known example of the geometrically frustrated system, hosts a dispersionless flat band that offers a unique platform for studying correlation-driven quantum phenomena. At appropriate particle concentrations, the existence of a flat band allows a representation of percolation with nontrivial weights. In this work, we investigate the paramagnetic-ferromagnetic transition in the repulsive SU($N$) Hubbard model on the kagome lattice within this percolation framework. In this representation, the model can be rigorously mapped to a classical $N$-state site-percolation problem on a triangular lattice, with the SU($N$) symmetry reflected in the nontrivial weights. By large-scale Monte Carlo simulations for SU($3$), SU($4$), and SU($10$) symmetries, we demonstrate that the critical particle concentration for ferromagnetism exceeds the standard percolation threshold and increases with $N$, indicating a strengthening of the effective entropic repulsion.