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

TL;DR

This paper explores how flat bands in the kagome lattice influence ferromagnetism in the SU(N) Hubbard model, revealing that higher N values raise the critical concentration needed for ferromagnetic order, using a percolation approach.

Contribution

It introduces a novel percolation framework to analyze ferromagnetism in the SU(N) Hubbard model on kagome lattices, connecting quantum phenomena with classical percolation theory.

Findings

Critical particle concentration for ferromagnetism exceeds standard percolation threshold.

Critical concentration increases with N, indicating stronger entropic effects.

Monte Carlo simulations confirm the theoretical predictions.

Abstract

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.