We present rigorous results for the SU( n ) Fermi–Hubbard models with finite-range hopping in d ( $$\ge 2$$ ≥ 2 ) dimensions. The models are defined on a class of decorated lattices. We first study the models with flat bands at the bottom of the single-particle spectrum and prove that the ground states exhibit SU( n ) ferromagnetism when the number of particles is equal to the number of unit cells. We then perturb the models by adding particular hopping terms and make the bottom bands dispersive. Under the same filling condition, it is proved that the ground states remain SU( n ) ferromagnetic when the bottom bands are sufficiently flat and the Coulomb repulsion is sufficiently large.

中文翻译：

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具有近平带的 d 维 SU(n) 哈伯德模型中的铁磁性

我们给出了在 d ($$\ge 2$$ ≥ 2 ) 维度上具有有限范围跳跃的 SU( n ) Fermi-Hubbard 模型的严格结果。这些模型是在一类装饰格子上定义的。我们首先研究了单粒子光谱底部平坦带的模型，并证明当粒子数等于晶胞数时，基态表现出 SU(n) 铁磁性。然后我们通过添加特定的跳跃项来扰乱模型并使底带分散。证明在相同填充条件下，当底带足够平坦且库仑斥力足够大时，基态保持SU(n)铁磁性。