Abstract In this paper, we have studied spinless fermions in four specific quasi one-dimensional systems that are known to host flat bands in the noninteracting limit: the triangle lattice, the stub lattice, the diamond lattice, and the diamond lattice with transverse hopping. The influence of the nearest neighbour interaction on the flat bands was investigated. We used exact diagonalization of finite size lattices employing the Lanczos technique and determine the single particle spectral functions of the interacting system. Our results are compared with mean field calculations. In the cases of the triangle lattice and the stub lattice we found that the flat bands become dispersive in the presence of a finite interaction. For the diamond lattice and the diamond lattice with transverse hopping, we demonstrated that the flat bands are robust under the influence of the interaction in certain parameter ranges. Such systems could be realised experimentally with cold atoms in optical lattices.

中文翻译：

---

费米子准一维平带晶格中的最近邻粒子-粒子相互作用

摘要 在本文中，我们研究了四种特定准一维系统中的无自旋费米子，这些系统已知在非相互作用极限中包含平坦带：三角形晶格、短节晶格、菱形晶格和具有横向跳跃的菱形晶格。研究了最近邻相互作用对平坦带的影响。我们使用 Lanczos 技术对有限尺寸晶格进行精确对角化，并确定相互作用系统的单粒子谱函数。我们的结果与平均场计算进行了比较。在三角形格子和短节格子的情况下，我们发现在有限相互作用的情况下，平带变得分散。对于菱形格子和横向跳跃的菱形格子，我们证明了在某些参数范围内的相互作用的影响下，平坦带是稳健的。这样的系统可以通过光学晶格中的冷原子实验实现。