论文标题
用革兰氏矩阵构建平面晶格型号
Building Flat-Band Lattice Models from Gram Matrices
论文作者
论文摘要
我们提出了一种功能强大且方便的方法来系统地设计平面晶格模型，从而克服了先前方法的困难。特别是，我们的方法不需要精心计算，适用于任意空间维度，并保证导致完全平坦的地面带。我们使用此方法来生成几类晶格模型，包括具有短距离和长距离跳的模型，包括拓扑和非平凡的平坦频段。这些模型中的一些以前是已知的。但是，我们的方法提供了至关重要的新见解。例如，我们已经重现并概括了Kapit-Mueller模型[Kapit and Mueller，Phys。莱特牧师。 \ textbf {105}，215303（2010）]，并在以前的研究中没有注意到平面带退化和磁通量之间的普遍缩放规则。我们表明，该模型的平坦频段是由相干状态的（过度）完整性属性引起的。
We propose a powerful and convenient method to systematically design flat-band lattice models, which overcomes the difficulties underlying the previous method. Especially, our method requires no elaborate calculations, applies to arbitrary spatial dimensions, and guarantees to result in a completely flat ground band. We use this method to generate several classes of lattice models, including models with both short- and long-range hoppings, both topologically trivial and non-trivial flat bands. Some of these models were previously known. Our method, however, provides crucial new insights. For example, we have reproduced and generalized the Kapit-Mueller model [Kapit and Mueller, Phys. Rev. Lett. \textbf{105}, 215303 (2010)] and demonstrated a universal scaling rule between the flat band degeneracy and the magnetic flux that was not noticed in previous studies. We show that the flat band of this model results from the (over-)completeness properties of coherent states.
