论文标题
双曲线晶格中真实空间拓扑的平面乐队和乐队接触
Flat bands and band touching from real-space topology in hyperbolic lattices
论文作者
论文摘要
通过最近在电路量子电动力学和经典电路网络中对双曲线晶格的实验实现的动机，我们研究了此类晶格中的平坦频带和带触摸的现象。我们分析了与Kagome双曲线类似物的非相互作用的近邻居跳跃模型，并用七型和八角形对称性分析了骰子晶格。我们表明，这些模型的能量谱的两个特征特征，即平面频段中的状态的比例以及平面频段和色散频段之间的接触点数量，都可以通过真实空间拓扑参数和相互空间的相结合来捕获。此外，在具有周期性边界条件的有限晶格上使用真实空间数值对角线化，我们获得了对非欧几里得（Fuchsian）双曲线晶格翻译组的高维不可减少表示的新见解。首先，我们发现平面条带中的比例对于阿贝利安和非阿贝尔双曲线状态是相同的。其次，我们发现只有阿贝利亚国家参与平面和分散频段之间的接触点的形成。
Motivated by the recent experimental realizations of hyperbolic lattices in circuit quantum electrodynamics and in classical electric-circuit networks, we study flat bands and band-touching phenomena in such lattices. We analyze noninteracting nearest-neighbor hopping models on hyperbolic analogs of the kagome and dice lattices with heptagonal and octagonal symmetry. We show that two characteristic features of the energy spectrum of those models, namely the fraction of states in the flat band as well as the number of touching points between the flat band and the dispersive bands, can both be captured exactly by a combination of real-space topology arguments and a reciprocal-space description via the formalism of hyperbolic band theory. Furthermore, using real-space numerical diagonalization on finite lattices with periodic boundary conditions, we obtain new insights into higher-dimensional irreducible representations of the non-Euclidean (Fuchsian) translation group of hyperbolic lattices. First, we find that the fraction of states in the flat band is the same for Abelian and non-Abelian hyperbolic Bloch states. Second, we find that only Abelian states participate in the formation of touching points between the flat and dispersive bands.
