Line-Graph Lattices: Euclidean and Non-Euclidean Flat Bands, and Implementations in Circuit Quantum Electrodynamics
Line-Graph Lattices: Euclidean and Non-Euclidean Flat Bands, and Implementations in Circuit Quantum Electrodynamics
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DOI：
10.1007/s00220-019-03645-8
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发表时间：
2020-06-01
影响因子：
2.4
通讯作者：
Houck, Andrew A.
中科院分区：
文献类型：
--
作者：
Kollar, Alicia J.;Fitzpatrick, Mattias;Houck, Andrew A.
材料科学和固体电子性质的研究是物理学和工程学的一个主要领域。所有这些计算的出发点是单电子或非相互作用的能带结构计算，并且在强现场限制的限制下，这可以简化为图状紧束缚模型。在这种背景下，数学家和物理学家都开发了基本上独立的方法来解决这些模型。在本文中，我们将联合收割机和目前的结果，从这两个领域。特别是，我们将讨论一类格，它可以实现为其他格的线图，无论是在欧氏空间和双曲空间。这些晶格显示非常不寻常的功能，包括平带和本地化的本征态的紧凑的支持。我们将使用这两个领域的方法来展示这些属性是如何产生的，以及对这些晶格的现象学进行分类的系统，以及最大化间隙的标准。此外，我们将提出一个特定的硬件实现使用超导共面波导谐振器，可以实现各种各样的这些晶格在非相互作用和相互作用的形式。
Materials science and the study of the electronic properties of solids are a major field of interest in both physics and engineering. The starting point for all such calculations is single-electron, or non-interacting, band structure calculations, and in the limit of strong on-site confinement this can be reduced to graph-like tight-binding models. In this context, both mathematicians and physicists have developed largely independent methods for solving these models. In this paper we will combine and present results from both fields. In particular, we will discuss a class of lattices which can be realized as line graphs of other lattices, both in Euclidean and hyperbolic space. These lattices display highly unusual features including flat bands and localized eigenstates of compact support. We will use the methods of both fields to show how these properties arise and systems for classifying the phenomenology of these lattices, as well as criteria for maximizing the gaps. Furthermore, we will present a particular hardware implementation using superconducting coplanar waveguide resonators that can realize a wide variety of these lattices in both non-interacting and interacting form.