一维准晶与拓扑标记
1D quasicrystals and topological markers
摘要：
局部拓扑标记是确定齐次和非齐次系统拓扑性质的有效工具。Chern标记是一种已建立的拓扑标记，以前已被证明可以有效地揭示2D系统的拓扑特性。在早期的工作中，本文作者开发了一种标记，可以应用于一维时间依赖系统，可以用来探索它们的拓扑性质，如在无序存在下的电荷泵。在本文中，我们将展示如何改变1D标记，使其可以应用于准周期和非周期系统。然后，我们验证其有效性对不同的准晶哈密顿，其中一些已经解决了在以前的研究中使用现有的方法，和其他具有拓扑结构，在很大程度上尚未探索。我们还表明，改变的1D标记可以有效地应用于系统是完全非周期性的。
英文摘要：
Local topological markers are effective tools for determining the topological properties of both homogeneous and inhomogeneous systems. The Chern marker is an established topological marker that has previously been shown to effectively reveal the topological properties of 2D systems. In an earlier work, the present authors have developed a marker that can be applied to 1D time-dependent systems which can be used to explore their topological properties, like charge pumping under the presence of disorder. In this paper, we show how to alter the 1D marker so that it can be applied to quasiperiodic and aperiodic systems. We then verify its effectiveness against different quasicrystal Hamiltonians, some which have been addressed in previous studies using existing methods, and others which possess topological structures that have been largely unexplored. We also demonstrate that the altered 1D marker can be productively applied to systems that are fully aperiodic.
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