论文标题
奇数尺寸的本地拓扑标记
Local Topological Markers in Odd Dimensions
论文作者
论文摘要
事实证明，本地拓扑标记是研究具有拓扑非平凡带的系统的宝贵工具。由于其局部性质，这种标记可以在平等的基础上处理翻译不变的系统和空间不均匀的系统。其中最普遍的是所谓的Chern标记，该标记可用于两个空间维度的系统。在本文中，我们描述了如何将此标记概括为1D和3D系统，通过表明相关表达式准确地描述了分别在1D和3D中的第一和第二Chern数字给出的拓扑泵送现象。除了提供一般推导外，我们还通过数字考虑模型汉密尔顿人来验证标记。这些结果将为将来的研究打开大门，包括疾病对奇数差系统中拓扑泵送和拓扑相变的影响。
Local topological markers have proven to be a valuable tool for investigating systems with topologically non-trivial bands. Due to their local nature, such markers can treat translationally invariant systems and spatially inhomogeneous systems on an equal footing. Among the most prevalent of these is the so-called Chern marker, which is available for systems in two spatial dimensions. In this paper, we describe how to generalize this marker to 1d and 3d systems, by showing that the relevant expressions accurately describe the phenomenon of topological pumping given by the first and second Chern numbers in 1d and 3d respectively. In addition to providing general derivations, we verify the markers by numerically considering model Hamiltonians. These results will open the door for future studies including the influence of disorder on topological pumping and topological phase transitions in odd-dimensional systems.
