奇维上的局部拓扑标记
Local Topological Markers in Odd Dimensions
摘要：
局部拓扑标记已被证明是一个有价值的工具，研究系统的拓扑非平凡带。由于它们的局部性质，这样的标记可以平等地对待几何不变系统和空间非齐次系统。其中最流行的是所谓的陈氏标记，它可用于两个空间维度的系统。在本文中，我们描述了如何推广这一标记到一维和三维系统，通过显示相关的表达式准确地描述了拓扑泵的现象给出的第一和第二陈数在一维和三维分别。除了提供一般的推导，我们验证了标记，通过数值考虑模型哈密顿。这些结果将为今后的研究打开大门，包括在奇维系统中的拓扑泵浦和拓扑相变的无序的影响。
英文摘要：
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.
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