论文标题
在有限的开放性手性链中估算散装和边缘拓扑指数
Estimating bulk and edge topological indices in finite open chiral chains
论文作者
论文摘要
我们开发一种形式主义，同时扩展了从拓扑绝缘子到具有开放边界条件的有限样本的情况，通常将散装和边缘指数定义，并提供对这些数量的物理解释。然后，我们表明，当我们增加系统尺寸时，它们会呈指数级的汇合到整数值，并且在有限尺寸的情况下，大量和边缘的数量重合。该定理适用于任何非均匀系统，例如无序或缺陷构型。我们专注于带有手性对称性的一维链，例如Su-Schrieffer-Heeger模型，但实际上，证明只要求哈密顿量是短距离的，并且在散装中具有光谱差距。散装和边缘指数的定义依赖于开关功能形式的有限大小版本，在该版本中，使用精心选择的正则化参数在能量中平滑了费米投影仪。
We develop a formalism to extend, simultaneously, the usual definition of bulk and edge indices from topological insulators to the case of a finite sample with open boundary conditions, and provide a physical interpretation of these quantities. We then show that they converge exponentially fast to an integer value when we increase the system size, and also that bulk and edge quantities coincide at finite size. The theorem applies to any non-homogeneous system such as disordered or defect configurations. We focus on one-dimensional chains with chiral symmetry, such as the Su-Schrieffer-Heeger model, but the proof actually only requires the Hamiltonian to be short-range and with a spectral gap in the bulk. The definition of bulk and edge indices relies on a finite-size version of the switch-function formalism where the Fermi projector is smoothed in energy using a carefully chosen regularization parameter.
