In this paper, we review our non-Bloch band theory in one-dimensional non-Hermitian tight-binding systems. In our theory, it is shown that in non-Hermitian systems, the Brillouin zone is determined so as to reproduce continuum energy bands in a large open chain. By using simple models, we explain the concept of the non-Bloch band theory and the method to calculate the Brillouin zone. In particular, for the non-Hermitian Su-Schrieffer-Heeger model, the bulk-edge correspondence can be established between the topological invariant defined from our theory and existence of the topological edge states.

中文翻译：

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非厄米系统中的非布洛赫带理论和体边对应

在本文中，我们回顾了一维非厄米紧束缚系统中的非布洛赫能带理论。在我们的理论中，表明在非厄米系统中，确定布里渊区以在大的开链中再现连续能带。通过使用简单的模型，我们解释了非布洛赫带理论的概念和布里渊区的计算方法。特别是，对于非 Hermitian Su-Schrieffer-Heeger 模型，可以在我们的理论定义的拓扑不变量和拓扑边缘状态的存在之间建立体边缘对应关系。