The topological properties of a generalized non‐Hermitian Su–Schrieffer–Heeger model are investigated and it is demonstrated that the non‐Hermitian phase transition and the non‐Hermitian skin effect can be induced by intra‐cell asymmetric coupling under open boundary conditions. Through investigating and calculating the non‐Hermitian winding number with generalized Brillouin zone theory, it is found that the present non‐Hermitian system has an exact bulk‐boundary correspondence relationship. Meanwhile, the non‐Hermitian winding number is used to characterize the non‐Hermitian phase transition and determine the phase transition boundary, and it is found that the non‐Hermitian phase transition is not completely induced by the asymmetric coupling strength. By means of the mean inverse participation ratio, the factors that affect the eigenstates localization are shown and it is revealed that large system size or large asymmetric coupling strength can leave the system in the localized state. Additionally, it is found that for the asymmetric coupling strength and the system size, the eigenstates localization is much more sensitive to the asymmetric coupling strength.

中文翻译：

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广义非Hermitian Su-Schrieffer-Heeger模型中的拓扑相变和本征态局部化

研究了广义非Hermitian Su-Schrieffer-Heeger模型的拓扑性质，并证明了在开放边界条件下，细胞内非对称耦合可诱发非Hermitian相变和非Hermitian趋肤效应。通过用广义布里渊区理论研究和计算非厄密绕组数，发现当前的非厄密系统具有精确的体边界对应关系。同时，利用非埃尔米特绕组数来表征非埃尔米特相变并确定相变边界，并且发现非埃尔米特相变并非完全由非对称耦合强度引起。通过平均反向参与率，给出了影响本征态局部化的因素，结果表明，较大的系统尺寸或较大的不对称耦合强度会使系统处于局部状态。此外，发现对于不对称耦合强度和系统大小，本征态局部化对不对称耦合强度更为敏感。