| Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions |
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| 作者姓名： | 郭翠仙 陈澍 |
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| 作者单位： | 1.Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;2.School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;3.Yangtze River Delta Physics Research Center, Liyang 213300, China |
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| 基金项目： | the National Key Research and Development Program of China(Grant No.2016YFA0300600);the National Natural Science Foundation of China(Grant No.11974413);the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB33000000). |
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| 摘 要： | We study the one-dimensional general non-Hermitian models with asymmetric long-range hopping and explore how to analytically solve the systems under some specific boundary conditions.Although the introduction of long-range hopping terms prevents us from finding analytical solutions for arbitrary boundary parameters,we identify the existence of exact solutions when the boundary parameters fulfill some constraint relations,which give the specific boundary conditions.Our analytical results show that the wave functions take simple forms and are independent of hopping range,while the eigenvalue spectra display rich model-dependent structures.Particularly,we find the existence of a special point coined as pseudo-periodic boundary condition,for which the eigenvalues are the same as those of the periodical system when the hopping parameters fulfill certain conditions,whereas the eigenstates display the non-Hermitian skin effect.
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| 关 键 词： | non-Hermitian physics exact solution topological physics long-range hopping |
| 收稿时间： | 2021-09-13 |
Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions |
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| Cui-Xian Guo,Shu Chen.Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions[J].Chinese Physics B,2022,31(1):10313-010313. |
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| Authors: | Cui-Xian Guo Shu Chen |
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| Affiliation: | 1.Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;2.School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;3.Yangtze River Delta Physics Research Center, Liyang 213300, China |
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| Abstract: | We study the one-dimensional general non-Hermitian models with asymmetric long-range hopping and explore how to analytically solve the systems under some specific boundary conditions. Although the introduction of long-range hopping terms prevents us from finding analytical solutions for arbitrary boundary parameters, we identify the existence of exact solutions when the boundary parameters fulfill some constraint relations, which give the specific boundary conditions. Our analytical results show that the wave functions take simple forms and are independent of hopping range, while the eigenvalue spectra display rich model-dependent structures. Particularly, we find the existence of a special point coined as pseudo-periodic boundary condition, for which the eigenvalues are the same as those of the periodical system when the hopping parameters fulfill certain conditions, whereas the eigenstates display the non-Hermitian skin effect. |
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| Keywords: | non-Hermitian physics exact solution topological physics long-range hopping |
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