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Special Issue:
SPECIAL TOPIC — Non-Hermitian physics
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| SPECIAL TOPIC—Non-Hermitian physics |
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Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions |
| Cui-Xian Guo(郭翠仙)1 and Shu Chen(陈澍)1,2,3,† |
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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Received: 13 September 2021
Revised: 19 October 2021
Accepted manuscript online: 22 October 2021
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PACS:
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03.65.Yz
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(Decoherence; open systems; quantum statistical methods)
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03.65.Fd
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(Algebraic methods)
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03.65.Vf
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(Phases: geometric; dynamic or topological)
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| Fund: Project supported by the National Key Research and Development Program of China (Grant No. 2016YFA0300600), the National Natural Science Foundation of China (Grant No. 11974413), and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB33000000). |
Corresponding Authors:
Shu Chen
E-mail: schen@iphy.ac.cn
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Cite this article:
Cui-Xian Guo(郭翠仙) and Shu Chen(陈澍) Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions 2022 Chin. Phys. B 31 010313
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