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Non-Hermitian mosaic Aubry-Andre-Harper model |
| Yingshixiang Wang(王应时翔)1,2, Dongze Song(宋东泽)1,2, and Xu Xia(夏旭)1,† |
1 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
2 University of Chinese Academy of Sciences, Beijing 100190, China |
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Abstract We focus on a modified version of the non-Hermitian Aubry-Andre-Harper (AAH) model, which has garnered significant attention due to its ability to investigate localization phenomena, metal-insulator transitions, and topological phase transitions. We have made two key modifications to the non-Hermitian AAH model: First, we introduce a mosaic structure that allows for the mixing of localized and extended states, resulting in the appearance of mobility edges, which is a feature that is not present in the original non-Hermitian AAH model. In the insulating phase, leveraging Fields Medal winner Avila's global theory, our work derives a theoretical description of the localization length, a crucial parameter previously unavailable in the non-Hermitian AAH model, and obtains the exact expression for mobility edges. We studied the variation of the energy spectrum with the amplitude and quantitatively determined the topological phase transition point within the spectrum. Furthermore, we introduced an asymmetric parameter $g$ and calculated its corresponding localization length, the location of mobility edges, as well as the precise expressions for its extended and localized states. By quantitatively calculating the Lyapunov exponent of dual models, our work reveals an interesting fact about the robustness of localized states: within an appropriate relationship between $g$ and the coupling potential strength, the localized states exhibit similar characteristics to those in the mosaic non-Hermitian AAH model. Our work offers a more complete and nuanced understanding of localization phenomena in disordered non-Hermitian systems, paving the way for further research in this promising field.
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Received: 25 March 2025
Revised: 30 April 2025
Accepted manuscript online: 15 May 2025
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PACS:
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02.30.Tb
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(Operator theory)
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02.70.Hm
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(Spectral methods)
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72.20.Ee
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(Mobility edges; hopping transport)
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72.15.Rn
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(Localization effects (Anderson or weak localization))
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 12301218). |
Corresponding Authors:
Xu Xia
E-mail: xiaxu14@mails.ucas.ac.cn
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Cite this article:
Yingshixiang Wang(王应时翔), Dongze Song(宋东泽), and Xu Xia(夏旭) Non-Hermitian mosaic Aubry-Andre-Harper model 2025 Chin. Phys. B 34 090201
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