Extended imaginary gauge transformation in a general nonreciprocal lattice
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914236869902336 |
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| author | Qi, Yunyao Pi, Jinghui Wu, Yuquan Lin, Heng Zheng, Chao Long, Gui-Lu |
| author_facet | Qi, Yunyao Pi, Jinghui Wu, Yuquan Lin, Heng Zheng, Chao Long, Gui-Lu |
| contents | Imaginary gauge transformation (IGT) provides a clear understanding of the non-Hermitian skin effect by transforming the non-Hermitian Hamiltonians with real spectra into Hermitian ones. In this paper, we extend this approach to the complex spectrum regime in a general nonreciprocal lattice model. We unveil the validity of IGT hinges on a class of pseudo-Hermitian symmetry. The generalized Brillouin zone of Hamiltonians respect such pseudo-Hermiticity is demonstrated to be a circle, which enables easy access to the continuum bands, localization length of skin modes, and relevant topological numbers. Furthermore, we investigate the applicability of IGT and the underlying pseudo-Hermiticity beyond nearest-neighbor hopping, offering a graphical interpretation. Our theoretical framework is applied to establish bulk-boundary correspondence in the nonreciprocal trimer Su-Schrieffer-Heeger model and to analyze the localization behaviors of skin modes in the two-dimensional Hatano-Nelson model. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_12785 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extended imaginary gauge transformation in a general nonreciprocal lattice Qi, Yunyao Pi, Jinghui Wu, Yuquan Lin, Heng Zheng, Chao Long, Gui-Lu Quantum Physics Mesoscale and Nanoscale Physics Imaginary gauge transformation (IGT) provides a clear understanding of the non-Hermitian skin effect by transforming the non-Hermitian Hamiltonians with real spectra into Hermitian ones. In this paper, we extend this approach to the complex spectrum regime in a general nonreciprocal lattice model. We unveil the validity of IGT hinges on a class of pseudo-Hermitian symmetry. The generalized Brillouin zone of Hamiltonians respect such pseudo-Hermiticity is demonstrated to be a circle, which enables easy access to the continuum bands, localization length of skin modes, and relevant topological numbers. Furthermore, we investigate the applicability of IGT and the underlying pseudo-Hermiticity beyond nearest-neighbor hopping, offering a graphical interpretation. Our theoretical framework is applied to establish bulk-boundary correspondence in the nonreciprocal trimer Su-Schrieffer-Heeger model and to analyze the localization behaviors of skin modes in the two-dimensional Hatano-Nelson model. |
| title | Extended imaginary gauge transformation in a general nonreciprocal lattice |
| topic | Quantum Physics Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2401.12785 |