Extended imaginary gauge transformation in a general nonreciprocal lattice

• URL: http://arxiv.org/abs/2401.12785v2
• Date: Tue, 3 Sep 2024 16:57:43 GMT
• Title: Extended imaginary gauge transformation in a general nonreciprocal lattice
• Authors: Yunyao Qi, Jinghui Pi, Yuquan Wu, Heng Lin, Chao Zheng, Gui-Lu Long,
• Abstract summary: We unveil the validity of Imaginary gauge transformation (IGT) hinges on a class of pseudo-Hermitian symmetry. We investigate the applicability of IGT and the underlying pseudo-Hermiticity beyond nearest-neighbor hopping. Our theoretical framework is applied to establish bulk-boundary correspondence in the nonreciprocal trimer Su-Schrieffer-Heeger model.
• Score: 4.052015796522459
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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