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arXiv · 2506.08714

Non-Abelian Gauge Effect for 2-D Non-Hermitian Hatano-Nelson Model in Cylinder Type

Yiming Zhao·Yazhuang Miao·Yihang Xing·Tianhui Qiu·Hongyang Ma·Xiaolong Zhao
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Abstract

Non-Abelian gauge offers a powerful route to engineer novel topological phenomena. Here, we systematically investigate a two-dimensional (2D) non-Hermitian Hatano-Nelson model incorporating SU(2) non-Abelian gauge, demonstrating the emergence of Hopf-link bulk braiding topology in the complex energy spectrum solely with x-direction nearest-neighbor couplings. Because of the limitations of exceptional point (EP) topology in fully capturing the rich non-Hermitian skin effect (NHSE) under non-Abelian influence, we introduce a novel polarization parameter derived from the generalized Brillouin zone (GBZ). This parameter quantitatively discerns left-, right-, and notably, bipolar skin modes, with its accuracy corroborated by directly encoding real-space eigenstate. Our findings reveal that non-Abelian gauge provides unprecedented influence over NHSE, compared with Abelian gauge and without gauge cases. Furthermore, we uncover unique characteristics of zero-imaginary-energy eigenstates at these topological boundaries, including pronounced degeneracy and bipolar localization which is unaffected by size effects, investigated via dynamical evolution and Inverse Participation Ratio (IPR). This work establishes a new paradigm for synthesizing and manipulating non-Hermitian topological phases driven by non-Abelian structures, opening avenues for topological engineering and holding promise for experimental realization in synthetic dimensional platforms.

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Yiming Zhao, Yazhuang Miao, Yihang Xing, Tianhui Qiu, Hongyang Ma, Xiaolong Zhao. 2025-06-19. Non-Abelian Gauge Effect for 2-D Non-Hermitian Hatano-Nelson Model in Cylinder Type. https://arxiv.org/abs/2506.08714

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