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arXiv · 2505.10252

A Unified Framework for the Non-Hermitian Localization: Boundary-Insensitive Modes and Electric-Magnetic Analogy

Zheng Wei·Ji-Yao Fan·Kui Cao·Xin-Ran Ma·Cui-Xian Guo·Xue-Ping Ren·Su-Peng Kou
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Abstract

The non-Hermitian skin effect is fundamentally characterized by its sensitivity to boundary conditions, reflected in changes to the energy spectrum and boundary-localized eigenstates. Here, we demonstrate that a spatially inhomogeneous imaginary scalar potential field induces a skin effect that is insensitive to boundary conditions. Both the spectrum and eigenstate distribution remain invariant, a behavior not captured by existing theories. We attribute this anomaly to translational symmetry breaking induced by spatially varying imaginary potentials in finite systems. We further formulate a theory that universally predicts localization in single-particle non-Hermitian systems. This framework classifies skin effects into two fundamental types: electric, driven by imaginary scalar potentials, and magnetic, driven by imaginary vector potentials, and reveals a phase transition between them, where eigenstates become fully delocalized. Our work provides a unified theory for non-Hermitian localization, allowing full control over skin modes via potential engineering in various platforms like photonic crystals and cold-atom systems.

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Zheng Wei, Ji-Yao Fan, Kui Cao, Xin-Ran Ma, Cui-Xian Guo, Xue-Ping Ren, Su-Peng Kou. 2025-05-15. A Unified Framework for the Non-Hermitian Localization: Boundary-Insensitive Modes and Electric-Magnetic Analogy. https://arxiv.org/abs/2505.10252

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