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arXiv · 2507.06514

Algebraic States in Continuum in $ d\gt 1$ Dimensional Non-Hermitian Systems

Ao Yang·Kai Zhang·Chen Fang
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Abstract

We report the existence of algebraically localized eigenstates embedded within the continuum spectrum of 2D non-Hermitian systems with a single impurity. These modes, which we term algebraic states in continuum (AICs), decay algebraically as $1/|r|$ from the impurity site, and their energies lie within the bulk continuum spectrum under periodic boundary conditions. We analytically derive the threshold condition for the impurity strength required to generate such states. Remarkably, AICs are forbidden in Hermitian systems and in 1D non-Hermitian systems, making them unique to non-Hermitian systems in two and higher dimensions. To detect AICs, we introduce a local density of states as an experimental observable, which is readily accessible in photonic/acoustic platforms.

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Ao Yang, Kai Zhang, Chen Fang. 2025-07-09. Algebraic States in Continuum in $ d\gt 1$ Dimensional Non-Hermitian Systems. https://doi.org/10.1103/9dhm-k5kf

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