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

• URL: http://arxiv.org/abs/2507.06514v1
• Date: Wed, 09 Jul 2025 03:29:46 GMT
• Title: Algebraic States in Continuum in $ d\gt 1$ Dimensional Non-Hermitian Systems
• Authors: Ao Yang, Kai Zhang, Chen Fang,
• Abstract summary: We report the existence of localized eigenstates embedded within the continuum spectrum of 2D non-Hermitian systems with a single impurity.<n>We analytically derive the threshold condition for the impurity strength required to generate such states.<n>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.
• Score: 13.202410347156151
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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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