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Why finite-size non-Hermitian eigenvalues can miss asymptotic eigenstates in topological physics

Lucien Jezequel1, Loïc Herviou2, and Jens H. Bardarson1

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Phys. Rev. B 114, 204306 – Published 14 October, 2026

DOI: https://doi.org/10.1103/2vfv-47r1

Abstract

Non-Hermitian systems exhibit a fundamental spectral dichotomy absent in Hermitian physics: the eigenvalue spectrum and the eigenstate spectrum can deviate significantly in the thermodynamic limit. We explain how extrapolating finite-size eigenvalues can miss important asymptotic eigenstates, with the unidirectional Hatano-Nelson model serving as a minimal realization of this phenomenon. Through exact analytical solutions, we show that this model contains not only hidden asymptotic modes but also quasi-Jordan structures that become macroscopic in the thermodynamic limit and appear more generally in systems with nontrivial bulk winding. Our framework explains how the apparent failure of the bulk-edge correspondence in models such as the non-Hermitian Su-Schrieffer-Heeger (SSH) chain can reflect the failure of finite-size eigenvalue extrapolation to detect asymptotic edge states in systems with a skin effect. These results clarify the limitations of using finite-size eigenvalues alone to infer thermodynamic-limit topology.

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Phys. Rev. B 114, 204306– Published 14 October, 2026
  • Received 24 February 2026
  • Revised 2 July 2026
  • Accepted 10 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

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