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

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 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.

Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Physics (quant-ph)

arXiv:2601.05234 [cond-mat.mes-hall]

(or arXiv:2601.05234v2 [cond-mat.mes-hall] for this version)

https://doi.org/10.48550/arXiv.2601.05234 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. B 114, 204306 (2026)

https://doi.org/10.1103/2vfv-47r1 Focus to learn more DOI(s) linking to related resources

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