Work

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

Year: 2026

Type: article

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.

Source: Physical review. B./Physical review. B

DOI: 10.1103/2vfv-47r1

Authors: Lucien Jezequel, Loïc Herviou, Jens H. Bardarson

Institutions: KTH Royal Institute of Technology, Centre National de la Recherche Scientifique, Laboratoire de Physique et Modélisation des Milieux Condensés, Université Grenoble Alpes

Language: English

Topic: Quantum Mechanics and Non-Hermitian Physics

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Funders: European Commission, Vetenskapsrådet, Centre National de la Recherche Scientifique, European Research Council

Awards: G158799492, Topological nanowires: from fundamentals to application, G434337789, G7026481055