Non-Hermitian Delocalization Realizes Random Dirac Criticality in One Dimension

Bo Li; Shen Zhang; Ren Zhang

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arXiv · 2606.12089

Non-Hermitian Delocalization Realizes Random Dirac Criticality in One Dimension

Bo Li·Shen Zhang·Ren Zhang

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Abstract

Non-Hermitian systems can evade Anderson localization and exhibit delocalized states even in one dimension. Here, we show that such non-Hermitian delocalized states under periodic boundary conditions (PBC) are intrinsically critical, realizing the universality class of one-dimensional random Dirac fermions. By linking spectral winding to topological Anderson transitions via Hermitization, we demonstrate that the delocalized PBC states exhibit a Dirac-type criticality with universal algebraic correlations. In contrast to Hermitian systems, where this criticality occurs only at fine-tuned transition points, it emerges generically in non-Hermitian systems as a consequence of spectral topology. These results identify a universal mechanism by which non-Hermiticity promotes criticality, providing a unified description of non-Hermitian delocalization in one dimension.

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Bo Li, Shen Zhang, Ren Zhang. 2026-06-10. Non-Hermitian Delocalization Realizes Random Dirac Criticality in One Dimension. https://arxiv.org/abs/2606.12089

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