Non-Hermitian Delocalization Realizes Random Dirac Criticality in One Dimension

• URL: http://arxiv.org/abs/2606.12089v1
• Date: Wed, 10 Jun 2026 13:49:36 GMT
• Title: Non-Hermitian Delocalization Realizes Random Dirac Criticality in One Dimension
• Abstract summary: We show that non-Hermitian delocalized states under periodic boundary conditions are intrinsically critical.<n>We identify a universal mechanism by which non-Hermiticity promotes criticality.
• Score: 11.566689521600628
• License: http://creativecommons.org/licenses/by/4.0/
• 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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