Universal Critical Scaling and Phase Diagram of the Non-Hermitian Skin Effect under Disorder

Ali Tozar

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arXiv · 2511.19860

Universal Critical Scaling and Phase Diagram of the Non-Hermitian Skin Effect under Disorder

Ali Tozar

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Abstract

Standard scaling theory dictates that disorder leads to immediate localization in one-dimensional Hermitian systems. We demonstrate that non-Hermitian topology fundamentally alters this paradigm, protecting transport up to a substantial critical disorder strength. By employing a numerically stable log-space transfer matrix approach up to thermodynamic scales (N=1000), we identify a sharp phase transition from the topological skin phase to the Anderson localized phase. Finite-size scaling analysis reveals that this transition belongs to a unique universality class with critical exponents \nu\approx1.50 and \beta\approx0.65. Furthermore, we map the global phase diagram, confirming that the critical disorder scales as W_c\propto\sqrt\gamma, consistent with localization suppression by an imaginary vector potential. Our results establish the rigorous limits of non-Hermitian topological protection in imperfect media.

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Ali Tozar. 2025-11-25. Universal Critical Scaling and Phase Diagram of the Non-Hermitian Skin Effect under Disorder. https://arxiv.org/abs/2511.19860

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