Universal Critical Scaling and Phase Diagram of the Non-Hermitian Skin Effect under Disorder
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915667485130752 |
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| author | Tozar, Ali |
| author_facet | Tozar, Ali |
| contents | 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 ν\approx1.50 and β\approx0.65. Furthermore, we map the global phase diagram, confirming that the critical disorder scales as W_c\propto\sqrtγ, consistent with localization suppression by an imaginary vector potential. Our results establish the rigorous limits of non-Hermitian topological protection in imperfect media. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_19860 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal Critical Scaling and Phase Diagram of the Non-Hermitian Skin Effect under Disorder Tozar, Ali Disordered Systems and Neural Networks Statistical Mechanics 82B26 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 ν\approx1.50 and β\approx0.65. Furthermore, we map the global phase diagram, confirming that the critical disorder scales as W_c\propto\sqrtγ, consistent with localization suppression by an imaginary vector potential. Our results establish the rigorous limits of non-Hermitian topological protection in imperfect media. |
| title | Universal Critical Scaling and Phase Diagram of the Non-Hermitian Skin Effect under Disorder |
| topic | Disordered Systems and Neural Networks Statistical Mechanics 82B26 |
| url | https://arxiv.org/abs/2511.19860 |