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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.20843 |
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| _version_ | 1866909709200523264 |
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| author | Yi, Yifei Yang, Zhesen |
| author_facet | Yi, Yifei Yang, Zhesen |
| contents | We study the Green's functions in non-Hermitian systems exhibiting the critical non-Hermitian skin effect (critical NHSE) using a double-chain Hatano-Nelson model with inter-chain coupling $Δ$. For $Δ=0$, the system decouples into two independent chains, and the Green's functions follow predictable patterns based on the GBZ theory. For small $Δ$ ($Δ=1/10000$), in conventional regions with trivial OBC spectral winding numbers, inter-chain coupling induces a zigzag scaling structure in Green's functions due to competition between the two chains, explainable by first-order perturbation theory. In anomalous regions with non-trivial winding numbers, Green's functions match GBZ predictions in the bulk but diverge near boundaries, with residual contributions from the $Δ=0$ GBZ accounting for the deviations. These results reveal the unique non-perturbative features of critical NHSE and highlight the limitations of GBZ theory in capturing finite-size and boundary effects, emphasizing the need to consider both bulk and boundary dynamics in such systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20843 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anomalous Scaling Behaviors of the Green's Function in Critical Skin Effects Yi, Yifei Yang, Zhesen Mesoscale and Nanoscale Physics We study the Green's functions in non-Hermitian systems exhibiting the critical non-Hermitian skin effect (critical NHSE) using a double-chain Hatano-Nelson model with inter-chain coupling $Δ$. For $Δ=0$, the system decouples into two independent chains, and the Green's functions follow predictable patterns based on the GBZ theory. For small $Δ$ ($Δ=1/10000$), in conventional regions with trivial OBC spectral winding numbers, inter-chain coupling induces a zigzag scaling structure in Green's functions due to competition between the two chains, explainable by first-order perturbation theory. In anomalous regions with non-trivial winding numbers, Green's functions match GBZ predictions in the bulk but diverge near boundaries, with residual contributions from the $Δ=0$ GBZ accounting for the deviations. These results reveal the unique non-perturbative features of critical NHSE and highlight the limitations of GBZ theory in capturing finite-size and boundary effects, emphasizing the need to consider both bulk and boundary dynamics in such systems. |
| title | Anomalous Scaling Behaviors of the Green's Function in Critical Skin Effects |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2507.20843 |