Anomalous Scaling Behaviors of the Green's Function in Critical Skin Effects

2025/07/28 by Yi, Yifei, Yang, Zhesen
#FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

paper · doi:10.48550/arxiv.2507.20843

Abstract

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.

Citations

• Complex Frequency Detection in a Subsystem
• Complex Frequency Fingerprint: Basic Concept and Theory
• Non-Hermitian physics
• Generalized bulk–boundary correspondence in non-Hermitian topolectrical circuits
• Topological Origin of Non-Hermitian Skin Effects
• Non-Hermitian bulk–boundary correspondence in quantum dynamics

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