AI 中文总结
该研究揭示长程跳跃重构非厄米晶格的临界行为，发现非局域性消除常规临界非厄米皮肤行为的物理长度尺度，提供可在多种平台验证的临界层级研究框架。
AI 中文摘要
非厄米晶格中的光谱跃迁通常源于非互易皮肤积累与组分间杂化的竞争。在由两条耦合链构成的短程系统中，这种竞争通常会产生对数临界长度定律$N_c\sim\ln D$，其中$D$为链间的横向间距。本文表明，长程跳跃会从根本上重构这种临界行为，产生一系列不同的标度定律。当仅杂化耦合按幂律衰减（指数为$\alpha$）时，临界转变变为代数形式$N_c\sim D^{\alpha/3}$。当每条链内的跳跃也按幂律衰减（除杂化耦合外）时，系统在$\alpha<2$时进入标度协变区域，其中临界阈值方程仅依赖于系统的纵横比$N_c/D$；在$\alpha=2$及更大值时，该区域后分别出现对数修正和代数修正的边缘区域。我们确定了两种新的非局域机制来实现这种非常规的临界层级：来自长程链内跳跃的非解析带边色散，以及由非互易性诱导的宇称混合杂化。我们的结果表明，非局域性会系统性地消除常规临界非厄米皮肤行为所依赖的物理长度尺度（即皮肤深度），提供了一个可在可编程拓扑电路、光子晶格和数字量子模拟器中验证的平台无关框架。
英文摘要
Spectral transitions in non-Hermitian lattices often arise from the competition between non-reciprocal skin accumulation and inter-component hybridization. In short-range systems formed by two coupled chains, this competition conventionally leads to the logarithmic critical-length law $N_c\sim\ln D$, where $D$ is the transverse separation between the chains. Here we show that long-range hoppings fundamentally reorganizes this critical behavior, producing a hierarchy of distinct scaling laws. When only the hybridization couplings are power-law decaying with exponent $α$, the onset becomes algebraic, $N_c\sim D^{α/3}$. When the hoppings within each chain are themselves also power-law decaying, in addition to the hybridization couplings, the system enters a scale-covariant regime for $α<2$, in which the criticality threshold equation depends only on the system aspect ratio $N_c/D$. At $α=2$ and beyond, this regime is followed by a marginal logarithmically corrected and algebraically corrected regimes, respectively. We identify two new non-local mechanisms that enable this unconventional critical hierarchy: a nonanalytic band-edge dispersion from long-range intra-chain hoppings, and parity-mixing hybridization induced by non-reciprocity. Our results show that nonlocality systematically removes the physical length scales i.e. skin depth underlying conventional critical non-Hermitian skin behavior, offering a platform-independent framework testable in programmable topoelectrical circuits, photonic lattices and digital quantum simulators.
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