AI 中文总结
该研究揭示开放边界非厄米系统中，无穷小长程跃迁可通过衰减长度与非厄米皮肤模局域化长度的竞争重构谱与本征态，一维对应压缩GBZ，二维对应压缩阿米巴形式，且该效应可检测。
AI 中文摘要
指数衰减的长程跃迁在真实的紧束缚模型中普遍存在，且常被截断以获得有限范围的描述。我们证明，这种近似在开放边界条件下的非厄米系统中会严重失效：无穷小的长程跃迁可通过非微扰方式重构短程非厄米系统的谱与本征态。该机制由无穷小长程跃迁的衰减长度与非厄米皮肤模的局域化长度之间的竞争控制，随衰减率的调整会出现尖锐转变。在一维情况下，我们证明压缩的广义布里渊区（GBZ）会取代短程哈密顿量的原GBZ，产生重构的开放边界谱；在二维及更高维度，我们提出描述重构谱密度的压缩阿米巴形式。我们进一步证明，长程跃迁可定性重塑格林函数，且该效应可在实验中轻易检测到。
英文摘要
Exponentially decaying long-range hoppings are ubiquitous in realistic tight-binding models and are often truncated to obtain a finite-range description. We show that this approximation can fail dramatically in non-Hermitian systems under open boundary conditions: an infinitesimal long-range hopping can nonperturbatively reconstruct the spectrum and eigenstates of a short-range non-Hermitian system. The mechanism is controlled by a competition between the decay length of infinitesimal long-range hoppings and the localization length of non-Hermitian skin modes, leading to a sharp transition as the decay rate is tuned. In one dimension, we show that a squeezed generalized Brillouin zone (GBZ) replaces the original GBZ of the short-ranged Hamiltonian, yielding the reconstructed open-boundary spectrum. In two or higher dimensions, we formulate a squeezed amoeba formulation describing the reconstructed spectral density. We further show that long-range hoppings can qualitatively reshape Green's function, which can be readily detected in experiments.
Comments8+8 pages, 7+5 figures
