论文标题
与远距离耦合的非铁皮皮肤效应的缩放定律
Scaling laws for non-Hermitian skin effect with long-range couplings
论文作者
论文摘要
近年来，在具有有限范围耦合的一维晶格中，目睹了对非铁皮皮肤效应（NHSE）的大量研究。在这项工作中，我们表明，在距离$ l $下衰减为$ 1/l^α$的远距离耦合可以从根本上修改NHSE的行为和在存在非重新性的情况下的量子纠缠的缩放。在$α= 0 $时，耦合的非局部性产生了无尺度的皮肤模式，其定位长度与系统尺寸成正比。增加指数$α$可以驱动复杂到现实的光谱过渡，并从无标度到恒定的定位长度进行交叉。此外，与NHSE产生的区域定律相反，由于非局部性和复杂频谱，非平衡稳态纠缠熵的缩放表现出典型的定律。我们的结果对远程耦合与非热性之间的相互作用提供了理论上的理解。
Recent years have witnessed a surge of research on the non-Hermitian skin effect (NHSE) in one-dimensional lattices with finite-range couplings. In this work, we show that the long-range couplings that decay as $1/l^α$ at distance $l$ can fundamentally modify the behavior of NHSE and the scaling of quantum entanglement in the presence of nonreciprocity. At $α=0$, the nonlocality of couplings gives rise to the scale-free skin modes, whose localization length is proportional to the system size. Increasing the exponent $α$ drives a complex-to-real spectral transition and a crossover from a scale-free to constant localization length. Furthermore, the scaling of nonequilibrium steady-state entanglement entropy exhibits a subextensive law due to the nonlocality and the complex spectrum, in contrast to an area law arising from NHSE. Our results provide a theoretical understanding on the interplay between long-range couplings and non-Hermiticity.
