Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
复制标题
开放系统中的量子异常、非厄米集肤效应和纠缠熵
DOI：
10.1103/physrevb.103.085428
复制
发表时间：
2020-11
影响因子：
3.7
通讯作者：
N. Okuma;M. Sato
中科院分区：
文献类型：
--
作者：
N. Okuma;M. Sato
我们研究了非厄米拓扑在开放系统的谱特性和纠缠结构中的作用。从谱理论的角度，我们给出了对非厄米拓扑的两种解释：量子反常和非厄米趋肤效应的统一理解，其中体谱对边界条件的依赖性很强。在这种情况下，在完全开放的边界条件下的内在高维趋肤效应需要拓扑缺陷的存在的事实被理解的异常费米子的生产，如Rubakov-Callan效应的存在下的磁性粒子。通过使用统一的解释，我们分类的皮肤保护和高维的影响。在纠缠结构方面，我们研究了Liouvillian（快度）谱具有非厄米拓扑的费米子开放系统的定态。我们分析了零维开放系统中耗散驱动的Majorana定态，并利用纠缠熵将其与拓扑超导体的Majorana边模联系起来。我们还分析了一个非厄米拓扑谱的一维开放费米系统的稳态，并根据纠缠谱定义的迹指数将其与Chern绝缘体的手征边缘态联系起来。这种对应关系表明，在周期性边界条件下，纠缠产生了非互易的圆形电流，在开边界条件下，纠缠产生了费米子积累的趋肤效应电压.最后，我们讨论了Liouvillian动力学的伪谱行为和相互作用系统中的趋肤效应等相关问题。
We investigate the roles of non-Hermitian topology in spectral properties and entanglement structures of open systems. In terms of spectral theory, we give a unified understanding of two interpretations of non-Hermitian topology: quantum anomaly and non-Hermitian skin effects, in which the bulk spectra extremely depend on the boundary conditions. In this context, the fact that the intrinsic higher-dimensional skin effects under the full open boundary condition need the presence of the topological defects is understood in terms of the anomalous fermion production such as the Rubakov-Callan effect in the presence of the magnetic monopole. By using the unified interpretation, we classify the symmetry-protected and higher-dimensional skin effects. In terms of the entanglement structure, we investigate steady states of fermionic open systems whose Liouvillian (rapidity) spectra host non-Hermitian topology. We analyze dissipation-driven Majorana steady states in zero-dimensional open systems and relate them to the Majorana edge modes of topological superconductors by using the entanglement entropy. We also analyze a steady state of a one-dimensional open Fermi system with a non-Hermitian topological spectrum and relate it to the chiral edge states of the Chern insulator on the basis of the trace index defined from the entanglement spectrum. This correspondence indicates that the entanglement generates circular nonreciprocal currents under the periodic boundary condition and the skin-effect voltage with fermion accumulation under the open boundary condition. Finally, we discuss several related topics such as pseudospectral behaviors of Liouvillian dynamics and skin effects in interacting systems.