论文标题
受非正态保护的Hermitian零模式：伪斑的应用
Hermitian zero modes protected by nonnormality: Application of pseudospectra
论文作者
论文摘要
最近，已经确定存在非铁皮皮肤效应之间存在直接关系， - 光谱对非富米汉尔顿族人的边界条件的依赖性和Hermitian拓扑绝缘子的边界零模式之间存在直接关系。另一方面，就光谱理论而言，皮肤效应也可以解释为非正常（非甲米）汉密尔顿的光谱的不稳定性。将后者的解释应用于前者的关系，我们开发了一种用量子异常的零模式的理论，用于一般的Hermitian晶格系统。我们的理论适用于广泛的系统：Majorana链，非周期性晶格和远程跳跃系统。我们将遗传系统的精确零模式和准零模式与非赫米特式系统的光谱和伪谱相关联。即使没有拓扑保护，这些Hermitian系统的零和准零模式即使对一类扰动也是强大的。鲁棒性是通过相应非炎性系统的非正态性来衡量的。我们还使用晶格系统的图形表示，对这种零模式进行了明确的构建。我们的理论揭示了非正态保护的零模式的存在，以及非正态和伪斑的有用性，作为拓扑和/或非富勒物理学的工具。
Recently, it was established that there exists a direct relation between the non-Hermitian skin effects, -strong dependence of spectra on boundary conditions for non-Hermitian Hamiltonians-, and boundary zero modes for Hermitian topological insulators. On the other hand, in terms of the spectral theory, the skin effects can also be interpreted as instability of spectra for nonnormal (non-Hermitian) Hamiltonians. Applying the latter interpretation to the former relation, we develop a theory of zero modes with quantum anomaly for general Hermitian lattice systems. Our theory is applicable to a wide range of systems: Majorana chains, non-periodic lattices, and long-range hopping systems. We relate exact zero modes and quasi-zero modes of a Hermitian system to spectra and pseudospectra of a non-Hermitian system, respectively. These zero and quasi-zero modes of a Hermitian system are robust against a class of perturbations even if there is no topological protection. The robustness is measured by nonnormality of the corresponding non-Hermitian system. We also present explicit construction of such zero modes by using a graphical representation of lattice systems. Our theory reveals the presence of nonnormality-protected zero modes, as well as the usefulness of the nonnormality and pseudospectra as tools for topological and/or non-Hermitian physics.
