Hermitian zero modes protected by nonnormality: Application of pseudospectra
Hermitian zero modes protected by nonnormality: Application of pseudospectra
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DOI：
10.1103/physrevb.102.014203
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发表时间：
2020-07
影响因子：
3.7
通讯作者：
N. Okuma;M. Sato
中科院分区：
文献类型：
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作者：
N. Okuma;M. Sato
最近，人们发现非厄米集肤效应、非厄米哈密顿量的谱对边界条件的强依赖性以及厄米拓扑绝缘体的边界零模之间存在着直接的关系。另一方面，在光谱理论方面，集肤效应也可以解释为非正规(非厄米)哈密顿量的光谱不稳定性。将后一种解释应用于前一种关系，我们发展了一般厄米晶格系统的零模量子反常理论。我们的理论适用于广泛的系统：Majorana链、非周期晶格和远程跳跃系统。我们将厄米系统的精确零模和准零模分别与非厄米系统的谱和伪谱联系起来。即使没有拓扑保护，厄米系统的零模和准零模对一类扰动也是健壮的。稳健性是通过相应的非厄米系统的非正规性来衡量的。我们还利用格子系统的图形表示给出了这种零模的显式构造。我们的理论揭示了非正态保护零模的存在，以及非正态和伪谱作为拓扑和/或非厄米物理工具的有效性。
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, nonperiodic 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.