Non-Hermitian physics has attracted much attention and has become one of the most popular fields in the past few years. The discoveries of exotic phenomena, such as the non-Hermitian skin effect (NHSE), have significantly reshaped our understanding of non-Hermitian systems. Intriguingly, back in 1997, it was realized that the complex spectral density of a non-Hermitian matrix can be computed by constructing an auxiliary Hermitian matrix. This Hermitization technique provides a connection between non-Hermitian and Hermitian physics. In this talk, I will introduce two parts of results inspired by Hermitization. In the first part, I will explain how the efficient but mysterious amoeba formulation of non-Bloch band theory, i.e., a quantified theory of NHSE, can be understood via utilizing the similarity between the singular value decomposition and Hermitization. Furthermore, from this perspective, we found interesting models with unconventional asymptotic behaviors of Green's functions. This unconventional Green's function results in the spectral instability of the energy spectrum under the change of the system's geometry. In the second part, I will introduce a numerical method called the non-Hermitian kernel polynomial method, for which Hermitization is a key step.  I will demonstrate the applications of this method in detecting non-Hermitian topological phases and studying open quantum dynamics.

宋飞, 2018年本科毕业于中国科学技术大学; 2023年在汪忠教授指导下于清华大学取得物理学博士学位, 并获清华研究生特等奖学金。目前在"国家资助博士后计划"的支持下, 于中国科学院大学卡弗里理论科学研究中心从事博士后研究。其主要研究方向为非厄米物理特别是利用非厄米理论理解开放量子系统中的新奇现象。