Essay: Topological Phases and Exceptional Points in Non-Hermitian Systems

Non-Hermitian physics is an emerging field that intersects with condensed matter physics, quantum physics, and atomic, molecular, and optical physics. It provides a theoretical framework for open systems, which interact with their environment and undergo nonunitary evolution. This framework features mathematical structures, such as complex eigenvalues, exceptional points, and nonorthogonal eigenstates, fundamentally distinct from Hermitian theories. These structures not only facilitate new methods for precisely customizing non-Hermitian systems for various applications, but also give rise to topological phenomena absent in Hermitian systems, such as non-Hermitian skin effects, exceptional-point-enriched topological phases, and complex-energy band topology. As discoveries in non-Hermitian phenomena continue to grow, a key question arises: what critical impact will non-Hermitian physics have on fundamental physics? In this Essay, I will discuss my perspective on the important open problems and future applications associated with this research area, with an emphasis on novel topological phases and exceptional points in non-Hermitian systems that are relevant to fundamental physics and potential technological applications, aiming to inspire further ideas. Part of a series of Essays which concisely present author visions for the future of their field.