Symmetry and Topology in Non-Hermitian Systems

The ideas of topology have found great success in Hermitian physical systems, but the incorporation of non-Hermitian effects may lead to even richer possibilities. Here, we present two results regarding the roles of symmetry and topology in non-Hermitian physical systems. First, we provide a systematic classification of non-Hermitian symmetry protected topological phases in arbitrary spatial dimension, based on the Bernard-LeClair symmetry classes. We discuss the physical insights provided by such a classification, and how it can serve as an important guide for future searches of non-Hermitian topological systems. We then discuss how symmetries can protect the existence of a surface of exceptional points, which are a natural generalization of Hermitian topological nodal phases.