Defectiveness and anomaly from non-Hermitian perturbations in topological quantum states

Topological quantum states are important research fields in condensed matter physics, which can be divided into two categories: (1) symmetry-protected topological states (SPTs) with short-range entanglement and (2) symmetry-enriched topological states (SETs) with long-range entanglement. Recently, research on non-Hermitian topological quantum states (SPTs and SETs) has become a hot topic. In this review paper, we discuss the theory for non-Hermitian topological insulators-a particular type of SPTs and that for non-Hermitian Z(2) topological orders-a particular type of SETs based on the progress of our research group. These theories would help understand the physics of non-Hermitian topological quantum states.