  Quasi-particles described by Green's functions of equilibrium systems exhibit
non-Hermitian topological phenomena because of their finite lifetime. This
non-Hermitian perspective on equilibrium systems provides new insights into
correlated systems and attracts much interest because of its potential to solve
open questions in correlated compounds. In this paper, we provide a concise
review of the non-Hermitian topological band structures for quantum many-body
systems in equilibrium as well as their classification.
