  Recently, it has become clear that non-hermitian phenomena can be observed
not only in open quantum systems experiencing gain and loss but also in
equilibrium single-particle properties of strongly correlated systems. However,
the circumstances and requirements for the emergence of non-hermitian phenomena
in each field are entirely different. While the implementation of postselection
is a significant obstacle to observe non-hermitian phenomena in open quantum
systems, it is unnecessary in strongly correlated systems.
  Until now, a relation between both descriptions of non-hermitian phenomena
has not been revealed. In this paper, we close this gap and demonstrate that
the non-hermitian Hamiltonians emerging in both fields are identical, and we
clarify the conditions for the emergence of a non-hermitian Hamiltonian in
strongly correlated materials. Using this knowledge, we propose a method to
analyze non-hermitian properties without the necessity of postselection by
studying specific response functions of open quantum systems and strongly
correlated systems.
