The property of open quantum system and nonhermiticity in strongly-correlated electron system

The effective non-hermitian Hamiltonian(ENH) in strongly-correlated electron systems(SCES), which introduced by H.Shen and L.Fu{PhysRevLett.120.146402}, is derived by the spectral function, and the non-hermitian physics is now studied eagerly.

However, the essential questions, "Is this ENH the same one as the ENH in the context of open quantum system ?" and "Why is the post selection not necessary to derive the ENH in SCES?", still remain. In this paper, we prove that the ENH in each context, OQS and SCES, corresponds to each other and clarify why the post selection is not necessary in SCES by treating the model in SCES as in OQS. Moreover, we propose the method to detect the non-hermitian properties in OQS without post selection, which is the great obstacle to experimentall detection.