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We investigate the roles of non-Hermitian topology in spectral properties andentanglement structures of open systems. In terms of spectral theory, we give aunified understanding of two interpretations of non-Hermitian topology: quantumanomaly and non-Hermitian skin effects, in which the bulk spectra extremelydepend on the boundary conditions. In this context, the fact that the intrinsichigher-dimensional skin effects under the full open boundary condition need thepresence of the topological defects is understood in terms of the anomalousfermion production such as the Rubakov-Callan effect in the presence of themagnetic monopole. In terms of the entanglement structure, we investigatesteady states of fermionic open systems whose Liouvillian (rapidity) spectrahost non-Hermitian topology. We analyze dissipation-driven Majorana steadystates in zero-dimensional open systems and relate them to the Majorana edgemodes of topological superconductors by using the entanglement entropy. We alsoanalyze a steady state of a one-dimensional open Fermi system with anon-Hermitian topological spectrum and relate it to the chiral edge states ofthe Chern insulator on the basis of the trace index defined from theentanglement spectrum. These correspondences indicate that the entanglementgenerates circular nonreciprocal currents under the periodic boundary conditionand the skin-effect voltage with fermion accumulation under the open boundarycondition. Finally, we discuss several related topics such as pseudospectralbehaviors of Liouvillian dynamics and skin effects in interacting systems.

Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems