Entanglement dynamics in the many-body Hatano-Nelson model

The entanglement dynamics in a non-Hermitian quantum system is studied numerically and analyzed from the viewpoint of quasiparticle picture. As a concrete model, we consider a one-dimensional tight-binding model with asymmetric hopping (Hatano-Nelson model) under onsite disorder and nearest-neighbor interaction. As opposed to an assertion of previous studies, the entanglement dynamics in this non-Hermitian quantum system is very different from the one in its Hermitian counterpart, especially in the delocalized regime with weak disorder; there the entanglement entropy $S_{\rm ent}(t)$ shows a characteristic non-monotonic time evolution. We have clarified and quantified the nature of this behavior in the quasiparticle picture. In the asymptotic regime of $t\rightarrow\infty$, the entanglement entropy $S_{\rm ent}(t)$ in this regime saturates to a much suppressed value, which increases only logarithmically with respect to the size of the subsystem.