Entanglement dynamics in a many-body Hatano-Nelson model

Non-Hermitian quantum systems exhibit unusual features, which have no counterpart in Hermitian quantum systems. In this work, as a concrete example, we consider a one-dimensional tight-binding model with non-reciprocal hopping amplitudes (many-body Hatano-Nelson (HN) model) and focus on how non-Hermiticity (non-reciprocity of hopping term) affects entanglement dynamics [1]. Generally, in the case of the Hermitian system, the quasi-particle picture provides an intuitive picture of entanglement dynamics. However, in the case of the many-body HN model, quasi-particles tend to be suppressed/amplified due to the imaginary part of the eigenenergy, leading to the non-monotonic time dependence of entanglement entropy in a specific parameter regime. We numerically and analytically reveal the role of the imaginary part of eigenenergy on entanglement dynamics and why non-monotonic time dependence of entanglement dynamics appears [2].