Fate of entanglement in one-dimensional fermion liquid with coherent particle loss

Quantum many-body systems and quantum devices experience the detrimental effects of noise and particle losses, necessitating their treatment as open quantum systems or, in approximation, as non-Hermitian systems. These systems exhibit nontrivial characteristics in their time evolution that differ significantly from closed systems. In this Letter, we study the dynamic properties of a one-dimensional fermionic system with adjacent-lattice particle loss. By utilizing time-dependent correlation matrix methods and bosonization techniques, we demonstrate that, as the system evolves over time, its (bipartite) von Neumann entropy exhibits a universal behavior of rapid increase due to thermalization effects at short times, independent of the effective Hamiltonian and Liouvillian spectra, even in the presence of interactions. Additionally, we show that the asymmetric non-Hermitian terms in the effective Hamiltonian caused by adjacent-lattice quantum jumps lead to left-right asymmetry of quasiparticles in momentum space, which is ubiquitous in non-Hermitian skin effects and introduces momentum-space entanglement independent of the interaction strength at early times. Our study illuminates the universal fate of non-Hermitian fermionic liquids in the open quantum context, enriching our understanding of non-Hermitian many-body systems over the entire time range. Furthermore, our findings provide valuable insights for near-term quantum devices and the quantum simulation of open systems.