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Abstract
We investigate the entanglement dynamics in a free-fermion chain initially prepared in a Fermi sea and subjected to localized losses (dissipative impurity). We derive a formula describing the dynamics of the entanglement entropies in the hydrodynamic limit of long times and large intervals. The result depends only on the absorption coefficient of the effective delta potential describing the impurity in the hydrodynamic limit. Genuine dissipation-induced entanglement is certified by the linear growth of the logarithmic negativity. Finally, in the quantum Zeno regime at strong dissipation the entanglement growth is arrested (Zeno entanglement death).
Highlights
Common experience suggests that the interaction between a quantum system and its environment, and the ensuing dissipation, is detrimental for quantum entanglement
A promising direction is to extend the hydrodynamic framework to integrable systems subjected to dissipation [14, 18,19,20,21]. This is motivated by the tremendous success of Generalized Hydrodynamics (GHD) for integrable systems [22, 23]
We report the analytic result in the hydrodynamic limit (cf. (35))
Summary
Common experience suggests that the interaction between a quantum system and its environment, and the ensuing dissipation, is detrimental for quantum entanglement. The fact that the von Neumann entropy is not a good entanglement measure is reflected in a generic linear growth with time. This linear growth in open quantum systems has been observed already, for instance, in [81]. We review the formula for the fermionic correlators in the hydrodynamic limit, which are the main ingredients to compute the entanglement entropies and the negativity. These formulas where presented elsewhere [39, 44]. In Appendix A we report the derivation of the main result of section 4
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