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Monitored quantum many-body systems display a rich pattern of entanglementdynamics, which is unique to this non-unitary setting. This work studies theeffect of quantum jumps on the entanglement dynamics beyond the no-click limitcorresponding to a deterministic non-Hermitian evolution. We consider twoexamples, a monitored SSH model and a quantum Ising chain, for which we showthe jumps have remarkably different effects on the entanglement despite havingthe same statistics as encoded in their waiting-time distribution. Tounderstand this difference, we introduce a new metric, the statistics ofentanglement gain and loss due to jumps and non-Hermitian evolution. Thisinsight allows us to build a simple stochastic model of a random walk withpartial resetting, which reproduces the entanglement dynamics, and to dissectthe mutual role of jumps and non-Hermitian evolution on the entanglementscaling. We demonstrate that significant deviations from the no-click limitarise whenever quantum jumps strongly renormalize the non-Hermitian dynamics,as in the case of the SSH model at weak monitoring or in the Ising chain atlarge transverse field. On the other hand, we show that the weak monitoringphase of the Ising chain leads to a robust sub-volume logarithmic phase due toweakly renormalized non-Hermitian dynamics.

Entanglement Dynamics in Monitored Systems and the Role of Quantum Jumps