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Recent theoretical work has shown that the competition between coherentunitary dynamics and stochastic measurements, performed by the environment,along wavefunction trajectories can give rise to transitions in theentanglement scaling. In this work, complementary to these previous studies, weanalyze a situation where the role of Hamiltonian and dissipative dynamics isreversed. We consider an engineered dissipation, which stabilizes an entangledphase of a quantum spin$-1/2$ chain, while competing single-particle orinteracting Hamiltonian dynamics induce a disentangled phase. Focusing on thesingle-particle unitary dynamics, we find that the system undergoes anentanglement transition from a logarithmic growth to an area law when thecompetition ratio between the unitary evolution and the non-unitary dynamicsincreases. We evidence that the transition manifests itself in state-dependentobservables at a finite competition ratio for Hamiltonian and measurementdynamics. On the other hand, it is absent in trajectory-averaged steady-statedynamics, governed by a Lindblad master equation: although purely dissipativedynamics stabilizes an entangled state, for any non-vanishing Hamiltoniancontribution the system ends up irremediably in a disordered phase. Inaddition, a single trajectory analysis reveals that the distribution of theentanglement entropy constitutes an efficient indicator of the transition.Complementarily, we explore the competition of the dissipation with coherentdynamics generated by an interacting Hamiltonian, and demonstrate that theentanglement transition also occurs in this second model. Our results suggestthat this type of transition takes place for a broader class of Hamiltonians,underlining its robustness in monitored open quantum many-body systems.

Engineered dissipation induced entanglement transition in quantum spin chains: from logarithmic growth to area law