Ancilla quantum measurements on interacting chains: Sensitivity of entanglement dynamics to the type and concentration of detectors

We consider a quantum many-body lattice system that is coupled to ancillary degrees of freedom (``detectors''), which are periodically measured by means of strong projective measurements. The concentration ρₐ of ancillae and their coupling M to the main system are considered as parameters. We explore the dynamics of density and of entanglement entropy in the chain, for various values of ρₐ and M for two models of the detector-chain interaction that couple the local density in the chain to a detector degree of freedom. It is found that, for the density-density (Szsz-type in spin language) coupling, the critical values Mc for the measurement-induced entanglement transition depends sensitively on ρₐ. Moreover, our results indicate that for a sufficiently small ρₐ the transition in this model disappears; i.e., a finite density of detectors is needed to reach a disentangling phase. The behavior is qualitatively different for the second model, with density-hopping (Szsₓ-type) coupling. Specifically, the dynamics is much less sensitive to the concentration ρₐ of detectors than in the first model. Furthermore, the dependence of entanglement on the coupling strength M is strongly nonmonotonic, indicating reentrance of the entangling phase at large M.