Growth of entanglement entropy under local projective measurements

Non-equilibrium dynamics of many-body quantum systems under the effect measurement protocols is attracting an increasing amount attention. It has been recently revealed that measurements may induce abrupt change in scaling-law bipartite entanglement entropy, thus suggesting existence different non-equilibrium regimes. However, our understanding how these regimes appear and whether they survive thermodynamic limit much less established. Here we investigate questions on a one-dimensional quadratic fermionic model: this allows us to reach system sizes relevant sense. We show local projective qualitative modification time-growth entropy which changes from linear logarithmic. stationary regime, logarithmic behavior do not and, for any finite value rate, numerically single area-law phase entropy. Finally, exploiting quasi-particle picture, further support results analysing fluctuations its scaling behavior.