Igor Gornyi

We have developed an analytical approach to the study of free fermions subject to random measurements of local site occupation numbers, based on the Keldysh path-integral formalism and replica trick. On the Gaussian level, this model predicts a logarithmic behavior for the entanglement entropy of one-dimensional systems. However, the one-loop renormalization group analysis allows us to demonstrate that this logarithmic growth saturates at a finite value even for rare measurements, by developing "weak-localization" quantum corrections similar to those in 2D disordered systems. This yields the area-law phase in the thermodynamic limit and implies the absence of a measurement-induced entanglement phase transition for monitored 1D free fermions. For 2D systems, this approach predicts the entanglement transition from the area-law to the critical phase.  No volume-law phase is realized for fermions in arbitrary dimensions in the absence of interactions.