Entanglement phase transitions in non-unitary Gaussian fermionic circuits

Random quantum circuits with projective measurements are known to be a useful tool for simulating non-unitary quantum dynamics which results in a variety of non-equilibrium steady-state phases with different scaling laws for the entanglement entropy. In this talk, we consider a variant of such circuits based on random tensor networks of non-interacting fermions which exhibit two phases, logarithmic scaling law and area law, as the tensor parameters are tuned. We introduce several quantities to identify these two phases and characterize the critical theory at the phase transitions. Using these quantities, we present phase diagrams for a generic parametrization of tensors and discuss the effect of the Born rule on the critical theory.