Entanglement transition in unitary system-bath dynamics

The evolution of a system coupled to baths is commonly described by a master equation that, in the long-time limit, yields a steady-state density matrix. However, when the same evolution is unraveled into quantum trajectories, it is possible to observe a transition in the scaling of entanglement within the system as the system-bath coupling increases - a phenomenon that is invisible in the trajectory-averaged reduced density matrix of the system. Here, we go beyond the paradigm of trajectories from master equations and explore whether a qualitatively analogous entanglement-scaling transition emerges in the unitary evolution of the combined system-bath setup. We investigate the scaling of entanglement in a unitary quantum setup composed of a 2D lattice of free fermions, where each site is coupled to a fermionic bath. Varying the system-bath coupling reveals a transition from logarithmic-law to area-law scaling, visible in the logarithmic fermionic negativity, mutual information, and also in the correlations. This occurs while the system's steady-state properties are trivial, highlighting that the signatures of these different scalings are within the bath-bath correlations.