From area- to non-area-law scaling of entanglement in unitary system-bath dynamics

The evolution of a system coupled to baths is usually described by a master equation that – in the long-time limit – often leads to a fixed steady-state density matrix. Instead, unraveling the master-equation evolution into quantum trajectories can reveal a transition in the scaling of entanglement as the system-bath coupling increases, which cannot be observed from the density matrix alone.

Here, we go beyond the paradigm of trajectories from master equations and explore whether one can observe a qualitatively analogous behavior in the scaling of entanglement entropy when considering the unitary evolution of the system plus bath as a single entity. We investigate the scaling of entanglement in a unitary quantum setup composed of a 2D lattice of free fermions, coupled to a fermionic bath. We find that various quantities indicate a change from area to non-area law scaling with the system size as we vary the magnitude of the coupling between the system and the bath.