Logarithmic entanglement growth in two-dimensional disordered fermionic systems

We investigate the growth of the entanglement entropy S-ent following global quenches in two-dimensional free fermion models with potential and bond disorder. For the potential disorder case, we show that an intermediate weak localization regime exists in which S-ent(t) grows logarithmically in time t before Anderson localization sets in. For the case of binary bond disorder near the percolation transition, we find additive logarithmic corrections to area and volume laws as well as a scaling at long times, which is consistent with an infinite randomness fixed point.