Entanglement dynamics of a many-body localized system coupled to a bath

The combination of strong disorder and interactions in closed quantum systems can lead to many-body localization (MBL). However, this quantum phase is not stable when the system is coupled to a thermal environment. We investigate how MBL is destroyed in systems that are weakly coupled to a dephasive Markovian environment by focusing on their entanglement dynamics. We numerically study the third Rényi negativity R3, a recently proposed entanglement proxy based on the negativity that captures the unbounded logarithmic growth in the closed case and that can be computed efficiently with tensor networks. We also show that the decay of R3 follows a stretched exponential law, similarly to the imbalance, with, however, a smaller stretching exponent.