System-bath entanglement during Markovian relaxation of a fermionic impurity

We investigate the dynamics of entanglement between the system and the environment during thermalization of a noninteracting fermionic impurity coupled to a fermionic thermal bath. We show that transient entanglement can be observed even in the weak coupling regime, when the reduced dynamics and thermodynamics of the system can be well described by an effectively classical and Markovian master equation for the state populations. This entanglement vanishes for long times, but is preserved over timescales comparable to the relaxation time. Its magnitude depends only weakly on the system-environment coupling but instead strongly on the purity of the initial state of the system. We relate the presence of such transient entanglement to the unitary character of the system-bath dynamics underlying the reduced Markovian description.