Growth of mutual information in a quenched one-dimensional open quantum many body system

We study the temporal evolution of the mutual information (MI) of a one-dimensional integrable transverse Ising chain, coupled to a local fermionic Markovian bath, subsequent to a global quench of the transverse field. In the unitary case, where the MI (or equivalently the bipartite entanglement entropy) saturates to a steady state value (obeying a volume law) following a ballistic growth. On the contrary, we establish that in the dissipative case the MI is exponentially damped both during the initial ballistic growth as well as in the approach to the steady state. The functional form proposed to describe the time dependence of the MI, which matches perfectly with the numerical results, suggests that information propagates solely through entangled pairs of quasi-particles having a finite life time; this quasi-particle picture is further corroborated by the analysis of two-point correlations. Remarkably, in spite of the finite life time of the quasi-particles, a finite steady state value of the MI survives which is an artefact of non-vanishing two points correlations. Further, the finite life time renders a finite length scale in this steady state correlations resulting in a sub-volume law of the MI.