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

Abstract

We study the temporal evolution of the mutual information (MI) in a one-dimensional transverse Ising chain, coupled to a local fermionic Markovian bath, subsequent to a global quench of the transverse field. In the unitary case, 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.

Mixed-State Entanglement from Local Randomized Measurements

“…Figure 4 illustrates the time evolution of R 3 for (a) connected and (b) disconnected subsystems AB, respectively. The appearing peaks of R 3 have been predicted and analyzed for various one-dimensional quantum systems subject to local interactions [61,62] (and have also been studied in the context of Rényi mutual information [72,73]). They can be understood in terms of propagating quasi-particles which [10].…”

Nonlinear entanglement growth in inhomogeneous space-times

“…The linear spreading of entanglement entropy turns out to be very general and holds in various noninteracting [19][20][21][22][23][24][25] and short-range interacting [26][27][28][29][30] models, also for inhomogeneous initial states [32,33]. (However, deviations from the linear growth can be found in a presence of Markovian bath [49].) The linear growth of entanglement is due to the maximal speed of information.…”

Entanglement spreading in non-equilibrium integrable systems

“…In this respect, a main step forward has been taken in Ref. [235] (see also [236]), where it was shown that the quasiparticle picture can be adapted to the dynamic of some open quantum systems. In these systems, the spreading of entanglement is still governed by quasiparticles, but the environment introduces incoherent effects on top of it.…”