Comments on entanglement propagation

Abstract

We extend our work on entanglement propagation following a local quench in 2+1 dimensional holographic conformal field theories. We find that entanglement propagates along an emergent lightcone, whose speed of propagation v E seems distinct from other measures of quantum information spreading. We compare the relations we find to information and hydrodynamic velocities in strongly coupled 2+1 dimensional theories. While early-time entanglement velocities corresponding to small entangling regions are numerically close to the butterfly velocity, late-time entanglement velocities for large regions show less regularity. We also generalize and extend our previous results regarding the late-time decay of the entanglement entropy back to its equilibrium value.

Time evolution of entanglement for holographic steady state formation

“…For the case of time-dependent bulk spacetimes where the HRT prescription [44] applies, a proof of (6.10) was given in [89] using the null curvature condition, see also the review [90]. Similarly at n = 3, we encounter what is known as the monogamy of mutual information 22 or alternatively negativity of tripartite information…”

“…It is also interesting to note that the cases studied in [51,52] display a linear growth independent of the equation of state, showing more evidence that points towards a universal behavior. Related work on the evolution of entanglement entropy after a local quench also include [17][18][19][20][21][22][23][24][25]. In most of these references the authors complemented the holographic analysis with results from a CFT analysis.…”

“…From (5.3) and (5.4), it is obvious that 5) and the case d = 2 is the special case where 1 = v B = v E . Interestingly, the velocities seem to play an important role in the description of entanglement spreading not only for global quenches, but also for local quenches [20,22,25].…”

Thermalization after holographic bilocal quench

“…The universal result for global quenches in 2d CFT is v E = 1, and from comparing of (4.10) to (4.13) we see that this value for the entanglement velocity holds true for our bilocal quench scenario as well. Thus we obtain another argument for the fact that the notion of the entanglement velocity and its bounds is relevant not only for global quenches, but also for local quenches as well [29,30,32]. As it turns out, the linear growth regime in our case is directly related to the memory loss regime [8,9,19], since the function ∆S in the leading order only depends on the difference U = t = ∆ϕ 2 .…”

“…Another type of quantum quenches is the local quench [21][22][23][24][25][26][27][28][29][30][31][32]. Such quenches have been studied holographically as perturbations of the zero temperature vacuum [22,24] as well as of thermal equilibrium state [26,27,[29][30][31][32][33]. In the present paper we study the thermalization in holographic (1 + 1)-dimensional compact CFT after a particular variation of a local quantum quench.…”