Double local quenches in 2D CFTs and gravitational force

Abstract

In this work we extensively study the dynamics of excited states created by instantaneous local quenches at two different points, i.e. double local quenches. We focus on setups in two dimensional holographic and free Dirac fermion CFTs. We calculate the energy stress tensor and entanglement entropy for double joining and splitting local quenches. In the splitting local quenches we find an interesting oscillating behaviors. Finally, we study the energy stress tensor in double operator local quenches. In all these examples, we find that, in general, there are non-trivial interactions between the two local quenches. Especially, in holographic CFTs, the differences of the above quantities between the double local quench and the simple sum of two local quenches tend to be negative. We interpret this behavior as merely due to gravitational force in their gravity duals.

Subsystem distance after a local operator quench

“…While in previous studies, the focus has been on primary or descendent operators [12,24], here we also consider the case in which the local operator is a sum of several primary fields (as we shall see, this is not only done for academic curiosity, but because it is the right setup to describe the local operator quenches in spin chains and lattice models). This is different from the case of several operators inserted simultaneously at different positions investigated in [33,34].…”

“…In this paper, we consider the subsystem trace distance in latter category of quenches: at an initial time t = 0, a local operator is inserted somewhere in the ground state of the theory, and then the system is let evolve without further disturbance. The time evolution of entanglement and Rényi entropies, as well as of local operators, has been intensively studied in the literature [10][11][12][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. The main goal of this paper is to investigate the distance between the RDMs at different times after a local operator quench.…”

Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories

“…Furthermore, to fully understand the dynamics of information in 2D CFT, more generic non-equilibrium settings must be considered, such as those involving local operator insertions [45]. The interpolation from local to global quenches may provide new hints on the missing entanglement and mysterious correlations, which can be accomplished by considering, for example, multi-local excitation [80,81]. We leave this to future work.…”

Entanglement wedge cross section from CFT: dynamics of local operator quench

“…We first consider the setup, 0 < 18) which means that in the bulk side, the entanglement wedge for two intervals A = [u 1 , v 1 ] and B = [u 2 , v 2 ] is connected. 6 In this article, we only focus on this connected case because the reflected entropy for the disconnected case trivially vanishes, which is not interesting. Note that even if this connected condition is satisfied, the entanglement wedge could become disconnected under the time evolution (which is discussed later above (2.58)).…”

“…The Renyi entropy is a generalization of the entanglement entropy, which is defined as 2) and the limit n → 1 of the Renyi entropy defines the entanglement entropy S (A). For this measure, a large number of works have been done to characterize the dynamics, for example, after joining quench [1], global quench [2,3], splitting quench [4] and double quench [5][6][7].…”