Entanglement Entropy after Double Excitation as an Interaction Measure

Abstract

We study entanglement entropy after a double local quench in two-dimensional conformal field theories (CFTs), with any central charge c > 1. In the holographic CFT, such a state with double-excitation is dual to an AdS space with two massive particles introduced from the boundary. We show that the growth after the double local excitations cannot be given by the sum of two local quenches but with an additional negative term. This negative contribution can be naturally interpreted as due to the attractive force of gravity. In CFT side, this evaluation of the entanglement entropy is accomplished by a special limit of 6-point functions, where we employed the fusion matrix approach for multi-point conformal blocks developed in arXiv:1905.02191.

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

“…Fortunately, we find that the correct choice for u 2 < t < √ −v 1 u 2 is just the following channel without monodromy tranformations, In fact, this calculation cannot be found in previous works but we can calculate it by the method developed in this section (which is explained later in Section 4). 7 In the following, we will abbreviate σ n ⊗σ n by 2h n .…”

“…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].…”