Thermalization after holographic bilocal quench

TL;DR

The paper analyzes holographic thermalization after a bilocal quench in a (1+1)-D CFT by modeling two antipodal boundary excitations as colliding massless particles in AdS$_3$ that form a BTZ black hole. Using the HRT prescription and a detailed geodesic analysis in the quotient AdS$_3$ geometry, it derives time-dependent entanglement entropy, mutual information, and two-point correlators for subsystems of the boundary circle. Key results include an emergent light-cone for entanglement spreading with velocity $v_E=v_{LC}=1$, a memory-loss regime tied to the black-hole interior, a universal linear growth of entanglement, and a scrambling time $t_*=\pi/2$ after which an entanglement shadow forms. The work highlights how non-equilibrium observables probe interior bulk physics and shows parallels between bilocal and global quenches, with insights into the role of topological identifications and winding geodesics in driving late-time behavior. It also outlines several avenues for extending the framework to higher dimensions and finite central charge.

Abstract

We study thermalization in the holographic (1+1)-dimensional CFT after simultaneous generation of two high-energy excitations in the antipodal points on the circle. The holographic picture of such quantum quench is the creation of BTZ black hole from a collision of two massless particles. We perform holographic computation of entanglement entropy and mutual information in the boundary theory and analyze their evolution with time. We show that equilibration of the entanglement in the regions which contained one of the initial excitations is generally similar to that in other holographic quench models, but with some important distinctions. We observe that entanglement propagates along a sharp effective light cone from the points of initial excitations on the boundary. The characteristics of entanglement propagation in the global quench models such as entanglement velocity and the light cone velocity also have a meaning in the bilocal quench scenario. We also observe the loss of memory about the initial state during the equilibration process. We find that the memory loss reflects on the time behavior of the entanglement similarly to the global quench case, and it is related to the universal linear growth of entanglement, which comes from the interior of the forming black hole. We also analyze general two-point correlation functions in the framework of the geodesic approximation, focusing on the study of the late time behavior.

Figures (21)

• Figure 1: A. Cartoon of propagation of a massless particle in the AdS$_3$ spacetime projected onto synchronous time slices of the AdS$_3$ cylinder in different moments of time. The particle moves from left (right) to right (left), and the spacetime is obtained by cutting out the wedge behind (in front of) the particle between the surfaces $W_\pm$. B. $3$D plot of massless particle moving through the AdS$_3$ spacetime in global coordinates. The intersection of surfaces $W_\pm$ is the worldline of the particle.
• Figure 2: Maximally extended BTZ black hole in global coordinates. A. Projection of surfaces $V_\pm$ onto equal time slices in different moments of global time. The dashed lines are identified. B. $3$D plot of the BTZ black hole identification surfaces $V_\pm$ between $\tau = -\frac{\pi}{2}$ and $\tau = 0$.
• Figure 3: Collision of particles in the BTZ rest frame. The dark red curve represents the horizon of the black hole which is about to form. The dark red curve is the apparent horizon.
• Figure 4: $3$D picture of identification surfaces in AdS$_3$ which correspond to the BTZ black hole creation in the rest frame in global coordinates.
• Figure 5: Embedding of BTZ coordinate time slices into AdS$_3$ cylinder. The blue surface is the horizon, which coincides with the $t= \infty$ time slice.

Theorems & Definitions (4)

• Proposition 1
• Proposition 2
• Proposition 3
• Proposition 4