Entanglement Suppression Due to Black Hole Scattering

Abstract

We consider the evolution of entanglement entropy in a two-dimensional conformal field theory with a holographic dual. Specifically, we are interested in a class of excited states produced by a combination of pure-state (local operator) and mixed-state local quenches. We employ a method that allows us to determine the full time evolution analytically. While a single insertion of a local operator gives rise to a logarithmic time profile of entanglement entropy relative to the vacuum, we find that this growth is heavily suppressed in the presence of a mixed-state quench, reducing it to a time-independent constant bump. The degree of suppression depends on the relative position of the quenches as well as the ratio of regularization parameters associated with the quenches. This work sheds light on the interesting properties of gravitational scattering involving black holes.

Figures (19)

• Figure 1: Setup for the single local operator quench.
• Figure 2: Our setup of interest depicted on the Euclidean plane. The gluing of two holes produces a mixed-state excitation, while the insertion of operator $\cal O$ gives rise to a local excitation. We measure the entanglement entropy $S_A$ for the interval $A$.
• Figure 3: The original two-hole geometry $(X,\bar{X})$ is conformally transformed into a torus $(w,\bar{w})$. The two holes in figure \ref{['fig:setup']} are mapped onto the vertical boundaries of the strip, as indicated by the red lines. They are to be identified. The horizontal boundaries are also identified as the spatial direction is compactified.
• Figure 4: Our setup of interest depicted on the Lorentzian plane. The local operator excitation by ${\cal O}$ produces an entangled pair of modes that propagate in opposite directions at the speed of light. When $t_M+x_P=0$, one of the modes directly collides with the mixed-state excitation.
• Figure 5: Conformally transforming our initial two-hole geometry would eventually give us a torus (drawn as an annulus with its boundaries compactified), where the time direction is compactified tangentially and the space direction is compactified radially. The two identified holes in figure \ref{['fig:setup']} are mapped onto the red segment.