Evolution of Holographic Entanglement Entropy after Thermal and Electromagnetic Quenches

TL;DR

This work extends holographic entanglement entropy analyses to 2+1D field theories by studying time evolution after thermal and electromagnetic quenches in AdS$_4$. Using Vaidya-type backgrounds and minimal-surface calculations for strip and disc regions, it reveals a kinked saturation in the strip and a robust logarithmic growth in the electromagnetic quench, tied to the near-horizon AdS$_2$ structure. The disc typically shows linear-in-time entanglement growth toward saturation, consistent with subregion causality, while the strip exhibits richer branch structure and nontrivial saturation dynamics. Collectively, the results generalize known 1+1D quench behavior to higher dimensions and offer concrete predictions about how entanglement spreads in strongly coupled 2+1D systems under thermal and EM perturbations.

Abstract

We study the evolution and scaling of the entanglement entropy after two types of quenches for a 2+1 field theory, using holographic techniques. We study a thermal quench, dual to the addition of a shell of uncharged matter to four dimensional Anti-de Sitter (AdS_4) spacetime, and study the subsequent formation of a Schwarzschild black hole. We also study an electromagnetic quench, dual to the addition of a shell of charged sources to AdS_4, following the subsequent formation of an extremal dyonic black hole. In these backgrounds we consider the entanglement entropy of two types of geometries, the infinite strip and the round disc, and find distinct behavior for each. Some of our findings naturally supply results analogous to observations made in the literature for lower dimensions, but we also uncover several new phenomena, such as (in some cases) a discontinuity in the time derivative of the entanglement entropy as it nears saturation, and for the electromagnetic quench, a logarithmic growth in the entanglement entropy with time for both the disc and strip, before settling to saturation.

Figures (19)

• Figure 1: Diagrams of the two shapes we will consider for region $\mathcal{A}$.
• Figure 2: The finite contribution to the entanglement entropy as a function of $\tilde{\ell} = \ell/R$ in the pure AdS$_4$ background.
• Figure 3: The finite contribution to the entanglement entropy for the strip as a function of $\tilde{\ell} = \ell/z_0$ in the AdS$_4$--Schwarzschild background.
• Figure 4: The finite contribution to the entanglement entropy for the disc as a function of $\ell/z_0$ in the AdS$_4$--Schwarzschild background.
• Figure 5: The finite contribution to the entanglement entropy for the disc as a function of $\ell/R$ in the AdS$_4$ Dyonic black hole background.