Evolution of Holographic Entanglement Entropy after Thermal and Electromagnetic Quenches

TL;DR

This paper investigates how entanglement entropy evolves after thermal and electromagnetic quenches in a 2+1 dimensional field theory using holographic methods, revealing new phenomena like discontinuities and logarithmic growth patterns.

Contribution

It introduces a detailed holographic analysis of entanglement entropy dynamics after quenches, uncovering novel behaviors such as derivative discontinuities and logarithmic growth in a 2+1D setting.

Findings

Discontinuity in the time derivative of entanglement entropy near saturation.

Logarithmic growth of entanglement entropy before saturation.

Distinct behaviors for different geometries (strip and disc).

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.