Holographic entanglement of purification for thermofield double states and thermal quench

TL;DR

This paper investigates the behavior of holographic entanglement of purification (EoP) in black brane spacetimes, revealing bounds and conditions for its existence and how it responds to thermal quenches, advancing understanding of quantum entanglement in holography.

Contribution

It provides new insights into the conditions under which holographic EoP exists and its dynamics during thermal quenches in black brane backgrounds.

Findings

EoP vanishes beyond a certain separation in Schwarzschild-AdS.

EoP exists only for sufficiently wide strips in two-boundary scenarios.

Equilibrium time of EoP depends solely on strip width.

Abstract

We explore the properties of holographic entanglement of purification (EoP) for two disjoint strips in the Schwarzschild-AdS black brane and the Vaidya-AdS black brane spacetimes. For two given strips on the same boundary of Schwarzschild-AdS spacetime, there is an upper bound of the separation beyond which the holographic EoP will always vanish no matter how wide the strips are. In the case that two strips are in the two boundaries of the spacetime respectively, we find that the holographic EoP exists only when the strips are wide enough. If the width is finite, the EoP can be nonzero in a finite time region. For thermal quench case, we find that the equilibrium time of holographic EoP is only sensitive to the width of strips, while that of the holographic mutual information is sensitive not only to the width of strips but also to their separation.