Mixed state entanglement measures as probe for confinement

TL;DR

This paper investigates how various entanglement measures behave in confining holographic models, revealing model-independent phase transitions and inequalities that deepen understanding of confinement in gauge theories.

Contribution

It provides a comparative analysis of entanglement measures across different confining holographic models, highlighting universal features and phase transition behaviors.

Findings

Entanglement negativity and entropy undergo phase transitions at the same critical length.

Entanglement wedge cross-section shows discontinuous behavior at phase transitions.

The inequality that entanglement wedge cross-section exceeds half of mutual information always holds.

Abstract

We study holographic aspects of mixed state entanglement measures in various large $N$ top-down as well as bottom-up confining models. For the top-down models, we consider wrapped $D3$ and $D4$ branes gravity solutions whereas, for the bottom-up confining model, the Einstein-Maxwell-dilaton gravity solution is considered. We study entanglement entropy, mutual information, entanglement wedge cross-section and entanglement negativity for the strip subsystems and find model independent features of these entanglement measures in all confining theories. The entanglement negativity and entropy exhibit a phase transition at the same critical strip length $L_{crit}$, at which the order of these measures changes from $\mathcal{O}(N^2)$ to $\mathcal{O}(N^0)$. The entanglement wedge cross-section similarly shows an order change at $L_{crit}$ and exhibits a discontinuous behaviour each time a phase transition between different entangling surfaces occur. We further test the inequality involving mutual information and entanglement wedge cross-section, and find that the latter always exceeds half of the former.