Mutual information and holographic entanglement entropy for strongly-coupled R-charged plasmas

TL;DR

This paper numerically studies how mutual information and holographic entanglement entropy behave in strongly coupled R-charged plasmas at finite temperature, revealing critical phenomena and correlation lengths near phase transitions.

Contribution

It provides the first detailed numerical analysis of mutual information and entanglement entropy in R-charged holographic models at finite temperature and charge density, highlighting critical behavior.

Findings

Mutual information decreases with increasing μ/T at large separation, increases at small separation.

Near the critical point, mutual information increases with μ/T in the stable branch.

Entanglement entropy can change sign and detects the critical point.

Abstract

We numerically evaluate, for slab entangling geometries, the mutual information and the holographic entanglement entropy between strongly interacting fields in different spatial regions for two different conformal holographic models at finite temperature and R-charge density. The 1 R-Charge Black Hole (1RCBH) model describes a strongly interacting fluid with a critical point in its phase diagram, while the 2 R-Charge Black Hole (2RCBH) model has no critical point. In both models, we find that the mutual information tends to be overall reduced by increasing the value of $\mu/T$ at larger values of the separation length $x$ between two disjoint spatial regions of the medium, while the opposite tendency is observed at lower values of $x$. We also observe that very close to the critical point of the 1RCBH model, the mutual information tends to increase with increasing $\mu/T$ in the stable branch of black hole solutions. Moreover, the mutual information between the fields in the two disjoint regions is observed to be enhanced by increasing the characteristic size $\ell$ of these regions, with such an enhancement asymptotically saturating, thus suggesting the existence of a finite field correlation length between the disjoint regions of the system. The finite part of the entanglement entropy may change sign depending on the values of $\mu/T$ and $\ell$, and it correctly detects the critical point of the 1RCBH model, a feature that is also adequately detected by the mutual information.