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

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 cases, we find that the mutual information in the thermodynamically stable branch of black hole solutions is reduced by increasing the value of the dimensionless ratio of R-charge chemical potential over temperature, $\mu/T$, indicating that the R-charge chemical potential acts as a suppressor of total correlations between fields in two disjoint spatial regions of a hot and dense strongly interacting medium. Moreover, the mutual information between the fields in the two disjoint regions is observed to be enhanced by increasing the size of these regions, with such an enhancement asymptotically saturating. The finite part of the entanglement entropy may change sign depending on the values of $\mu/T$ and the variable size $\ell$ of the entangling slab geometry, and it correctly detects the critical point of the 1RCBH model, a feature that is also adequately detected by the mutual information.