Mutual information and holographic entanglement entropy for strongly coupled <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:math>-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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>R</a:mi></a:math>-charge density. The <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mn>1</c:mn><c:mrow><c:mi>R</c:mi></c:mrow></c:mrow></c:math>-Charge Black Hole (1RCBH) model describes a strongly interacting fluid with a critical point in its phase diagram, while the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mn>2</e:mn><e:mrow><e:mi>R</e:mi></e:mrow></e:mrow></e:math>-Charge Black Hole model has no critical point. In both models, we find that the mutual information tends to be overall reduced by increasing the value of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>μ</g:mi><g:mo>/</g:mo><g:mi>T</g:mi></g:math> at larger values of the separation length <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>x</i:mi></i:math> between two disjoint spatial regions of the medium, while the opposite tendency is observed at lower values of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>x</k:mi></k:math>. We also observe that, very close to the critical point of the 1RCBH model, the mutual information tends to increase with increasing <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>μ</m:mi><m:mo>/</m:mo><m:mi>T</m:mi></m:math> 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 <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mo>ℓ</o:mo></o:math> 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 <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>μ</q:mi><q:mo>/</q:mo><q:mi>T</q:mi></q:math> and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mo>ℓ</s:mo></s:math>, and it correctly detects the critical point of the 1RCBH model, a feature that is also adequately detected by the mutual information.