Holographic entanglement properties in the QCD phase diagram from EMD models

Abstract: In this study, we investigate the behavior of entanglement properties in the QCD phase diagram using holographic Einstein-Maxwell-Dilaton (EMD) models. We consider two representative holographic QCD models and examine various entanglement measures, including entanglement entropy, conditional mutual information, and entanglement of purification. We find that the entanglement entropy obtained using the direct UV-cutoff renormalization method shows significant dependence on the specific model being used. However, the outcomes of other non-divergent entanglement measures, such as cutoff-independent entanglement entropy, conditional mutual information, and entanglement of purification, exhibit congruence in our calculations. When we focus specifically on the temperature range below $300$ MeV, we observe a similar behavior among the three entanglement measures. This may suggests that within this temperature range, the entanglement of QCD matter decreases with increasing temperature. Additionally, we observe distinct phase transition behaviors of entanglement properties at the critical end point (CEP) and first-order phase transitions. This observation highlights the potential of entanglement properties as effective order parameters for QCD matter phase transitions.