The entanglement properties of holographic QCD model with a critical end point

We investigate different entanglement properties of a holographic QCD (hQCD) model with a critical end point at finite baryon density. Firstly we consider the holographic entanglement entropy (HEE) of this hQCD model in a spherical shaped region and a strip shaped region, respectively, and find that the HEE of this hQCD model in both regions can reflect QCD phase transition. What is more is that although the area formulas and minimal area equations of the two regions are quite different, the HEE have very similar behavior on the QCD phase diagram. So we argue that the behavior of HEE on the QCD phase diagram is independent of the shape of subregions. However, as we know that HEE is not a good quantity to characterize the entanglement between different subregions of a thermal system. So we then study the mutual information (MI), conditional mutual information (CMI) and the entanglement of purification (Ep) in different strip shaped regions. We find that the three entanglement quantities have very similar behavior: their values do not change so much in the hadronic matter phase and then rise up quickly with the increase of $T$ and $\m$ in the QGP phase. Near the phase boundary, these three entanglement quantities change smoothly in the crossover region, continuously but not smoothly at CEP and show discontinuity behavior in the first phase transition region. And all of them can be used to distinguish different phases of strongly coupled matter.