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

We investigated different entanglement properties of a holographic QCD(hQCD)model with a critical end point at the finite baryon density.Firstly,we considered the holographic entanglement entropy(HEE)of this hQCD model in a spherical shaped region and a strip shaped region.It was determined that the HEE of this hQCD model in both regions can reflect QCD phase transition.Moreover,although the area formulas and minimal area equations of the two regions were quite different,the HEE exhibited a similar behavior on the QCD phase diagram.Therefore,we assert that the behavior of the HEE on the QCD phase diagram is independent of the shape of the sub-regions.However,the HEE is not an ideal parameter for the characterization of the entanglement between different subregions of a thermal system.As such,we investigated the mutual information(MI),conditional mutual informa-tion(CMI),and the entanglement of purification(Ep)in different strip shaped regions.We determined that the three entanglement quantities exhibited some universal behavior;their values did not change significantly in the hadronic matter phase but increased rapidly with the increase in T and μ in the QGP phase.Near the phase boundary,these three entanglement quantities changed smoothly in the crossover region and continuously but not smoothly at CEP;they exhibited discontinuous behavior in the first phase transition region.These properties can be used to distinguish between the different phases of strongly coupled matter.