In the presence of finite chemical potential $$\mu $$ μ , we holographically compute the entanglement of purification in a $$2+1$$ 2 + 1 - and $$3+1$$ 3 + 1 -dimensional field theory and also in a $$3+1$$ 3 + 1 -dimensional field theory with a critical point, at which a phase transition takes place. We observe that compared to $$2+1$$ 2 + 1 - and $$3+1$$ 3 + 1 -dimensional field theories, the behavior of entanglement of purification near critical point is different and it is not a monotonic function of $$\frac{\mu }{T}$$ μ T where T is the temperature of the field theory. Therefore, the entanglement of purification distinguishes the critical point in the field theory. We also discuss the dependence of the holographic entanglement of purification on the various parameters of the theories. Moreover, the critical exponent is calculated.

We study the holographic entanglement measures such as the holographic mutual information, HMI, and the holographic entanglement of purification, EoP, in a holographic QCD model at finite temperature and zero chemical potential. This model can realize various types of phase transitions including crossover, first order and second order phase transitions. We use the HMI and EoP to probe the phase structure of this model and we find that at the critical temperature they can characterize the phase structure of the model. Moreover we obtain the critical exponent using the HMI and EoP.

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We evaluate the holographic entanglement entropy, HEE, holographic mutual information, HMI, and holographic entanglement of purification, EoP, in a non-conformal model at zero and finite temperature. In order to find the analytical results we consider some specific regimes of the parameter space. We find that the non-conformal effects decrease the redefined HEE and increase the redefined HMI and EoP in the all studied regimes. On the other side, the temperature effects increase (decrease) the redefined HEE (HMI) in the all studied regimes while it has no definite effect on the redefined EoP. Finally, from the information point of view, we find that in the vicinity of the phase transition the zero temperature state is more favorable than the finite temperature one.