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|Paper IPM / Particles And Accelerator / 16473||
Using holographic idea, we study the entanglement of purification in a field theory with a critical point in intermediate and low temperature regime. This theory includes temperature TTT as well as chemical potential Î¼Î¼. In the intermediate regime, due to chemical potential, we observe that new terms proportional to temperature square appear in the final result of entanglement of purification or equivalently, apart from T0T^0T0 and T4T^4T4 terms in the case of Î¼=0Î¼=0, it contains the terms proportional to T2T^2T2. Our results also indicate that the entanglement of purification, i.e. the correlation between subsystems, can decrease or increase depending on the value of Î¼T TÎ¼ï¿½?? when the other parameters are kept fixed. However, in the low temperature limit, the correlation always decreases, comparing to the Î¼=0Î¼=0 case, independent of the value of Î¼T TÎ¼ï¿½?? when the other parameters do not alter. The existence of a critical point in the theory changes the behavior of entanglement of purification in such a way that the entanglement of purification experiences a maximum or minimum. Moreover, near the critical point, we analytically show that the critical exponent is equal to 0.5 in both regimes and also the term proportional to T2T^2T2 changes sign and becomes negative in the intermediate regime.
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