Holographic Entanglement Entropy in the QCD Phase Diagram with a Critical Point

We calculate the holographic entanglement entropy for the holographic QCD phase diagram considered in [Knaute, Yaresko, K\"ampfer (2017), arXiv:1702.06731] and explore the resulting qualitative behavior over the temperature-chemical potential plane. In agreement with the thermodynamic result, the phase diagram exhibits the same critical point as the onset of a first-order phase transition curve. We compare the phase diagram of the entanglement entropy to that of the thermodynamic entropy density and find a striking agreement in the vicinity of the critical point. Thus, the holographic entanglement entropy qualifies to characterize different phase structures. The scaling behavior near the critical point is analyzed through the calculation of critical exponents.