Holographic entanglement entropy under external magnetic field from the EMD model

Abstract

In this work, we explore holographic entanglement entropy in the QCD phase diagram under an external magnetic field using an Einstein-Maxwell-dilaton model. We consider both the specious-confinement and deconfined phases. In the perpendicular magnetic field orientation, the strip length shows three distinct branches, and the entanglement entropy develops a swallow-tail structure, indicating a transition between connected and disconnected entanglement surfaces. For the parallel orientation, the behavior is monotonic and no transition occurs. In addition, the difference in entanglement entropy changes smoothly with temperature at small chemical potential, but becomes multivalued at large chemical potential. Increasing the magnetic field restores single-valued behavior. These results are consistent with the black hole thermodynamics and the QCD phase diagram. Our findings show that entanglement entropy can serve as an effective probe of the QCD phase transition.