Chiral and deconfinement phase transitions at finite temperature $T$ and quark number chemical potential $mu$ are simultaneously studied in the quenched dynamical holographic QCD model within the Einstein-Dilaton-Maxwell framework. By calculating the corresponding order parameters, i.e., the chiral condensate and Polyakov loop, it is shown that the transition lines of these two phase transitions are separated in the $T-mu $ plane. The deconfinement phase transition is shown to be always of crossover type and the transition line depends weakly on the baryon number density. Differently, the chiral transition is of crossover at small baryon number density and it turns to be of first order at sufficient large baryon number density. A critical endpoint (CEP), at which the transition becomes second order type, appears in the chiral transition line. This is the first time to realize the CEP of chiral phase transition in the $(T, mu)$ plane using the holographic EMD(Einstein-Maxwell-Dilaton) model for two flavour case. It is observed that between these two phase transition lines, there is a region with chiral symmetry restored and color degrees still confined, which could be considered as the quarkyonic phase. Qualitatively, this behavior is in consistent with the result in the Polyakov-loop improved Nambu-Jona-Lasinio (PNJL) model.
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