Gluon condensation, entanglement entropy and phase transition from holography

We consider the effect of gluon condensation on the holographic entanglement entropy, which can be regarded as an order parameter of deconfinement phase transition, in a holographic model at zero and finite temperature. At zero temperature, it is found that phase transition can occur at critical length for small gluon condensation. With the increase of gluon condensation, the critical length becomes small which means the phase transition is easy to occur. The difference of entanglement entropy between the connected and disconnected surfaces is always negative at large gluon condensation, which indicates no phase transition can occur in the deconfined phase as the subsystem size varies. These results show that the gluon condensation is related to the phase transition and contributes to deconfinement. At finite temperature, we can see that the difference of the entanglement entropy is also always negative and the system is always deconfined for vanishing and non-vanishing gluon condensation in this model. These results confirm that the difference of entanglement entropy is a useful probe to detect whether a system is in the confinement or deconfinement phase.