  In a recent paper, arXiv:1309.4877, a holographic p-wave model has been
proposed in an Einstein-Maxwell-complex vector field theory with a negative
cosmological constant. The model exhibits rich phase structure depending on the
mass and the charge of the vector field. We investigate the behavior of the
entanglement entropy of dual field theory in this model. When the above two
model parameters change, we observe the second order, first order and zeroth
order phase transitions from the behavior of the entanglement entropy at some
intermediate temperatures. These imply that the entanglement entropy can
indicate not only the occurrence of the phase transition, but also the order of
the phase transition. The entanglement entropy is indeed a good probe to phase
transition. Furthermore, the "retrograde condensation" which is a sub-dominated
phase is also reflected on the entanglement entropy.
