Entanglement entropy and complexity in the holographic model of superfluid

We numerically study the holographic entanglement entropy and complexity conjectured with the volume in the holographic superfluid with full backreaction which can realize first and second order phase transitions. Our results show that both the entanglement entropy and complexity exhibit the behaviors characterizing the type of the transition. For the first order phase transition, there is a fast drop of the entanglement entropy and a fast jump of the complexity at the critical temperature, while both of them are continuous but non-differentiable at the second order phase transition point. These suggest that both of holographic entanglement entropy and complexity may be used as a good probe to the type of superfluid phase transition. Moreover, at a fixed temperature in the superfluid phase, we observe that the increasing superfluid velocity increases the entanglement entropy but decreases the complexity. Interestingly, we find that, for the condensation operators O+ and O-, the dependence of holographic entanglement entropy on the backreaction is inconsistent and so is the dependence of holographic complexity on the superfluid velocity in the normal phase, which indicates that the entanglement entropy and complexity may reflect deep physics about the difference between the two operators in the superfluid dual system.