Abstract:  We examine the behavior of entanglement entropy SEE of a subsystem A in a fully backreacted holographic model of a 1plus1 dimensional p wave superconductor across the phase transition. For a given temperature, the system goes to a superconducting phase beyond a critical value of the charge density. The entanglement entropy, considered as a function of the charge density at a given temperature, has a cusp at the critical point. In addition, we find that there are three different behaviors in the condensed phase, depending on the subsystem size. For a subsystem size l smaller than a critical size lc1, SEE continues to increase as a function of the charge density as we cross the phase transition. When l lies between lc1 and another critical size lc2 the entanglement entropy displays a nonmonotonic behavior, while for l larger than lc2 it decreases monotonically. At large charge densities SEE appears to saturate.
