Holographic entanglement entropy of a 1+1 dimensional p-wave superconductor

We examine the behavior of entanglement entropy S-A(EE) of a subsystem A in a fully backreacted holographic model of a 1 + 1 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 l(c1), S-A(EE) continues to increase as a function of the charge density as we cross the phase transition. When l lies between l(c1) and another critical size l(c2) the entanglement entropy displays a non monotonic behavior, while for l > l(c2) it decreases monotonically. At large charge densities S-A(EE) appears to saturate. The non-monotonic behavior leads to a novel phase diagram for this system.