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.
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Article funded by SCOAP3 . This work is partially supported by the grants NSF-PHY-1521045.
Das, Sumit R.; Fujita, Mitsutoshi; and Kim, Bom Soo, "Holographic Entanglement Entropy of a 1 + 1 Dimensional p-Wave Superconductor" (2017). Physics and Astronomy Faculty Publications. 502.