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

Abstract

We examine the behavior of entanglement entropy S EEA 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 EE A 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 nonmonotonic behavior, while for l > l c2 it decreases monotonically. At large charge densities S EE A appears to saturate. The non-monotonic behavior leads to a novel phase diagram for this system.

Holographic subregion complexity of a (1+1)-dimensional $p$-wave superconductor

“…The holographic entanglement entropy S EE f in in the normal phase was analyzed by using charged black holes with hyperbolic horizons [55] and 2nd order excitations [52,56]. The charge q dependence of the finite part S EE f in was analyzed in [23], whenκ 2 < 0.31. The finite part S EE f in has a cusp at the intersecting critical point between normal and condensed phases.…”

“…where S EE is Ryu-Takayanagi formula S EE = 2π κ 2 (γ A ). The renormalized EE of an AdS 3 black hole is given by (23) when the minimal surface does not wrap the black hole horizon.…”

“…Ryu-Takayanagi surface is a useful way of analyzing the entanglement entropy of strongly coupled systems. The holographic entanglement entropy has been an order parameter of the confinement/deconfinement phase transition [11]- [15] and the probe of superconductor phase transitions [16]- [23].…”

“…In the large N limit, one can evade Coleman-Mermin-Wagner theorem in this lower dimensional system [34]: quantum fluctuations preventing formation of condensates are suppressed in the large N limit. The holographic entanglement entropy is computed in a fully backreacted metric of a 1 + 1 dimensional p-wave superconductor across the phase transition [23]. The backreacted metric turns out to be a black hole with the vector hair in the condensed phase, while it turns out to be the AdS 3 charged black hole in the normal phase.…”

Holographic entanglement entropy and complexity in Stückelberg superconductor

“…Later, the authors of [23] found that the entanglement entropy has a different behavior near the contact interface of the superconducting to normal phase due to the proximity effect. Further effort in using holographic entanglement entropy as a probe of phase transition has been made in [24][25][26][27][28][29][30][31][32][33][34] and therein. The authors studied the behaviors of holographic entanglement entropy in different orders phase transition and also in quantum phase transition.…”