On the complexity of a 2  +  1-dimensional holographic superconductor

Abstract

We present the results of our computation of the subregion complexity and also compare it with the entanglement entropy of a 2 + 1-dimensional holographic superconductor which has a fully backreacted gravity dual with a stable ground sate. We follow the "complexity equals volume" or the CV conjecture. We find that there is only a single divergence for a strip entangling surface and the complexity grows linearly with the large strip width. During the normal phase the complexity increases with decreasing temperature, but during the superconducting phase it behaves differently depending on the order of phase transition. We also show that the universal term is finite and the phase transition occurs at the same critical temperature as obtained previously from the free energy computation of the system. In one case, we observe multivaluedness in the complexity in the form of an "S" curve.

Holographic subregion complexity in metal/superconductor phase transition with Born–Infeld electrodynamics

“…2, the values of HSC for the superconducting state is always larger than that for the normal state and increases as the temperature decreases. This result is in agreement with that reported in [39,43].…”

“…This phenomenon does not only appear in this system. In fact, the HSC of two different operators also exhibit different behaviors in 2+1 dimensional holographic superconductor, see [43], but the underlying mechanism remains mysterious.…”

“…Because the complexity measures the difficulty of turning one state into another, it is expected that the HSC should capture the behavior of the phase transition and can provide useful information as well. In fact, some authors have recently discussed the holographic complexity in different types of holographic superconducting models where the backreaction is taken into account [38][39][40][41][42][43]. Reference [38] discussed the HSC for two dimensional holographic superconductor with backreactions and argued that extra divergence terms are generated at critical points.…”

“…It is worth noting that Ref. [43] has investigated the HSC of a 2 + 1 dimensional holographic superconductor, which is very similar to the set up in [42] (involves the first order phase transition and second order phase transition), the results of HSC of the superconducting phase during the second order phase transition are opposite to what is found in [42]. For the holographic metal/superconductor phase transition, the HEE in the superconducting case is always less than that in the normal phase [15].…”

Holographic entanglement entropy and complexity in Stückelberg superconductor

“…The complexity essentially measures the difficulty of turning a quantum state into another and so it could reflect a phase transition on the boundary field theory. Holographic complexity has been studied in one dimensional s-wave superconductor in [36][37][38], p-wave superconductor in [39] and QCD phase transition [40]. It was found that holographic complexity behave in the different way with holographic entanglement entropy and both of them can reflect the one dimensional phase transitions.…”