Complexity for holographic superconductors with the nonlinear electrodynamics

Abstract

We systematically study the complexity of a strip-shaped subregion in a fully backreacted holographic model of a superconductor with the nonlinear electrodynamics by the “complexity=volume” (CV) conjecture, and compare it with the holographic entanglement entropy. We consider three types of typical nonlinear electrodynamics and find that the holographic complexity can be utilized as a good probe of the superconductor phase transition in the nonlinear electrodynamics like the holographic entanglement entropy does. For the operator O−, the complexity decreases (or increases) monotonically as the absolute value of the nonlinear parameter |b| grows in the superconducting (or normal) phase, which is the opposite of the behavior of the holographic entanglement entropy, and this property holds for various types of the nonlinear electrodynamics. For the operator O+, in the superconducting phase, it is interesting to note that the complexity is a monotonic decreasing function of |b| for the Logarithmic nonlinear electrodynamics (LNE), but in systems with the Born-Infeld nonlinear electrodynamics (BINE) and Exponential nonlinear electrodynamics (ENE), as the parameter |b| increases, the complexity first decreases and arrives at its minimum at some threshold, then increases monotonously. Whereas the non-monotonic variation of the holographic entanglement entropy can be seen in all the three types of the nonlinear electrodynamics, concretely, it first rises, then descends with larger |b|, and has a peak at the inflection point. Furthermore, comparing with the BINE and LNE, we find that the ENE has stronger effect on the condensation formation, the subregion complexity and the entanglement entropy of the holographic superconductors with backreaction.