Numerical study of holographic entanglement entropy and subregion complexity for a p-wave superconductor in massive gravity

Abstract

We invastigate numerically the holographic entanglement entropy (HEE) and holographic subregion complexity (HSC) for a p-wave superconductor with backreaction in the framework of dRGT massive gravity. We calculate the HEE and HSC as functions of subregion strip-width or temperature by following the RT formula and CV conjecture. It is shown that both the HEE and HSC exhibit a discontinuity in their slope at the critical temperature, hence the two physical quantities can be able to probe the p-wave superconducting phase transition. Both the HEE and HSC increase linearly at the large strip-widths, which is consistent with the “area law” of entanglement entropy and the definition of complexity in quantum information. We notice that the HEE in the superconducting phase is always lower than that in the normal phase. In contrast, the behavior of HSC shows a distinct and intriguing dependence on the strip-width. Through comparing the values of HEE and HSC for different massive coupling constants or backreaction, we find that increasing backreaction or introducing massive gravity term results in a notable increase in both HEE and HSC.