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

Abstract

We investigate the holographic subregion complexity (HSC) and compare it with the holographic entanglement entropy (HEE) in the metal/superconductor phase transition for the Born–Infeld (BI) electrodynamics with full backreaction. Based on the subregion CV conjecture, we find that the universal terms of HSC remain finite during phase transitions, and the HSC is a good probe to the critical temperature in the holographic superconducting system. Furthermore, we observe that for the operator $$\mathcal {O}_{+}$$ O + , the HSC of the superconducting phase decreases first and then increases as the BI parameter increases, which is completely different from that of HEE, and the value of the BI parameter corresponding to the inflection point of HSC is larger than that of HEE. But for the operator $$\mathcal {O}_{-}$$ O - , the HSC increases monotonically as the BI parameter increases, which is similar to that of HEE.

Holographic subregion complexity in unbalanced holographic superconductors

“…However, there are still many ambiguities about the behavior of HSC in holographic superconductors. Especially for the behavior of HSC with temperature changes, it is different from the HEE in some models [38,41], while it is similar to the behavior of HEE in some cases [42,43]. As pointed out in [44], since the entanglement entropy grows in a very short time during the thermalization process of a strongly coupled system, it is usually not enough to describe the rich geometric structure.…”

“…In fact, for the HSC in two different operators, similar phenomena have also been found in the Refs. [42,43], but the underlying mechanism is still unclear.…”

Holographic entanglement entropy and complexity for D-wave superconductors

“…Similar phenomena that the different behaves of the HSC for different fixed strip-widths in superconducting phase transitions have also been found recently in Refs. [50,51], but the physical mechanism is still unknown. Furthermore, in the Figs.…”