Holographic Entanglement Entropy And Holographic Subregion Complexity In Holographic Superconductors

The holographic principle provides a new perspective to understand the world.The AdS/CFT duality,as the most important concrete realization of the holo-graphic principle,reveals the deep connection between gravitational theory and quantum field theory,and provides us a useful theoretical method to study the strongly coupled systems in various fields of physics.According to the AdS/CFT duality,the holographic superconductor model was constructed,which provides a new method for studying high-temperature superconductors.On the other hand,the holographic entanglement entropy(HEE)and holographic complexity conjec-ture play a crucial role in understanding the origin of spacetime and the quantum properties of black holes,which have received extensive attention.In this paper,we investigate the HEE and holographic subregion complexity(HSC)in holographic superconductors.By using the subregion“complexity equal volume”(CV)conjecture,we inves-tigate the HSC and compare it with the HEE in the metal/superconductor phase transition for the Born-Infeld electrodynamics.We find that the HSC remain fi-nite during phase transitions.Both HEE and HSC can capture the information of phase transition,but they have different behaviors.The behavior of HEE with respect to temperature is consistent in two different operators:the HEE in the superconducting phase is always less than the one in the metal case and drops as the temperature decreases.The behavior of HSC with respect to temperature is not consistent in two different operators.The behavior of HSC of operator(?)_+is completely opposite to the HEE,while the HSC of operator(?)_-shows a similar behavior with HEE.In addition,we also found that for a fixed temperature below the critical temperature,when the Born-Infeld coupling parameter increases,the HEE of operator(?)_+first increases and then decreases,while the HSC of opera-tor(?)_+first decreases and then increases,but the HEE and HSC of operator(?)_-remain monotonically increasing.Based on the subregion CV conjecture,we investigate the behavior of the HSC and compare it with the HEE in the unbalanced holographic superconductors,which indicates that both the HEE and HSC can be used as good probes to the phase transition in unbalanced holographic superconductors.We observe that the HEE and HSC exhibit a similar linear growth behavior with the change of width for a strip geometry.We find that the HEE always decreases as the temperature decreases,and the HEE of the superconducting phase is always less than the value in the normal phase.At the critical temperature,HEE is continuous,but the slope of the HEE curve is discontinuous.However,for different fixed widths,the HSC exhibits different behaviors with the change of the temperature.For a small subsystem,the HSC behaves in the opposite way to the HEE,while for a large subsystem,the behavior of HSC is consistent with the HEE.In particular,we find that under certain conditions,the curve of HSC become smooth near the citical temperature,which make it difficult to observe the phase transition of this system through the HSC approach.Furthermore,we also note that for subsystems with different widths,the HSC exhibits three different behaviors with respect to the change relationship of unbalance parameter,while the HEE always increases as the unbalance parameter increases.