The mixed-state entanglement in holographic p-wave superconductor model

Abstract: In this paper, we investigate the mixed-state entanglement in a model of p-wave superconductivity phase transition using holographic methods. We calculate several entanglement measures, including holographic entanglement entropy (HEE), mutual information (MI), and entanglement wedge cross-section (EWCS). Our results show that these measures display critical behavior at the phase transition points, with the EWCS exhibiting opposite temperature behavior compared to the HEE. Additionally, we find that the critical exponents of all entanglement measures are twice those of the condensate. Moreover, we find that the EWCS is a more sensitive indicator of the critical behavior of phase transitions than the HEE. Furthermore, we uncover a universal inequality in the growth rates of EWCS and MI near critical points in thermal phase transitions, such as p-wave and s-wave superconductivity, suggesting that MI captures more information than EWCS when a phase transition first occurs.