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

TL;DR

This paper explores how various entanglement measures behave during a holographic p-wave superconductor phase transition, revealing critical behaviors, sensitivities, and universal inequalities among these quantum information indicators.

Contribution

It introduces a detailed analysis of multiple entanglement measures in a holographic p-wave superconductor model, highlighting their critical behaviors and interrelations.

Findings

EWCS exhibits opposite temperature behavior to HEE.

Critical exponents are twice those of the condensate.

EWCS is more sensitive to phase transition than HEE.

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.