Diagnosing Effective Metal-Insulator and Hawking-Page Transitions: A Mixed-State Entanglement Perspective in Einstein-Born-Infeld-Massive Gravity

TL;DR

This paper investigates mixed-state entanglement measures in Einstein-Born-Infeld massive gravity, demonstrating EWCS's superior sensitivity in detecting phase transitions like metal-insulator and Hawking-Page transitions at finite temperatures.

Contribution

It introduces the use of entanglement wedge cross-section (EWCS) as a sensitive probe for phase transitions in a complex gravity model, outperforming traditional measures.

Findings

EWCS aligns with critical points in metal-insulator transitions.

All measures diagnose Hawking-Page transitions effectively.

Universal critical exponent of 1/3 near second-order phase transition.

Abstract

We study mixed-state entanglement measures in Einstein-Born-Infeld (EN-BI) massive gravity theory, a model exhibiting both Hawking-Page transitions and effective metal-insulator transitions (MIT) at finite temperatures. Our comprehensive investigation reveals that the entanglement wedge cross-section (EWCS), a novel mixed-state entanglement measure, demonstrates unique properties in detecting phase transitions. For effective MIT, we find the higher-order terms of EWCS align closely with the critical point, outperforming measures like holographic entanglement entropy (HEE) and mutual information (MI) in finite temperature systems. This enhanced sensitivity provides a more accurate tool for probing effective phase transitions in a finite temperature system. In Hawking-Page transitions, we observe that all entanglement measures effectively diagnose both first-order and second-order phase transitions, with EWCS showing configuration-independent behavior. Importantly, we discover that all geometry-related quantities, including entanglement measures, demonstrate a universal critical exponent of 1/3 near the second-order phase transition point, suggesting fundamental connections between quantum information theory and critical phenomena in gravitational systems. Our results highlight EWCS's potential as a powerful probe for phase transitions.