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

TL;DR

This work probes metal-insulator and Hawking-Page transitions in Einstein-Born-Infeld massive gravity through mixed-state entanglement measures. Using holographic tools, it compares HEE, MI, and EWCS, finding that EWCS uniquely captures MIT via peaks in higher-order derivatives and exhibits configuration-independent behavior at Hawking-Page transitions. A universal critical exponent of $1/3$ governs the scaling of entropy-related and geometry-related quantities near the second-order point, linking quantum information to critical phenomena in gravitational contexts. The results position EWCS as a powerful, robust diagnostic for phase transitions in strongly coupled systems and motivate future exploration of quantum phase transitions and RG-flow structures in holographic settings.

Abstract

We study mixed-state entanglement measures in Einstein-Born-Infeld (EN-BI) massive gravity theory, a model exhibiting both Hawking-Page transitions and 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 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 quantum phase transitions in strongly correlated systems. 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.

Figures (15)

• Figure 1: The temperature $T$ versus entropy density $s$ of EN-BI massive gravity theory with different parameters.
• Figure 2: Left panel: The red surface represents the HEE of the blue subregion with width $w$. Right panel: The red surfaces represent the minimal surfaces, and the green surface represents the EWCS.
• Figure 3: The illustration of MI, the subsystems $a$ and $c$ is separated by the region $b$. The red and blue surfaces represent the HEE of different subsystems.
• Figure 4: DC-conductivity $\sigma_{DC}$ versus temperature $T$. Left panel: Parameters $(\alpha,\gamma,\beta)=(0.6,-1.2,0.3)$ with different $q$. Right panel: Parameters $(q,\alpha,\gamma)=(4,0.6,-1.2)$ with different BI parameter $\beta$.
• Figure 5: Behavior of parameters $\alpha=0.6, \gamma=-1.2, \beta=0.3$ with different $q$ when MIT occurs. Left panel: DC-conductivity $\sigma_{DC}$ versus temperature $T$. The inset shows the phase transition region of MIT. Right panel: EWCS $E_w$ versus temperature $T$ with configuration $(a, b, c)=(0.5, 0.05, 0.45)$. The inset shows the second-order partial derivative of $E_w$ with respect to temperature.