Diagnosing Metal-Insulator and Hawking-Page Transitions: A Mixed-State Entanglement Perspective in Einstein-Born-Infeld-Massive Gravity (2601.00071v1)

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.