Diagnosing Emergent Isotropy in Anisotropic Holographic Systems using Quantum Information Measures

Abstract: This study presents a comprehensive investigation of anisotropy in a holographic p-wave superconductor model, revealing novel insights into the behavior of quantum information measures in strongly coupled systems. Through rigorous semi-analytical methods, we uncover the existence of an isotropic point emerging at a critical temperature $T_{II}$, marking a significant transition in the system's anisotropic properties. We offer a systematic analysis of the mechanisms driving anisotropy and isotropy transitions, finding that this phenomenon is unique to the p-wave model and absent in other anisotropic systems like anisotropic axion models with metal-insulator transitions. We propose that the explicit component dependence of the vector field manifesting anisotropy is the key driver of the emergent isotropy. Our analysis of holographic entanglement entropy (HEE), entanglement wedge cross-section (EWCS), and butterfly velocity demonstrates their distinct sensitivities to bulk anisotropy, with EWCS and butterfly velocity emerging as superior probes for detecting the isotropic point.