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 in strongly coupled systems. Through rigorous semi-analytical methods, we uncover the existence of an isotropic point emerging at a critical temperature $$T_{II},$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi>II</mml:mi> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> 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 emergent isotropy point 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 dependence of the vector field components in 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. Among them, EWCS and butterfly velocity stand out as superior probes for detecting the isotropic point. Our findings provide a novel perspective on the interplay between unique emergent isotropic point and quantum information measures in strongly correlated systems.