Diagnosing Critical Behavior in AdS Einstein-Maxwell-Scalar Theory via Holographic Entanglement Measures

TL;DR

This paper explores how various holographic entanglement measures and butterfly velocity can diagnose phase transitions in Einstein-Maxwell-Scalar theory, revealing universal behaviors and contrasting dynamics of static and dynamic quantum information quantities.

Contribution

It introduces a comprehensive analysis of multiple entanglement measures and butterfly velocity in EMS theory, highlighting their diagnostic power and universal critical exponents.

Findings

EWCS and MI behave oppositely to HEE during phase transitions.

Butterfly velocity initially dominated by entanglement, then by thermal entropy.

All critical exponents are equal to 1, twice that of the scalar field.

Abstract

We investigate the holographic mixed-state entanglement measures in the Einstein-Maxwell-Scalar (EMS) theory. Several quantities are computed, including the holographic entanglement entropy (HEE), mutual information (MI), entanglement wedge cross-section (EWCS), and butterfly velocity ($v_B$). Our findings demonstrate that these measures can effectively diagnose phase transitions. Notably, EWCS and MI, as mixed-state entanglement measures, exhibit behavior opposite to that of the HEE. Additionally, we study the butterfly velocity, a dynamic quantum information measure, and observe that it behaves differently from the static quantum information measures. We propose that the butterfly velocity is initially dominated by entanglement and subsequently by thermal entropy as the coupling constant increases. Moreover, we examine the scaling behavior of the holographic entanglement measures and find that all the critical exponents are equal to $1$, which is twice that of the scalar field. We also explore the inequality between EWCS and MI, noting that the growth rate of MI consistently exceeds that of EWCS during phase transitions. These features are expected to be universal across thermodynamic phase transitions, with the inequalities becoming more significant as one moves away from the critical point.