Entanglement Wedge Minimum Cross-section in Holographic Massive Gravity Theory

TL;DR

This paper investigates the entanglement wedge cross-section in holographic massive gravity, revealing its role in characterizing phase transitions and its distinct behavior from mutual information, with analytical insights into quantum information scaling.

Contribution

It introduces the analysis of EWCS and MI in holographic massive gravity, highlighting their opposite behaviors and shared scaling in phase transitions, with analytical explanations.

Findings

EWCS and MI characterize phase transitions.

EWCS and MI show opposite behavior in the critical region.

EWCS, MI, and HEE share the same scaling behavior.

Abstract

We study the entanglement wedge cross-section (EWCS) in holographic massive gravity theory, in which a first and second-order phase transition can occur. We find that the mixed state entanglement measures, the EWCS and mutual information (MI) can characterize the phase transitions. The EWCS and MI show exactly the opposite behavior in the critical region, which suggests that the EWCS captures distinct degrees of freedom from that of the MI. More importantly, EWCS, MI and HEE all show the same scaling behavior in the critical region. We give an analytical understanding of this phenomenon. By comparing the quantum information behavior in the thermodynamic phase transition of holographic superconductors, we analyze the relationship and difference between them, and provide two mechanisms of quantum information scaling behavior in the thermodynamic phase transition.