Entanglement wedge minimum cross-section in holographic massive gravity theory

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.

Automated summary

In the holographic massive gravity theory, the entanglement wedge cross-section (EWCS) and mutual information (MI) exhibit opposite behaviors in the critical region, indicating that EWCS captures different degrees of freedom from MI. Furthermore, EWCS, MI, and HEE show the same scaling behavior in the critical region. We provide an analytical understanding of this phenomenon, as well as two mechanisms of quantum information scaling behavior in the thermodynamic phase transition by comparing the behavior in holographic superconductors.