Mixed State Entanglement For Holographic Systems With A Scalar Hair

TL;DR

This paper investigates the behavior of mixed state entanglement measures in holographic systems with scalar hair, revealing non-monotonic and monotonic patterns depending on parameters, supported by numerical and analytical analysis.

Contribution

It provides the first detailed numerical and analytical study of mixed state entanglement measures in scalar-hairy AdS black holes, highlighting their complex parameter dependence.

Findings

HEE exhibits non-monotonic behavior with system parameters.

Mutual information shows non-monotonic behavior in certain ranges.

Entanglement wedge cross-section increases monotonically with AdS radius, non-monotonically with temperature.

Abstract

We study the mixed state entanglement of an asymptotic AdS black hole system with scalar hair. Through numerical calculations, we find that the holographic entanglement entropy (HEE) presents a non-monotonic behavior with the system parameter, depending on the size of the subregion. In addition, the mutual information (MI) also shows non-monotonic behavior in certain ranges of system parameters. However, the entanglement wedge minimum cross-section (EWCS), which is a mixed state entanglement measure, increases monotonically with the AdS radius; meanwhile, shows non-monotonic with the temperature. We also give analytical understandings of the phenomena above.