Holographic Study of Reflected Entropy in Anisotropic Theories

TL;DR

This paper investigates how anisotropy in boundary theories affects reflected entropy and other entanglement measures using holography, revealing that anisotropy influences phase transitions and the structure of entanglement entropy.

Contribution

It introduces a holographic prescription for reflected entropy in anisotropic theories and analyzes the impact of anisotropy on entanglement phase transitions and entropy structure.

Findings

Critical separation increases with anisotropy, indicating stronger correlations.

Anisotropy affects the universal terms of entanglement entropy based on orientation.

Reflected entropy behavior aligns with mutual information in anisotropic regimes.

Abstract

We evaluate reflected entropy in certain anisotropic boundary theories dual to nonrelativistic geometries using holography. It is proposed that this quantity is proportional to the minimal area of the entanglement wedge cross section. Using this prescription, we study in detail the effect of anisotropy on reflected entropy and other holographic entanglement measures. In particular, we study the discontinuous phase transition of this quantity for a symmetric configuration consisting of two disjoint strips. We find that in the specific regimes of the parameter space the critical separation is an increasing function of the anisotropy parameter and hence the correlation between the subregions becomes more pronounced. We carefully examine how these results are consistent with the behavior of other correlation measures including the mutual information. Finally, we show that the structure of the universal terms of entanglement entropy is corrected depending on the orientation of the entangling region with respect to the anisotropic direction.