Holographic study of reflected entropy in anisotropic theories

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 cooguration 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.

Automated summary

In this study, we use holography to evaluate the reflected entropy in anisotropic boundary theories dual to nonrelativistic geometries. It is suggested that this quantity is proportional to the minimal area of the entanglement wedge cross section. By applying this prescription, we investigate the impact of anisotropy on reflected entropy and other holographic entanglement measures. We particularly focus on the discontinuous phase transition of this quantity in a symmetric configuration consisting of two disjoint strips.