On Holographic Entanglement Entropy of Charged Matter

TL;DR

This paper explores holographic entanglement entropy in charged dilatonic black hole backgrounds, revealing phase transitions and the effects of higher curvature corrections, with implications for dual finite density states.

Contribution

It provides new insights into entanglement entropy behavior in charged dilatonic black holes, including phase transitions and the impact of Gauss-Bonnet terms.

Findings

Second order phase transition for slab entanglement entropy

Smooth entanglement entropy for spherical regions

No logarithmic violation of the area law observed

Abstract

We study holographic entanglement entropy in the background of charged dilatonic black holes which can be viewed as holographic duals of certain finite density states of N=4 super Yang-Mills. These charged black holes are distinguished in that they have vanishing ground state entropy. The entanglement entropy for a slab experiences a second order phase transition as the thickness of the slab is varied, while the entanglement entropy for a sphere is a smooth function of the radius. This suggests that the second scale introduced by the anisotropy of the slab plays an important role in driving the phase transition. In both cases we do not observe any logarithmic violation of the area law indicative of hidden Fermi surfaces. We investigate how these results are affected by the inclusion of the Gauss-Bonnet term in the bulk gravitational action. We also observe that such addition to the bulk action does not change the logarithmic violation of the area law in the backgrounds with hyperscaling violation.