Holographic Entanglement Entropy

Mukund Rangamani, Tadashi Takayanagi

Jun Tsujimura

The Ryu-Takayanagi conjecture provides a holographic description for the entanglement entropy for the strongly coupled holographic CFTs in the semi-classical limit. It proposes that the entanglement entropy is given by the area of the minimal homologous surface in the dual bulk. We show that the common terms of the entanglement entropy for the free massless fermions or bosons on a torus in the high-temperature expansion can be described by the sum of the signed area of extremal surfaces in the BTZ spacetime. The resulting EE and the corresponding bunch of the exgremal surfaces have preferable properties rather than those from the Ryu-Takayanagi conjecture.

Shinsei Ryu, Tadashi Takayanagi

Yi Ling, Peng Liu, Chao Niu +2 more

We investigate the holographic entanglement entropy (HEE) of a strip geometry in four dimensional Q-lattice backgrounds, which exhibit metal-insulator transitions in the dual field theory. Remarkably, we find that the HEE always displays a peak in the vicinity of the quantum critical points. Our model provides the first direct evidence that the HEE can be used to characterize the quantum phase transition (QPT). We also conjecture that the maximization behavior of HEE at quantum critical points would be universal in general holographic models.

Ali Mollabashi, Noburo Shiba, Tadashi Takayanagi

In this paper we discuss behaviors of entanglement entropy between two interacting CFTs and its holographic interpretation using the AdS/CFT correspondence. We explicitly perform analytical calculations of entanglement entropy between two free scalar field theories which are interacting with each other in both static and time-dependent ways. We also conjecture a holographic calculation of entanglement entropy between two interacting $ \mathcal{N} $ = 4 super Yang-Mills theories by introducing a minimal surface in the S5 direction, instead of the AdS5 direction. This offers a possible generalization of holographic entanglement entropy.

Mukund Rangamani, Tadashi Takayanagi