Corrections to holographic entanglement plateau

Understand

We investigate the robustness of the Araki-Lieb inequality in a two-dimensional (2D) conformal field theory (CFT) on torus.

• The inequality requires that $\Delta S=S(L)-|S(L-\ell)-S(\ell)|$ is nonnegative, where $S(L)$ is the thermal entropy and $S(L-\ell)$, $S(\ell)$ are the entanglement entropies.
• Holographically there is an entanglement plateau in the BTZ black hole background, which means that there exists a critical length such that when $\ell \leq \ell_c$ the inequality saturates $\Delta S=0$.
• In thermal AdS background, the holographic entanglement entropy leads to $\Delta S=0$ for arbitrary $\ell$.