Holographic Mutual Information at Finite Temperature

TL;DR

This paper explores how mutual information behaves at finite temperature in holographic theories, revealing a universal transition to zero and demonstrating its role in capturing quantum entanglement beyond thermal effects.

Contribution

It provides a detailed analysis of the mutual information transition at finite temperature in holographic theories, including universal features and analytical results.

Findings

Mutual information undergoes a transition to zero beyond a critical separation.

Analytical expressions for mutual information are derived in specific parameter regimes.

Mutual information isolates quantum entanglement from thermal entropy at high temperatures.

Abstract

Using the Ryu-Takayanagi conjectured formula for entanglement entropy in the context of gauge-gravity duality, we investigate properties of mutual information between two disjoint rectangular sub-systems in finite temperature relativistic conformal field theories in d-spacetime dimensions and non-relativistic scale-invariant theories in some generic examples. In all these cases mutual information undergoes a transition beyond which it is identically zero. We study this transition in detail and find universal qualitative features for the above class of theories which has holographic dual descriptions. We also obtain analytical results for mutual information in the specific regime of the parameter space. This demonstrates that mutual information contains the quantum entanglement part of the entanglement entropy, which is otherwise dominated by the thermal entropy at large temperatures.