Thermalization of mutual and tripartite information in strongly coupled two dimensional conformal field theories

TL;DR

This paper investigates how mutual and tripartite information evolve over time in strongly coupled 2D conformal field theories following energy injection, revealing dynamic correlation spreading and differences from quantum quench scenarios.

Contribution

It provides a holographic computation of the time-dependent mutual and tripartite information during thermalization in 2D CFTs with a gravity dual, highlighting their dynamic behavior.

Findings

Mutual information increases then decreases to thermal equilibrium value.

Tripartite information remains non-zero and time-dependent.

Behavior explained by causality considerations.

Abstract

The mutual and tripartite information between pairs and triples of disjoint regions in a quantum field theory are sensitive probes of the spread of correlations in an equilibrating system. We compute these quantities in strongly coupled two-dimensional conformal field theories with a gravity dual following the homogenous deposition of energy. The injected energy is modeled in anti-de Sitter space as an infalling shell, and the information shared by disjoint intervals is computed in terms of geodesic lengths in this background. For given widths and separation of the intervals, the mutual information typically starts at its vacuum value, then increases in time to reach a maximum, and then declines to the value at thermal equilibrium. A simple causality argument qualitatively explains this behavior. The tripartite information is generically non-zero and time-dependent throughout the process. This contrasts with (but does not contradict) the time-independent tripartite information one finds after a two-dimensional quantum quench in the limit of large time and distance scales compared to the initial inverse mass gap.