Phase Transitions of Correlations in Black Hole Geometries

TL;DR

This paper explores how various quantum correlation measures in two-dimensional thermal states with black hole duals are represented by different bulk surface configurations, revealing phase transitions and complex behaviors in their geometric duals.

Contribution

It provides a detailed holographic analysis of optimized quantum correlation measures, identifying phase transitions and topological changes in bulk surface configurations.

Findings

Multiple correlation measures exhibit phase transitions as parameters vary.

Q-correlation shows complex nested optimization leading to multiple equally valid bulk configurations.

Distinct phases correspond to different degrees of correlation between boundary regions and the black hole environment.

Abstract

We study the holographic realization of optimized correlation measures -- measures of quantum correlation that generalize elementary entropic formulas -- in two-dimensional thermal states dual to spacetimes with a black hole horizon. We consider the symmetric bipartite optimized correlation measures: the entanglement of purification, Q-correlation, R-correlation, and squashed entanglement, as well as the mutual information, a non-optimized correlation measure, and identify the bulk surface configurations realizing their geometric duals over the parameter space of boundary region sizes and the black hole radius. This parameter space is divided into phases associated with given topologies for these bulk surface configurations, and first-order phase transitions occur as a new topology of bulk surfaces becomes preferred. The distinct phases can be associated with different degrees of correlation between the boundary regions and the thermal environment. The Q-correlation has the richest behavior, with a structure of nested optimizations leading to two topologically distinct bulk surface configurations being equally valid as geometric duals at generic points in the phase diagram.