Bulk area law for boundary entanglement in spin network states: entropy corrections and horizon-like regions from volume correlations

TL;DR

This paper investigates how boundary entanglement entropy in spin network states relates to bulk data, revealing corrections to the Ryu-Takayanagi formula and mechanisms for black hole-like region formation due to entanglement effects.

Contribution

It demonstrates the impact of bulk quantum correlations on boundary entanglement entropy and introduces a model for black hole-like regions emerging from entanglement structures.

Findings

Recovery of the Ryu-Takayanagi formula with quantum gravity corrections

Bulk entanglement influences the minimal-area surface deformation

Highly entangled bulk regions can form black hole-like structures

Abstract

For quantum gravity states associated to open spin network graphs, we study how the entanglement entropy of the boundary degrees of freedom (spins on open edges) is affected by the bulk data, specifically by its combinatorial structure and by the quantum correlations among intertwiner degrees of freedom. For a specific assignment of bulk edge spins and slightly entangled intertwiners, we recover the Ryu-Takayanagi formula (with a properly (discrete) geometric notion of area, thanks to the underlying quantum gravity formalism) and its corrections due to the entanglement entropy of the bulk state. We also show that the presence of a region with highly entangled intertwiners deforms the minimal-area surface, which is then prevented from entering that region when the entanglement entropy of the latter exceeds a certain bound. This entanglement-based mechanism leads thus to the formation of a black hole-like region in the bulk.