Entanglement entropy and correlations in loop quantum gravity

TL;DR

This paper investigates the entanglement entropy and correlations in loop quantum gravity, focusing on states that obey an area law and exploring how holonomy operators influence entanglement across boundaries.

Contribution

It introduces a class of states in loop quantum gravity inspired by condensed matter physics that satisfy an area law for entanglement entropy and analyzes the role of holonomy operators in generating entanglement.

Findings

States satisfy an area law for entanglement entropy.

Entanglement arises from holonomy operators crossing boundaries.

Non-trivial correlations are present in the analyzed states.

Abstract

Black hole entropy is one of the few windows toward the quantum aspects of gravitation and its study over the years have highlighted the holographic nature of gravity. At the non-perturbative level in quantum gravity, promising explanations are being explored in terms of the entanglement entropy between regions of space. In the context of loop quantum gravity, this translates into the analysis of the correlations between regions of the spin network states defining the quantum state of geometry of space. In this paper, we explore a class of states, motivated by results in condensed matter physics, satisfying an area law for entanglement entropy and having non-trivial correlations. We highlight that entanglement comes from holonomy operators acting on loops crossing the boundary of the region.