A class of entangled and diffeomorphism-invariant states in loop quantum gravity: Bell-network states

TL;DR

This paper introduces Bell-network states in loop quantum gravity, which are entangled, diffeomorphism-invariant, and satisfy an area-law, providing insights into quantum geometry and potential boundary states.

Contribution

It characterizes a new class of entangled, diffeomorphism-invariant states in LQG with area-law entanglement, analyzing their effective geometry on a dipole graph.

Findings

Bell-network states satisfy an area-law for entanglement entropy.

Fluctuations of geometry in Bell-network states are entangled, akin to semiclassical limits.

The analysis provides a detailed quantum geometric characterization of these states.

Abstract

Bell-network states constitute a class of diffeomorphism-invariant and entangled states of the geometry within loop quantum gravity (LQG) that satisfy an area-law for the entanglement entropy in the limit of large spins. The fluctuations of the geometry for a Bell-network state are entangled, similar to those in the semiclassical limit as described by quantum field theory in curved spacetimes. We present a comprehensive analysis of the effective geometry of Bell-network states on a dipole graph. This analysis provides a detailed characterization of the quantum geometry of a class of diffeomorphism-invariant, area-law states representing homogeneous and isotropic configurations in loop quantum gravity, which may be explored as boundary states for the dynamics of the theory.