Area Law from Loop Quantum Gravity

TL;DR

This paper investigates how the area law for entanglement entropy can be realized within loop quantum gravity, identifying specific wave-functions and states that preserve the law and are ground states of local Hamiltonians.

Contribution

It introduces a unique semi-classical wave-function solution, generalizes to multi-link states, and constructs Hamiltonian ground states that uphold the area law in loop quantum gravity.

Findings

Single link wave-function satisfies the area law in the semi-classical limit

Multi-link coherent states generally preserve the area law

Constructed local Hamiltonians have ground states that maintain the area law

Abstract

We explore the constraints following from requiring the Area Law in the entanglement entropy in the context of loop quantum gravity. We find a unique solution to the single link wave-function in the large j limit, believed to be appropriate in the semi-classical limit. We then generalize our considerations to multi-link coherent states, and find that the area law is preserved very generically using our single link wave-function as a building block. Finally, we develop the framework that generates families of multi-link states that preserve the area law while avoiding macroscopic entanglement, the space-time analogue of "Schroedinger cat". We note that these states, defined on a given set of graphs, are the ground states of some local Hamiltonian that can be constructed explicitly. This can potentially shed light on the construction of the appropriate Hamiltonian constraints in the LQG framework.