Entanglement entropy in loop quantum gravity and geometrical area law
Han M (2026)
Publication Type: Journal article
Publication year: 2026
Journal
Book Volume: 113
Article Number: 084045
Journal Issue: 8
DOI: 10.1103/8L48-QHKS
Abstract
The nonfactorizing nature of the Hilbert space in loop quantum gravity (LQG) due to gauge invariance requires a generalized definition of entanglement entropy. This work employs the framework of von Neumann algebras to investigate the entanglement entropy in LQG. On a graph, the holonomy and flux operators within a region and on the boundary generate a nonfactor type I von Neumann algebra, which is used to define the entanglement entropy for LQG states. This algebraic formalism is applied to “fixed-area states”—superpositions of spin networks associated with a surface with a definite macroscopic area given by the LQG area spectrum. By maximizing the entropy, we derive a geometrical area law where the entanglement entropy is proportional to the area. In addition, we show that bulk entanglement can renormalize the area-law coefficient and produce logarithmic corrections. The results in this paper closely relate to LQG black hole entropy.
Involved external institutions
United States (USA) (US)How to cite
APA:
Han, M. (2026). Entanglement entropy in loop quantum gravity and geometrical area law. Physical Review D, 113(8). https://doi.org/10.1103/8L48-QHKS
MLA:
Han, Muxin. "Entanglement entropy in loop quantum gravity and geometrical area law." Physical Review D 113.8 (2026).
BibTeX: Download