Topological Network Entanglement as Order Parameter for the Emergence of Geometry
High Energy Physics - Theory
2017-11-22 v1 General Relativity and Quantum Cosmology
Abstract
We show that, in discrete models of quantum gravity, emergent geometric space can be viewed as the entanglement pattern in a mixed quantum state of the "universe", characterized by a universal topological network entanglement. As a concrete example we analyze the recently proposed model in which geometry emerges due to the condensation of 4-cycles in random regular bipartite graphs, driven by the combinatorial Ollivier-Ricci curvature. Using this model we show that the emergence of geometric order decreases the entanglement entropy of random configurations. The lowest geometric entanglement entropy is realized in four dimensions.
Keywords
Cite
@article{arxiv.1710.00221,
title = {Topological Network Entanglement as Order Parameter for the Emergence of Geometry},
author = {M. C. Diamantini and C. A. Trugenberger},
journal= {arXiv preprint arXiv:1710.00221},
year = {2017}
}