Topological network entanglement as order parameter for the emergence of geometry

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...

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Bibliographic Details
Published inNew journal of physics Vol. 19; no. 10; pp. 103024 - 103028
Main Authors Diamantini, M Cristina, Trugenberger, Carlo A
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 24.10.2017
Subjects
Combinatorial analysis
complex networks
Emergence
entanglement entropy
Entropy
Geometry
Graphs
Order parameters
Physics
Quantum entanglement
Quantum gravity
Spacetime
Topology
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Summary: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.
Bibliography:NJP-106741.R3
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/aa8f08