On the entanglement entropy of quantum fields in causal sets. (28th February 2018)

• Record Type: Journal Article
• Authors: Belenchia, Alessio; Benincasa, Dionigi M T; Letizia, Marco; Liberati, Stefano
• Is Part Of: Classical and quantum gravity. Volume 35:Number 7(2018:Apr.)
• Publication Date: 2018-02-28
• Subjects: causal sets -- entanglement entropy -- discrete spacetime; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/1361-6382/aaae27
• Languages: English
• ISSNs: 0264-9381

Abstract

Abstract: In order to understand the detailed mechanism by which a fundamental discreteness can provide a finite entanglement entropy, we consider the entanglement entropy of two classes of free massless scalar fields on causal sets that are well approximated by causal diamonds in Minkowski spacetime of dimensions 2, 3 and 4. The first class is defined from discretised versions of the continuum retarded Green functions, while the second uses the causal set's retarded nonlocal d'Alembertians parametrised by a length scale l k . In both cases we provide numerical evidence that the area law is recovered when the double-cutoff prescription proposed in Sorkin and Yazdi (2016 Entanglement entropy in causal set theory (arXiv:1611.10281)) is imposed. We discuss in detail the need for this double cutoff by studying the effect of two cutoffs on the quantum field and, in particular, on the entanglement entropy, in isolation. In so doing, we get a novel interpretation for why these two cutoff are necessary, and the different roles they play in making the entanglement entropy on causal sets finite.