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 lk. In both cases we provide numerical evidence that the area law is recovered when the double-cutoff prescription proposed in arXiv:hep-th/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.

On the entanglement entropy of quantum fields in causal sets / Belenchia, Alessio; Benincasa, Dionigi M T; Letizia, Marco; Liberati, Stefano. - In: CLASSICAL AND QUANTUM GRAVITY. - ISSN 0264-9381. - 35:7(2018), pp. 1-26. [10.1088/1361-6382/aaae27]

On the entanglement entropy of quantum fields in causal sets

Belenchia, Alessio;Letizia, Marco;Liberati, Stefano
2018

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 lk. In both cases we provide numerical evidence that the area law is recovered when the double-cutoff prescription proposed in arXiv:hep-th/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.
35
7
1
26
074002
https://arxiv.org/abs/1712.04227
Belenchia, Alessio; Benincasa, Dionigi M T; Letizia, Marco; Liberati, Stefano
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/86080
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