Entanglement Entropy of Disjoint Spacetime Intervals in Causal Set Theory

Duffy, Callum F.; Jones, Joshua Y. L.; Yazdi, Yasaman K.

doi:10.48550/arxiv.2110.07627

Cited by 3 publications

(2 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This formula has been applied in the continuum to the d = 2 nested causal diamonds and shown to give the expected Calabrese-Cardy logarithmic behaviour [39]. It has also been calculated in the discrete setting, i.e., for causal sets approximated by causal diamonds in Minkowski and de Sitter spacetimes: in d = 2 where it shows the expected logarithmic behaviour and in d = 4 where it shows the expected area behaviour [40,41,42,43,37].…”

Section: Spacetime Entanglement Entropy Of Quantum Fieldsmentioning

confidence: 99%

Spacetime entanglement entropy: covariance and discreteness

2022

View full text Add to dashboard Cite

We review some recent results on Sorkin's spacetime formulation of the entanglement entropy (SSEE) for a free quantum scalar field both in the continuum and in manifold-like causal sets. The SSEE for a causal diamond in a 2d cylinder spacetime has been shown to have a Calabrese-Cardy form, while for de Sitter and Schwarzschild de Sitter horizons in dimensions d > 2, it matches the mode-wise von-Neumann entropy. In these continuum examples the SSEE is regulated by imposing a UV cut-off. Manifold-like causal sets come with a natural covariant spacetime cut-off and thus provide an arena to study regulated QFT. However, the SSEE for different manifold-like causal sets in d = 2 and d = 4 has been shown to exhibit a volume rather than an area law. The area law is recovered only when an additional UV cut-off is implemented in the scaling regime of the spectrum which mimics the continuum behaviour. We discuss the implications of these results and suggest that a volume-law may be a manifestation of the fundamental non-locality of causal sets and a sign of new UV physics.

show abstract

Section: Spacetime Entanglement Entropy Of Quantum Fieldsmentioning

confidence: 99%

Spacetime entanglement entropy: covariance and discreteness

2022

View full text Add to dashboard Cite

show abstract

“…Attempts have been made to extend the results of [7] to more general settings such as higher dimensions, nonlocal field theories, disjoint regions, and spacetimes with curvature [13][14][15]. These attempts have had various degrees of success.…”

Section: Introductionmentioning

confidence: 99%

Insights on entanglement entropy in 1 + 1 dimensional causal sets

Keseman

Muneesamy

Yazdi

2022

Class. Quantum Grav.

View full text Add to dashboard Cite

Entanglement entropy in causal sets offers a fundamentally covariant characterisation of quantum field degrees of freedom. A known result in this context is that the degrees of freedom consist of a number of contributions that have continuum-like analogues, in addition to a number of contributions that do not. The latter exhibit features below the discreteness scale and are excluded from the entanglement entropy using a ``truncation scheme''. This truncation is necessary to recover the standard spatial area law of entanglement entropy. In this paper we build on previous work on the entanglement entropy of a massless scalar field on a causal set approximated by a $1+1$D causal diamond in Minkowski spacetime. We present new insights into the truncated contributions, including evidence that they behave as fluctuations and encode features specific to a particular causal set sprinkling. We extend previous results in the massless theory to include R\'enyi entropies and include new results for the massive theory. We also discuss the implications of our work for the treatment of entanglement entropy in causal sets in more general settings.

show abstract

Insights on Entanglement Entropy in $1+1$ Dimensional Causal Sets

Keseman¹,

Muneesamy²,

Yazdi³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Entanglement entropy in causal sets offers a fundamentally covariant characterisation of quantum field degrees of freedom. A known result in this context is that the degrees of freedom consist of a number of contributions that have continuumlike analogues, in addition to a number of contributions that do not. The latter exhibit features below the discreteness scale and are excluded from the entanglement entropy using a "truncation scheme". This truncation is necessary to recover the standard spatial area law of entanglement entropy. In this paper we build on previous work on the entanglement entropy of a massless scalar field on a causal set approximated by a 1 + 1D causal diamond in Minkowski spacetime. We present new insights into the truncated contributions, including evidence that they behave as fluctuations and encode features specific to a particular causal set sprinkling. We extend previous results in the massless theory to include Rényi entropies and include new results for the massive theory. We also discuss the implications of our work for the treatment of entanglement entropy in causal sets in more general settings.

show abstract

Entanglement Entropy of Disjoint Spacetime Intervals in Causal Set Theory

Cited by 3 publications

References 39 publications

Spacetime entanglement entropy: covariance and discreteness

Spacetime entanglement entropy: covariance and discreteness

Insights on entanglement entropy in 1 + 1 dimensional causal sets

Insights on Entanglement Entropy in $1+1$ Dimensional Causal Sets

Contact Info

Product

Resources

About