A spacetime calculation of the Calabrese-Cardy entanglement entropy

Mathur, Abhishek; Surya, Sumati; Nomaan, X

doi:10.1016/j.physletb.2021.136567

Cited by 5 publications

(17 citation statements)

References 10 publications

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“…(3.14). Instead, as shown in [18] we use a combination of analytical and numerical techniques to calculate the generalised spectrum.…”

Section: Ssee In the Continuummentioning

confidence: 99%

“…Solving the generalised eigenvalue equation numerically therefore requires an additional cut-off. In [18] it was noticed that when the γ = 2T /L is a half integer and the ratio α = /L is rational then W D 2 simplifies considerably into a closed form expression. We refer the reader to [18] for details.…”

Section: Ssee In the Continuummentioning

confidence: 99%

“…Sorkin's spacetime entanglement entropy (SSEE) formulation for Gaussian free scalar fields provides an alternative measure for entanglement in terms of spacetime correlators [16]. In the continuum the SSEE has been calculated for different types of horizons, in d ≥ 2 and shown to satisfy the expected area law behaviour [17,18,19]. On a causal set the SSEE can be calculated using the SJ vacuum, given the discrete Green's function.…”

Section: Introductionmentioning

confidence: 99%

“…In Section 3 we discuss results in the the continuum which show that the SSEE gives the expected area laws for d > 2 de Sitter and Schwarzschild-de Sitter horizons [19]. For the d = 2 causal diamond in the cylinder spacetime the Calabrese-Cardy form for the EE is recovered, but the coefficients are not universal [18]. In Section 4 we summarise results on the causal set SSEE volume law as well as the truncation dependent area law [20,21].…”

Section: Introductionmentioning

confidence: 99%

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Spacetime entanglement entropy: covariance and discreteness

2022

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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.

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“…(3.14). Instead, as shown in [18] we use a combination of analytical and numerical techniques to calculate the generalised spectrum.…”

Section: Ssee In the Continuummentioning

confidence: 99%

Section: Ssee In the Continuummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spacetime entanglement entropy: covariance and discreteness

2022

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“…It is worth highlighting again that the formulas above are covariant and they solely involve spacetime correlation functions. The formulas (2) and (3) have been used in several settings both in the continuum theory and in causal set theory to compute entanglement entropies [29][30][31][32][33]. It has also been shown that these formulae capture the entanglement entropy even in non-Gaussian and interacting theories, up to first order in perturbation theory [27].…”

Section: Entropy From Spacetime Correlation Functionsmentioning

confidence: 99%

Entanglement Entropy of Disjoint Spacetime Intervals in Causal Set Theory

Duffy,

Jones,

Yazdi

2021

Preprint

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A more complete understanding of entanglement entropy in a covariant manner could inform the search for quantum gravity. We build on work in this direction by extending previous results to disjoint regions in 1 + 1D. We investigate the entanglement entropy of a scalar field in disjoint intervals within the causal set framework, using the spacetime commutator and correlator, i∆ and W (or the Pauli-Jordan and Wightman functions), respectively. A new truncation scheme for disjoint causal diamonds is presented, which follows from the single diamond truncation scheme. We investigate setups including two and three disjoint causal diamonds, as well as a single causal diamond that shares a boundary with a larger global causal diamond. In all the cases that we study, our results agree with the expected area laws. In addition, we study the mutual information in the two disjoint diamonds setup. The ease of our calculations indicate our methods to be a useful tool for numerically studying such systems. We end with a discussion of some of the strengths and future applications of the spacetime formulation we use in our entanglement entropy computations, both in causal set theory and in the continuum.

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