arXiv:2106.06803 · Physical review. D/Physical review. D.

Universal terms of the entanglement entropy in a static closed universe

Rodolfo Reis Soldati, Lucas Menicucci, Nelson Yokomizo

Published Dec 20, 2021• 0 citations

Abstract

Subdominant contributions to the entanglement entropy of quantum fields include logarithmic corrections to the area law characterized by universal coefficients that are independent of the ultraviolet regulator and capture detailed information on the geometry around the entangling surface. We determine two universal coefficients of the entanglement entropy for a massive scalar field in a static closed universe $\mathbb{R}\ifmmode\times\else\texttimes\fi{}{\mathbb{S}}^{3}$ perturbatively and verify the results numerically. The first coefficient describes a well-known generic correction to the area law independent of the geometry of the entangling surface and background. The second coefficient describes a curvature-dependent universal term with a nontrivial dependence on the intrinsic and extrinsic geometries of the entangling surface and curvature of the background. The numerical calculations confirm the analytical results to a high accuracy. The first and second universal coefficients are determined numerically with a relative error with respect to the analytical values of the orders ${10}^{\ensuremath{-}4}$ and ${10}^{\ensuremath{-}2}$, respectively.

DOI: 10.1103/physrevd.104.125016

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arXiv:2106.06803 · Physical review. D/Physical review. D.

Universal terms of the entanglement entropy in a static closed universe

Rodolfo Reis Soldati, Lucas Menicucci, Nelson Yokomizo

Published Dec 20, 2021• 0 citations

arXiv HTML PDF

Abstract

\mathbb{R}\ifmmode\times\else\texttimes\fi{}{\mathbb{S}}^{3}

perturbatively and verify the results numerically. The first coefficient describes a well-known generic correction to the area law independent of the geometry of the entangling surface and background. The second coefficient describes a curvature-dependent universal term with a nontrivial dependence on the intrinsic and extrinsic geometries of the entangling surface and curvature of the background. The numerical calculations confirm the analytical results to a high accuracy. The first and second universal coefficients are determined numerically with a relative error with respect to the analytical values of the orders

{10}^{\ensuremath{-}4}

and

{10}^{\ensuremath{-}2}

, respectively.

DOI: 10.1103/physrevd.104.125016

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\mathbb{R}\ifmmode\times\else\texttimes\fi{}{\mathbb{S}}^{3}

{10}^{\ensuremath{-}4}

and

{10}^{\ensuremath{-}2}

, respectively.

We extend the entanglement entropy calculation performed in the seminal paper by Srednicki (Phys Rev Lett 71:666, 1993) for free real massive scalar field theories in

1+1

1 + 1 ,

2+1

2 + 1 and

3+1

3 + 1 dimensions. We show that the inverse of the scalar field mass can be used as an expansion parameter for a perturbative calculation of the entanglement entropy. We perform the calculation for the ground state of the system and for a spherical entangling surface at third order in the inverse mass expansion. The calculated entanglement entropy contains a leading area law term, as well as subleading terms that depend on the regularization scheme, as expected. Universal terms are non-perturbative effects in this approach. Interestingly, this perturbative expansion can be used to approximate the coefficient of the area law term, even in the case of a massless scalar field in

2+1

2 + 1 and

3+1

3 + 1 dimensions. The presented method provides the spectrum of the reduced density matrix as an intermediate result, which is an important advantage in comparison to the replica trick approach. Our perturbative expansion underlines the relation between the area law and the locality of the underlying field theory.