Entanglement entropy in all dimensions

Journal of High Energy Physics, 2013

We examine the idea that in quantum gravity, the entanglement entropy of a general region should be finite and the leading contribution is given by the Bekenstein-Hawking area law. Using holographic entanglement entropy calculations, we show that this idea is realized in the Randall-Sundrum II braneworld for sufficiently large regions in smoothly curved backgrounds. Extending the induced gravity action on the brane to include the curvature-squared interactions, we show that the Wald entropy closely matches the expression describing the entanglement entropy. The difference is that for a general region, the latter includes terms involving the extrinsic curvature of the entangling surface, which do not appear in the Wald entropy. We also consider various limitations on the validity of these results.

Classical and Quantum Gravity, 2014

defines an entropy for a gaussian scalar field φ in an arbitrary region of either a causal set or a continuous spacetime, given only the correlator φ(x)φ(y) within the region. As a first application, we compute numerically the entanglement entropy in two cases where the asymptotic form is known or suspected from conformal field theory, finding excellent agreement when the required ultraviolet cutoff is implemented as a truncation on spacetime mode-sums. We also show how the symmetry of entanglement entropy reflects the fact that RS and SR share the same eigenvalues, R and S being arbitrary matrices. arXiv:1311.7146v1 [hep-th]

Journal of High Energy Physics, 2013

We identify various universal contributions to the entanglement entropy for massive free fields. As well as the 'area' terms found in [1], we find other geometric contributions of the form discussed in [2]. We also compute analogous contributions for a strongly coupled field theory using the AdS/CFT correspondence. In this case, we find the results for strong and weak coupling do not agree. 4 Discussion 26 A Separation of variables in the case of spin-1 2 fields 34 B Waveguides with hyperbolic cross-section 36 B.1 Rényi entropy for a massive scalar 37 B.2 Rényi entropy for a massive fermion 41

Journal of Statistical Mechanics: Theory and Experiment, 2011

We introduce a systematic framework to calculate the bipartite entanglement entropy of a compact spatial subsystem in a one-dimensional quantum gas which can be mapped into a noninteracting fermion system. We show that when working with a finite number of particles N , the Rényi entanglement entropies grow as ln N , with a prefactor that is given by the central charge. We apply this novel technique to the ground state and to excited states of periodic systems. We also consider systems with boundaries. We derive universal formulas for the leading behavior and for subleading corrections to the scaling. The universality of the results allows us to make predictions for the finite-size scaling forms of the corrections to the scaling.

Physics Letters B, 2004

The entanglement entropy of the event horizon is known to be plagued by the UV divergence due to the infinitely blue-shifted near horizon modes. In this paper we calculate the entanglement entropy using the transplanckian dispersion relation, which has been proposed to model the quantum gravity effects. We show that, very generally, the entropy is rendered UV finite due to the suppression of high energy modes effected by the transplanckian dispersion relation.

Classical and Quantum Gravity, 2022

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...

2016

Abstract: We examine the idea that in quantum gravity, the entanglement entropy of a general region should be finite and the leading contribution is given by the Bekenstein-Hawking area law. Using holographic entanglement entropy calculations, we show that this idea is realized in the Randall-Sundrum II braneworld for sufficiently large regions in smoothly curved backgrounds. Extending the induced gravity action on the brane to include the curvature-squared interactions, we show that the Wald entropy closely matches the expression describing the entanglement entropy. The difference is that for a general region, the latter includes terms involving the extrinsic curvature of the entangling surface, which do not appear in the Wald entropy. We also consider various limitations on the validity of these results. ar X iv

Physical Review A, 2001

Entanglement is the fundamental quantum property behind the now popular field of quantum transport of information. This quantum property is incompatible with the separation of a single system into two uncorrelated subsystems. Consequently, it does not require the use of an additive form of entropy. We discuss the problem of the choice of the most convenient entropy indicator, focusing our attention on a system of 2 qubits, and on a special set, denoted by ℑ. This set contains both the maximally and the partially entangled states that are described by density matrices diagonal in the Bell basis set. We select this set for the main purpose of making more straightforward our work of analysis. As a matter of fact, we find that in general the conventional von Neumann entropy is not a monotonic function of the entanglement strength. This means that the von Neumann entropy is not a reliable indicator of the departure from the condition of maximum entanglement. We study the behavior of a form of non-additive entropy, made popular by the 1988 work by Tsallis. We show that in the set ℑ, implying the key condition of non-vanishing entanglement, this non-additive entropy indicator turns out

Cornell University - arXiv, 2022

The European Physical Journal Plus, 2015

Assuming that the dominant contribution, to the entropy due to entanglement across a spherical hypersurface, comes from the near horizon degrees of freedom, we analytically derive the entropy of a free massless scalar field in Minkowski spacetime across a spherical entangling surface. The resulting entanglement entropy is found to be proportional to the entangling surface as expected. A logarithmic subleading term with positive coefficient is also found through numerical computation. We have extended the analysis to higher dimensions as well.