Towards spacetime entanglement entropy for interacting theories

Abstract Entanglement entropy of quantum fields in gravitational settings is a topic of growing importance. This entropy of entanglement is conventionally computed relative to Cauchy hypersurfaces where it is possible via a partial tracing to associate a reduced density matrix to the spacelike region of interest. In recent years Sorkin has proposed an alternative, manifestly covariant, formulation of entropy in terms of the spacetime two-point correlation function. This formulation, developed for a Gaussian scalar field theory, is explicitly spacetime in nature and evades some of the possible non-covariance issues faced by the conventional formulation. In this paper we take the first steps towards extending Sorkin’s entropy to non-Gaussian theories where Wick’s theorem no longer holds and one would expect higher correlators to contribute. We consider quartic perturbations away from the Gaussian case and find that to first order in perturbation theory, the entropy formula derived by Sorkin continues to hold but with the two-point correlators replaced by their perturbation-corrected counterparts. We then show that our results continue to hold for arbitrary perturbations (of both bosonic and fermionic theories). This is a non-trivial and, to our knowledge, novel result. Furthermore we also derive closed-form formulas of the entanglement entropy for arbitrary perturbations at first and second order. Our work also suggests avenues for further extensions to generic interacting theories.

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Entanglement spectrum of geometric states

Journal of High Energy Physics ◽

10.1007/jhep02(2021)085 ◽

2021 ◽

Vol 2021 (2) ◽

Author(s):

Wu-zhong Guo

Keyword(s):

Entanglement Entropy ◽

Vacuum State ◽

Reduced Density Matrix ◽

Microcanonical Ensemble ◽

Equality Case ◽

Entanglement Spectrum ◽

The Matrix ◽

Point Correlation ◽

Single Interval ◽

Reduced Density

Abstract The reduced density matrix of a given subsystem, denoted by ρA, contains the information on subregion duality in a holographic theory. We may extract the information by using the spectrum (eigenvalue) of the matrix, called entanglement spectrum in this paper. We evaluate the density of eigenstates, one-point and two-point correlation functions in the microcanonical ensemble state ρA,m associated with an eigenvalue λ for some examples, including a single interval and two intervals in vacuum state of 2D CFTs. We find there exists a microcanonical ensemble state with λ0 which can be seen as an approximate state of ρA. The parameter λ0 is obtained in the two examples. For a general geometric state, the approximate microcanonical ensemble state also exists. The parameter λ0 is associated with the entanglement entropy of A and Rényi entropy in the limit n → ∞. As an application of the above conclusion we reform the equality case of the Araki-Lieb inequality of the entanglement entropies of two intervals in vacuum state of 2D CFTs as conditions of Holevo information. We show the constraints on the eigenstates. Finally, we point out some unsolved problems and their significance on understanding the geometric states.

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Clustering of primordial black holes with non-Gaussian initial fluctuations

Progress of Theoretical and Experimental Physics ◽

10.1093/ptep/ptz105 ◽

2019 ◽

Vol 2019 (10) ◽

Cited By ~ 9

Author(s):

Teruaki Suyama ◽

Shuichiro Yokoyama

Keyword(s):

Black Holes ◽

Correlation Function ◽

Functional Integration ◽

Formation Time ◽

Primordial Black Holes ◽

Local Type ◽

Integration Approach ◽

Point Correlation ◽

Point Correlation Function ◽

Non Gaussian

Abstract We formulate the two-point correlation function of primordial black holes (PBHs) at their formation time, based on the functional integration approach which has often been used in the context of halo clustering. We find that PBH clustering on super-Hubble scales could never be induced in the case where the initial primordial fluctuations are Gaussian, while it can be enhanced by the so-called local-type trispectrum (four-point correlation function) of the primordial curvature perturbations.

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Weak lensing cosmology with convolutional neural networks on noisy data

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz2610 ◽

2019 ◽

Vol 490 (2) ◽

pp. 1843-1860 ◽

Cited By ~ 8

Author(s):

Dezső Ribli ◽

Bálint Ármin Pataki ◽

José Manuel Zorrilla Matilla ◽

Daniel Hsu ◽

Zoltán Haiman ◽

...

Keyword(s):

Neural Networks ◽

Correlation Function ◽

Power Spectrum ◽

Convolutional Neural Networks ◽

Higher Order ◽

Weak Lensing ◽

Noise Levels ◽

Point Correlation ◽

Point Correlation Function ◽

Non Gaussian

ABSTRACT Weak gravitational lensing is one of the most promising cosmological probes of the late universe. Several large ongoing (DES, KiDS, HSC) and planned (LSST, Euclid, WFIRST) astronomical surveys attempt to collect even deeper and larger scale data on weak lensing. Due to gravitational collapse, the distribution of dark matter is non-Gaussian on small scales. However, observations are typically evaluated through the two-point correlation function of galaxy shear, which does not capture non-Gaussian features of the lensing maps. Previous studies attempted to extract non-Gaussian information from weak lensing observations through several higher order statistics such as the three-point correlation function, peak counts, or Minkowski functionals. Deep convolutional neural networks (CNN) emerged in the field of computer vision with tremendous success, and they offer a new and very promising framework to extract information from 2D or 3D astronomical data sets, confirmed by recent studies on weak lensing. We show that a CNN is able to yield significantly stricter constraints of (σ8, Ωm) cosmological parameters than the power spectrum using convergence maps generated by full N-body simulations and ray-tracing, at angular scales and shape noise levels relevant for future observations. In a scenario mimicking LSST or Euclid, the CNN yields 2.4–2.8 times smaller credible contours than the power spectrum, and 3.5–4.2 times smaller at noise levels corresponding to a deep space survey such as WFIRST. We also show that at shape noise levels achievable in future space surveys the CNN yields 1.4–2.1 times smaller contours than peak counts, a higher order statistic capable of extracting non-Gaussian information from weak lensing maps.

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Entanglement entropy: non-Gaussian states and strong coupling

Journal of High Energy Physics ◽

10.1007/jhep02(2021)106 ◽

2021 ◽

Vol 2021 (2) ◽

Author(s):

José J. Fernández-Melgarejo ◽

Javier Molina-Vilaplana

Keyword(s):

Ground State ◽

Entanglement Entropy ◽

Energy Functional ◽

Field Theories ◽

Quantum Field Theories ◽

Quantum Field ◽

Gaussian States ◽

Strong Subadditivity ◽

Point Correlation ◽

Non Gaussian

Abstract In this work we provide a method to study the entanglement entropy for non-Gaussian states that minimize the energy functional of interacting quantum field theories at arbitrary coupling. To this end, we build a class of non-Gaussian variational trial wavefunctionals with the help of exact nonlinear canonical transformations. The calculability bonanza shown by these variational ansatze allows us to compute the entanglement entropy using the prescription for the ground state of free theories. In free theories, the entanglement entropy is determined by the two-point correlation functions. For the interacting case, we show that these two-point correlators can be replaced by their nonperturbatively corrected counterparts. Upon giving some general formulae for general interacting models we calculate the entanglement entropy of half space and compact regions for the ϕ4 scalar field theory in 2D. Finally, we analyze the rôle played by higher order correlators in our results and show that strong subadditivity is satisfied.

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Anti-de-Sitter-Maxwell-Yang-Mills Black Holes Thermodynamics from Nonlocal Observables Point of View

Advances in High Energy Physics ◽

10.1155/2019/6870793 ◽

2019 ◽

Vol 2019 ◽

pp. 1-13 ◽

Cited By ~ 1

Author(s):

H. El Moumni

Keyword(s):

Black Hole ◽

Phase Structure ◽

Entanglement Entropy ◽

Point Of View ◽

De Sitter ◽

Yang Mills ◽

Fixed Charges ◽

Point Correlation ◽

Point Correlation Function ◽

Grand Canonical

In this paper we analyze the thermodynamic properties of the Anti-de-Sitter black hole in the Einstein-Maxwell-Yang-Mills-AdS gravity (EMYM) via many approaches and in different thermodynamical ensembles (canonical/grand canonical). First, we give a concise overview of this phase structure in the entropy-thermal diagram for fixed charges and then we investigate this thermodynamical structure in fixed potentials ensemble. The next relevant step is recalling the nonlocal observables such as holographic entanglement entropy and two-point correlation function to show that both observables exhibit a Van der Waals-like behavior in our numerical accuracy and just near the critical line as the case of the thermal entropy for fixed charges by checking Maxwell’s equal area law and the critical exponent. In the light of the grand canonical ensemble, we also find a newly phase structure for such a black hole where the critical behavior disappears in the thermal picture as well as in the holographic one.

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Characteristic Polynomials of Complex Random Matrices and Painlevé Transcendents

International Mathematics Research Notices ◽

10.1093/imrn/rnaa111 ◽

2020 ◽

Cited By ~ 1

Author(s):

Alfredo Deaño ◽

Nick Simm

Keyword(s):

Correlation Function ◽

Random Matrices ◽

Characteristic Polynomials ◽

Painlevé Transcendents ◽

Ginibre Ensemble ◽

Painleve Transcendents ◽

Point Correlation ◽

Point Correlation Function ◽

Non Gaussian ◽

Unitary Ensemble

Abstract We study expectations of powers and correlation functions for characteristic polynomials of $N \times N$ non-Hermitian random matrices. For the $1$-point and $2$-point correlation function, we obtain several characterizations in terms of Painlevé transcendents, both at finite $N$ and asymptotically as $N \to \infty $. In the asymptotic analysis, two regimes of interest are distinguished: boundary asymptotics where parameters of the correlation function can touch the boundary of the limiting eigenvalue support and bulk asymptotics where they are strictly inside the support. For the complex Ginibre ensemble this involves Painlevé IV at the boundary as $N \to \infty $. Our approach, together with the results in [ 49], suggests that this should arise in a much broader class of planar models. For the bulk asymptotics, one of our results can be interpreted as the merging of two “planar Fisher–Hartwig singularities” where Painlevé V arises in the asymptotics. We also discuss the correspondence of our results with a normal matrix model with $d$-fold rotational symmetries known as the lemniscate ensemble, recently studied in [ 15, 18]. Our approach is flexible enough to apply to non-Gaussian models such as the truncated unitary ensemble or induced Ginibre ensemble; we show that in the former case Painlevé VI arises at finite $N$. Scaling near the boundary leads to Painlevé V, in contrast to the Ginibre ensemble.

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From correlation functions to event shapes in QCD

Journal of High Energy Physics ◽

10.1007/jhep02(2021)053 ◽

2021 ◽

Vol 2021 (2) ◽

Cited By ~ 2

Author(s):

D. Chicherin ◽

J. M. Henn ◽

E. Sokatchev ◽

K. Yan

Keyword(s):

Correlation Function ◽

Correlation Functions ◽

Event Shape ◽

Proof Of Concept ◽

Yang Mills ◽

Point Correlation ◽

Point Correlation Function ◽

Event Shapes ◽

A Charge ◽

Conserved Currents

Abstract We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.

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