Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1705.04705 · Journal of Physics A Mathematical and Theoretical

Holographic entanglement entropy of local quenches in AdS4/CFT3: a finite-element approach

Alexander Jahn, Tadashi Takayanagi

Published Sep 7, 2017• 13 citations
arXivHTMLPDF

Abstract

Abstract Understanding quantum entanglement in interacting higher-dimensional conformal field theories is a challenging task, as direct analytical calculations are often impossible to perform. With holographic entanglement entropy, calculations of entanglement entropy turn into a problem of finding extremal surfaces in a curved spacetime, which we tackle with a numerical finite-element approach. In this paper, we compute the entanglement entropy between two half-spaces resulting from a local quench, triggered by a local operator insertion in a CFT 3 . We find that the growth of entanglement entropy at early time agrees with the prediction from the first law, as long as the conformal dimension Δ of the local operator is small. Within the limited time region that we can probe numerically, we observe deviations from the first law and a transition to sub-linear growth at later time. In particular, the time dependence at large Δ shows qualitative differences to the simple logarithmic time dependence familiar from the CFT 2 case. We hope that our work will motivate further studies, both numerical and analytical, on entanglement entropy in higher dimensions.

DOI
10.1088/1751-8121/aa8afa

Related papers

Holographic entanglement entropy of local quenches in AdS4/CFT3: a finite-element approach

A. Jahn, Tadashi Takayanagi

Understanding quantum entanglement in interacting higher-dimensional conformal field theories is a challenging task, as direct analytical calculations are often impossible to perform. With holographic entanglement entropy, calculations of entanglement entropy turn into a problem of finding extremal surfaces in a curved spacetime, which we tackle with a numerical finiteelement approach. In this paper, we compute the entanglement entropy between two half-spaces resulting from a local quench, triggered by a local operator insertion in a CFT3. We find that the growth of entanglement entropy at early time agrees with the prediction from the first law, as long as the conformal dimension Δ of the local operator is small. Within the limited time region that we can probe numerically, we observe deviations from the first law and a transition to sub-linear growth at later time. In particular, the time dependence at large Δ shows qualitative differences to the simple logarithmic time dependence familiar from the CFT2 case. We hope that our work will motivate further studies, both numerical and analytical, on entanglement entropy in higher dimensions.

•Jan 1, 2017•14 citations

Holographic entanglement entropy from 2d CFT: heavy states and local quenches

Curtis T. Asplund, Alice Bernamonti, Federico Galli +1 more

We consider the entanglement entropy in 2d conformal field theory in a class of excited states produced by the insertion of a heavy local operator. These include both high-energy eigenstates of the Hamiltonian and time-dependent local quenches. We compute the universal contribution from the stress tensor to the single interval Renyi entropies and entanglement entropy, and conjecture that this dominates the answer in theories with a large central charge and a sparse spectrum of low-dimension operators. The resulting entanglement entropies agree precisely with holographic calculations in three-dimensional gravity. High-energy eigenstates are dual to microstates of the BTZ black hole, so the corresponding holographic calculation is a geodesic length in the black hole geometry; agreement between these two answers demonstrates that these individual microstates of holographic CFTs effectively thermalize at the level of the single-interval entanglement entropy. For local quenches, the dual geometry is a highly boosted black hole or conical defect. On the CFT side, the rise in entanglement entropy after a quench is directly related to the monodromy of a Virasoro conformal block.

arXiv:1410.1392•Journal of High Energy Physics•Feb 1, 2015•279 citations

On holographic entanglement density

Nikola I. Gushterov, Andy O’Bannon, Ronnie Rodgers

We use holographic duality to study the entanglement entropy (EE) of Conformal Field Theories (CFTs) in various spacetime dimensions d, in the presence of various deformations: a relevant Lorentz scalar operator with constant source, a temperature T , a chemical potential μ, a marginal Lorentz scalar operator with source linear in a spatial coordinate, and a circle-compactified spatial direction. We consider EE between a strip or sphere sub-region and the rest of the system, and define the “entanglement density” (ED) as the change in EE due to the deformation, divided by the sub-region’s volume. Using the deformed CFTs above, we show how the ED’s dependence on the strip width or sphere radius, L, is useful for characterizing states of matter. For example, the ED’s small-L behavior is determined either by the dimension of the perturbing operator or by the first law of EE. For Lorentz-invariant renormalization group (RG) flows between CFTs, the “area theorem” states that the coefficient of the EE’s area law term must be larger in the UV than in the IR. In these cases the ED must therefore approach zero from below as L→∞. However, when Lorentz symmetry is broken and the IR fixed point has different scaling from the UV, we find that the ED often approaches the thermal entropy density from above, indicating area theorem violation.

arXiv:1708.09376•Journal of High Energy Physics•Oct 1, 2017•13 citations

Entanglement entropy in holographic CFTs with generic boundaries

Fabio Ori, Peng-Xiang Hao

Entanglement entropy in holographic conformal field theories with boundaries of generic spacetime signature cannot be described entirely within the standard holographic duality to a real bulk spacetime. We show, both in static and time-dependent setups, that an exact match with the conformal field theory predictions in two boundary dimensions entails an extension of the dual spacetime to complex coordinates. As a consequence, relevant bulk objects such as Ryu-Takayanagi surfaces and branes are in general complex, yet anchored on a real asymptotic boundary preserving the physical meaning of field-theoretical quantities. We also provide a third numerical check of the holographic prediction with a two-dimensional system of free Gaussian fermions exhibiting the same asymptotic regimes across different entanglement phases.

hep-thCross-listedarXiv:2609.21370•Sep 21, 2026•0 citations

Aspects of Holographic Entanglement Entropy

Shinsei Ryu, Tadashi Takayanagi

This is an extended version of our short report hep-th/0603001, where a holographic interpretation of entanglement entropy in conformal field theories is proposed from AdS/CFT correspondence. In addition to a concise review of relevant recent progresses of entanglement entropy and details omitted in the earlier letter, this paper includes the following several new results: We give a more direct derivation of our claim which relates the entanglement entropy with the minimal area surfaces in the AdS3/CFT2 case as well as some further discussions on higher dimensional cases. Also the relation between the entanglement entropy and central charges in 4D conformal field theories is examined. We check that the logarithmic part of the 4D entanglement entropy computed in the CFT side agrees with the AdS5 result at least under a specific condition. Finally we estimate the entanglement entropy of massive theories in generic dimensions by making use of our proposal.

•May 6, 2006•1,097 citations

Universal corrections to entanglement entropy of local quantum quenches

Justin R. David, Surbhi Khetrapal, S. Prem Kumar

We study the time evolution of single interval Rényi and entanglement entropies following local quantum quenches in two dimensional conformal field theories at finite temperature for which the locally excited states have a finite temporal width ϵ. We show that, for local quenches produced by the action of a conformal primary field, the time dependence of Rényi and entanglement entropies at order ϵ2 is universal. It is determined by the expectation value of the stress tensor in the replica geometry and proportional to the conformal dimension of the primary field generating the local excitation. We also show that in CFTs with a gravity dual, the ϵ2 correction to the holographic entanglement entropy following a local quench precisely agrees with the CFT prediction. We then consider CFTs admitting a higher spin symmetry and turn on a higher spin chemical potential μ. We calculate the time dependence of the order ϵ2 correction to the entanglement entropy for small μ, and show that the contribution at order μ 2 is universal. We verify our arguments against exact results for minimal models and the free fermion theory.

arXiv:1605.05987•Journal of High Energy Physics•Aug 1, 2016•36 citations
Abstract Understanding quantum entanglement in interacting higher-dimensional conformal field theories is a challenging task, as direct analytical calculations are often impossible to perform. With holographic entanglement entropy, calculations of entanglement entropy turn into a problem of finding extremal surfaces in a curved spacetime, which we tackle with a numerical finite-element approach. In this paper, we compute the entanglement entropy between two half-spaces resulting from a local quench, triggered by a local operator insertion in a CFT 3 . We find that the growth of entanglement entropy at early time agrees with the prediction from the first law, as long as the conformal dimension Δ of the local operator is small. Within the limited time region that we can probe numerically, we observe deviations from the first law and a transition to sub-linear growth at later time. In particular, the time dependence at large Δ shows qualitative differences to the simple logarithmic time dependence familiar from the CFT 2 case. We hope that our work will motivate further studies, both numerical and analytical, on entanglement entropy in higher dimensions.
Understanding quantum entanglement in interacting higher-dimensional conformal field theories is a challenging task, as direct analytical calculations are often impossible to perform. With holographic entanglement entropy, calculations of entanglement entropy turn into a problem of finding extremal surfaces in a curved spacetime, which we tackle with a numerical finiteelement approach. In this paper, we compute the entanglement entropy between two half-spaces resulting from a local quench, triggered by a local operator insertion in a CFT3. We find that the growth of entanglement entropy at early time agrees with the prediction from the first law, as long as the conformal dimension Δ of the local operator is small. Within the limited time region that we can probe numerically, we observe deviations from the first law and a transition to sub-linear growth at later time. In particular, the time dependence at large Δ shows qualitative differences to the simple logarithmic time dependence familiar from the CFT2 case. We hope that our work will motivate further studies, both numerical and analytical, on entanglement entropy in higher dimensions.
We consider the entanglement entropy in 2d conformal field theory in a class of excited states produced by the insertion of a heavy local operator. These include both high-energy eigenstates of the Hamiltonian and time-dependent local quenches. We compute the universal contribution from the stress tensor to the single interval Renyi entropies and entanglement entropy, and conjecture that this dominates the answer in theories with a large central charge and a sparse spectrum of low-dimension operators. The resulting entanglement entropies agree precisely with holographic calculations in three-dimensional gravity. High-energy eigenstates are dual to microstates of the BTZ black hole, so the corresponding holographic calculation is a geodesic length in the black hole geometry; agreement between these two answers demonstrates that these individual microstates of holographic CFTs effectively thermalize at the level of the single-interval entanglement entropy. For local quenches, the dual geometry is a highly boosted black hole or conical defect. On the CFT side, the rise in entanglement entropy after a quench is directly related to the monodromy of a Virasoro conformal block.
We use holographic duality to study the entanglement entropy (EE) of Conformal Field Theories (CFTs) in various spacetime dimensions d, in the presence of various deformations: a relevant Lorentz scalar operator with constant source, a temperature T , a chemical potential μ, a marginal Lorentz scalar operator with source linear in a spatial coordinate, and a circle-compactified spatial direction. We consider EE between a strip or sphere sub-region and the rest of the system, and define the “entanglement density” (ED) as the change in EE due to the deformation, divided by the sub-region’s volume. Using the deformed CFTs above, we show how the ED’s dependence on the strip width or sphere radius, L, is useful for characterizing states of matter. For example, the ED’s small-L behavior is determined either by the dimension of the perturbing operator or by the first law of EE. For Lorentz-invariant renormalization group (RG) flows between CFTs, the “area theorem” states that the coefficient of the EE’s area law term must be larger in the UV than in the IR. In these cases the ED must therefore approach zero from below as L→∞. However, when Lorentz symmetry is broken and the IR fixed point has different scaling from the UV, we find that the ED often approaches the thermal entropy density from above, indicating area theorem violation.
Entanglement entropy in holographic conformal field theories with boundaries of generic spacetime signature cannot be described entirely within the standard holographic duality to a real bulk spacetime. We show, both in static and time-dependent setups, that an exact match with the conformal field theory predictions in two boundary dimensions entails an extension of the dual spacetime to complex coordinates. As a consequence, relevant bulk objects such as Ryu-Takayanagi surfaces and branes are in general complex, yet anchored on a real asymptotic boundary preserving the physical meaning of field-theoretical quantities. We also provide a third numerical check of the holographic prediction with a two-dimensional system of free Gaussian fermions exhibiting the same asymptotic regimes across different entanglement phases.
This is an extended version of our short report hep-th/0603001, where a holographic interpretation of entanglement entropy in conformal field theories is proposed from AdS/CFT correspondence. In addition to a concise review of relevant recent progresses of entanglement entropy and details omitted in the earlier letter, this paper includes the following several new results: We give a more direct derivation of our claim which relates the entanglement entropy with the minimal area surfaces in the AdS3/CFT2 case as well as some further discussions on higher dimensional cases. Also the relation between the entanglement entropy and central charges in 4D conformal field theories is examined. We check that the logarithmic part of the 4D entanglement entropy computed in the CFT side agrees with the AdS5 result at least under a specific condition. Finally we estimate the entanglement entropy of massive theories in generic dimensions by making use of our proposal.
We study the time evolution of single interval Rényi and entanglement entropies following local quantum quenches in two dimensional conformal field theories at finite temperature for which the locally excited states have a finite temporal width ϵ. We show that, for local quenches produced by the action of a conformal primary field, the time dependence of Rényi and entanglement entropies at order ϵ2 is universal. It is determined by the expectation value of the stress tensor in the replica geometry and proportional to the conformal dimension of the primary field generating the local excitation. We also show that in CFTs with a gravity dual, the ϵ2 correction to the holographic entanglement entropy following a local quench precisely agrees with the CFT prediction. We then consider CFTs admitting a higher spin symmetry and turn on a higher spin chemical potential μ. We calculate the time dependence of the order ϵ2 correction to the entanglement entropy for small μ, and show that the contribution at order μ 2 is universal. We verify our arguments against exact results for minimal models and the free fermion theory.