Abstract
We study the time dependence of Rényi/entanglement entropies of locally excited states created by fields with integer spins s ≤ 2 in 4 dimensions. For spins 0, 1 these states are characterised by localised energy densities of a given width which travel as a spherical wave at the speed of light. For the spin 2 case, in the absence of a local gauge invariant stress tensor, we probe these states with the Kretschmann scalar and show they represent localised curvature densities which travel at the speed of light. We consider the reduced density matrix of the half space with these excitations and develop methods which include a convenient gauge choice to evaluate the time dependence of Rényi/entanglement entropies as these quenches enter the half region. In all cases, the entanglement entropy grows in time and saturates at log 2. In the limit, the width of these excitations tends to zero, the growth is determined by order 2s + 1 polynomials in the ratio of the distance from the co-dimension-2 entangling surface and time. The polynomials corresponding to quenches created by the fields can be organized in terms of their representations under the SO(2)T × SO(2)L symmetry preserved by the presence of the co-dimension 2 entangling surface. For fields transforming as scalars under this symmetry, the order 2s + 1 polynomial is completely determined by the spin.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
H. Liu and J. Sonner, Holographic systems far from equilibrium: a review, arXiv:1810.02367 [INSPIRE].
P. Calabrese and J.L. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech. 0504 (2005) P04010 [cond-mat/0503393] [INSPIRE].
P. Calabrese and J. Cardy, Quantum Quenches in Extended Systems, J. Stat. Mech. 0706 (2007) P06008 [arXiv:0704.1880] [INSPIRE].
P. Calabrese and J. Cardy, Entanglement and correlation functions following a local quench: a conformal field theory approach, J. Stat. Mech. 0710 (2007) P10004 [arXiv:0708.3750] [INSPIRE].
V. Eisler and I. Peschel, Evolution of entanglement after a local quench, Journal of Statistical Mechanics: Theory and Experiment 2007 (2007) P06005–P06005.
J.-M. Stéphan and J. Dubail, Local quantum quenches in critical one-dimensional systems: entanglement, the Loschmidt echo, and light-cone effects, Journal of Statistical Mechanics: Theory and Experiment 2011 (2011) P08019.
C.T. Asplund and A. Bernamonti, Mutual information after a local quench in conformal field theory, Phys. Rev. D 89 (2014) 066015 [arXiv:1311.4173] [INSPIRE].
P. Calabrese and J. Cardy, Quantum quenches in 1 + 1 dimensional conformal field theories, J. Stat. Mech. 1606 (2016) 064003 [arXiv:1603.02889] [INSPIRE].
D.S. Ageev, A.I. Belokon and V.V. Pushkarev, From locality to irregularity: Introducing local quenches in massive scalar field theory, arXiv:2205.12290 [INSPIRE].
C.T. Asplund and S.G. Avery, Evolution of Entanglement Entropy in the D1-D5 Brane System, Phys. Rev. D 84 (2011) 124053 [arXiv:1108.2510] [INSPIRE].
M. Nozaki, T. Numasawa and T. Takayanagi, Holographic Local Quenches and Entanglement Density, JHEP 05 (2013) 080 [arXiv:1302.5703] [INSPIRE].
M. Nozaki, T. Numasawa and T. Takayanagi, Quantum Entanglement of Local Operators in Conformal Field Theories, Phys. Rev. Lett. 112 (2014) 111602 [arXiv:1401.0539] [INSPIRE].
P. Caputa, M. Nozaki and T. Takayanagi, Entanglement of local operators in large-N conformal field theories, PTEP 2014 (2014) 093B06 [arXiv:1405.5946] [INSPIRE].
M. Nozaki, Notes on Quantum Entanglement of Local Operators, JHEP 10 (2014) 147 [arXiv:1405.5875] [INSPIRE].
S. He, T. Numasawa, T. Takayanagi and K. Watanabe, Quantum dimension as entanglement entropy in two dimensional conformal field theories, Phys. Rev. D 90 (2014) 041701 [arXiv:1403.0702] [INSPIRE].
P. Caputa and A. Veliz-Osorio, Entanglement constant for conformal families, Phys. Rev. D 92 (2015) 065010 [arXiv:1507.00582] [INSPIRE].
C.T. Asplund, A. Bernamonti, F. Galli and T. Hartman, Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches, JHEP 02 (2015) 171 [arXiv:1410.1392] [INSPIRE].
P. Caputa, J. Simón, A. Štikonas and T. Takayanagi, Quantum Entanglement of Localized Excited States at Finite Temperature, JHEP 01 (2015) 102 [arXiv:1410.2287] [INSPIRE].
J.R. David, S. Khetrapal and S.P. Kumar, Universal corrections to entanglement entropy of local quantum quenches, JHEP 08 (2016) 127 [arXiv:1605.05987] [INSPIRE].
J.R. David, S. Khetrapal and S.P. Kumar, Local quenches and quantum chaos from higher spin perturbations, JHEP 10 (2017) 156 [arXiv:1707.07166] [INSPIRE].
Y. Kusuki and T. Takayanagi, Rényi entropy for local quenches in 2D CFT from numerical conformal blocks, JHEP 01 (2018) 115 [arXiv:1711.09913] [INSPIRE].
J. Zhang and P. Calabrese, Subsystem distance after a local operator quench, JHEP 02 (2020) 056 [arXiv:1911.04797] [INSPIRE].
Y. Kusuki and K. Tamaoka, Entanglement Wedge Cross Section from CFT: Dynamics of Local Operator Quench, JHEP 02 (2020) 017 [arXiv:1909.06790] [INSPIRE].
C.A. Agón, S.F. Lokhande and J.F. Pedraza, Local quenches, bulk entanglement entropy and a unitary Page curve, JHEP 08 (2020) 152 [arXiv:2004.15010] [INSPIRE].
M. Nozaki, T. Numasawa and S. Matsuura, Quantum Entanglement of Fermionic Local Operators, JHEP 02 (2016) 150 [arXiv:1507.04352] [INSPIRE].
M. Nozaki and N. Watamura, Quantum Entanglement of Locally Excited States in Maxwell Theory, JHEP 12 (2016) 069 [arXiv:1606.07076] [INSPIRE].
V. Benedetti and H. Casini, Entanglement entropy of linearized gravitons in a sphere, Phys. Rev. D 101 (2020) 045004 [arXiv:1908.01800] [INSPIRE].
J.R. David and J. Mukherjee, Hyperbolic cylinders and entanglement entropy: gravitons, higher spins, p-forms, JHEP 01 (2021) 202 [arXiv:2005.08402] [INSPIRE].
J.R. David and J. Mukherjee, Entanglement entropy of gravitational edge modes, JHEP 08 (2022) 065 [arXiv:2201.06043] [INSPIRE].
P. Candelas and D. Deutsch, On the vacuum stress induced by uniform acceleration or supporting the ether, Proc. Roy. Soc. Lond. A 354 (1977) 79 [INSPIRE].
A. Laddha, S.G. Prabhu, S. Raju and P. Shrivastava, The Holographic Nature of Null Infinity, SciPost Phys. 10 (2021) 041 [arXiv:2002.02448] [INSPIRE].
S. Raju, Failure of the split property in gravity and the information paradox, Class. Quant. Grav. 39 (2022) 064002 [arXiv:2110.05470] [INSPIRE].
H. Osborn and A.C. Petkou, Implications of conformal invariance in field theories for general dimensions, Annals Phys. 231 (1994) 311 [hep-th/9307010] [INSPIRE].
M. Billò, V. Gonçalves, E. Lauria and M. Meineri, Defects in conformal field theory, JHEP 04 (2016) 091 [arXiv:1601.02883] [INSPIRE].
T. Anegawa, N. Iizuka and D. Kabat, Defining entanglement without tensor factoring: A Euclidean hourglass prescription, Phys. Rev. D 105 (2022) 085003 [arXiv:2111.03886] [INSPIRE].
T. Anegawa, N. Iizuka and D. Kabat, Extractable entanglement from a Euclidean hourglass, Phys. Rev. D 106 (2022) 085010 [arXiv:2205.01137] [INSPIRE].
M. Lemos, P. Liendo, M. Meineri and S. Sarkar, Universality at large transverse spin in defect CFT, JHEP 09 (2018) 091 [arXiv:1712.08185] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2209.05792
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
David, J.R., Mukherjee, J. Entanglement entropy of local gravitational quenches. J. High Energ. Phys. 2023, 28 (2023). https://doi.org/10.1007/JHEP04(2023)028
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2023)028