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Journal of High Energy Physics

, 2019:107 | Cite as

Universal local operator quenches and entanglement entropy

  • Arpan BhattacharyyaEmail author
  • Tadashi Takayanagi
  • Koji Umemoto
Open Access
Regular Article - Theoretical Physics
  • 35 Downloads

Abstract

We present a new class of local quenches described by mixed states, parameterized universally by two parameters. We compute the evolutions of entanglement entropy for both a holographic and Dirac fermion CFT in two dimensions. This turns out to be equivalent to calculations of two point functions on a torus. We find that in holographic CFTs, the results coincide with the known results of pure state local operator quenches. On the other hand, we obtain new behaviors in the Dirac fermion CFT, which are missing in the pure state counterpart. By combining our results with the inequalities known for von-Neumann entropy, we obtain an upper bound of the pure state local operator quenches in the Dirac fermion CFT. We also explore predictions about the behaviors of entanglement entropy for more general mixed states.

Keywords

AdS-CFT Correspondence Conformal Field Theory Black Holes 

Notes

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

References

  1. [1]
    P. Calabrese and J. Cardy, Entanglement entropy and conformal field theory, J. Phys.A 42 (2009) 504005 [arXiv:0905.4013] [INSPIRE].
  2. [2]
    H. Casini and M. Huerta, Entanglement entropy in free quantum field theory, J. Phys.A 42 (2009) 504007 [arXiv:0905.2562] [INSPIRE].
  3. [3]
    T. Nishioka, Entanglement entropy: holography and renormalization group, Rev. Mod. Phys.90 (2018) 035007 [arXiv:1801.10352] [INSPIRE].
  4. [4]
    S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett.96 (2006) 181602 [hep-th/0603001] [INSPIRE].
  5. [5]
    S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP08 (2006) 045 [hep-th/0605073] [INSPIRE].
  6. [6]
    V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
  7. [7]
    M.A. Niesen and I.L. Chuang, Quantum Computations and Quantum Information, Cambridge University Press, (2000).Google Scholar
  8. [8]
    A. Almheiri, X. Dong and B. Swingle, Linearity of Holographic Entanglement Entropy, JHEP02 (2017) 074 [arXiv:1606.04537] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    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].ADSCrossRefGoogle Scholar
  10. [10]
    M. Nozaki, Notes on Quantum Entanglement of Local Operators, JHEP10 (2014) 147 [arXiv:1405.5875] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    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].
  12. [12]
    T. Shimaji, T. Takayanagi and Z. Wei, Holographic Quantum Circuits from Splitting/Joining Local Quenches, JHEP03 (2019) 165 [arXiv:1812.01176] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  13. [13]
    T. Ugajin, Two dimensional quantum quenches and holography, arXiv:1311.2562 [INSPIRE].
  14. [14]
    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].
  15. [15]
    M. Nozaki, T. Numasawa and T. Takayanagi, Holographic Local Quenches and Entanglement Density, JHEP05 (2013) 080 [arXiv:1302.5703] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  16. [16]
    C.T. Asplund, A. Bernamonti, F. Galli and T. Hartman, Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches, JHEP02 (2015) 171 [arXiv:1410.1392] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  17. [17]
    C. Holzhey, F. Larsen and F. Wilczek, Geometric and renormalized entropy in conformal field theory, Nucl. Phys.B 424 (1994) 443 [hep-th/9403108] [INSPIRE].
  18. [18]
    P. Caputa, M. Nozaki and T. Takayanagi, Entanglement of local operators in large-N conformal field theories, PTEP2014 (2014) 093B06 [arXiv:1405.5946] [INSPIRE].
  19. [19]
    P. Caputa, J. Simón, A. Štikonas and T. Takayanagi, Quantum Entanglement of Localized Excited States at Finite Temperature, JHEP01 (2015) 102 [arXiv:1410.2287] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    J. de Boer, A. Castro, E. Hijano, J.I. Jottar and P. Kraus, Higher spin entanglement and \( \mathcal{W} \) Nconformal blocks, JHEP07 (2015) 168 [arXiv:1412.7520] [INSPIRE].
  21. [21]
    W.-Z. Guo and S. He, Rényi entropy of locally excited states with thermal and boundary effect in 2D CFTs, JHEP04 (2015) 099 [arXiv:1501.00757] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    B. Chen, W.-Z. Guo, S. He and J.-q. Wu, Entanglement Entropy for Descendent Local Operators in 2D CFTs, JHEP10 (2015) 173 [arXiv:1507.01157] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    M. Nozaki, T. Numasawa and S. Matsuura, Quantum Entanglement of Fermionic Local Operators, JHEP02 (2016) 150 [arXiv:1507.04352] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    P. Caputa and A. Veliz-Osorio, Entanglement constant for conformal families, Phys. Rev.D 92 (2015) 065010 [arXiv:1507.00582] [INSPIRE].
  25. [25]
    P. Caputa, J. Sim´on, A. Štikonas, T. Takayanagi and K. Watanabe, Scrambling time from local perturbations of the eternal BTZ black hole, JHEP08 (2015) 011 [arXiv:1503.08161] [INSPIRE].
  26. [26]
    M. Rangamani, M. Rozali and A. Vincart-Emard, Dynamics of Holographic Entanglement Entropy Following a Local Quench, JHEP04 (2016) 069 [arXiv:1512.03478] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  27. [27]
    A. Sivaramakrishnan, Localized Excitations from Localized Unitary Operators, Annals Phys.381 (2017) 41 [arXiv:1604.00965] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    P. Caputa and M.M. Rams, Quantum dimensions from local operator excitations in the Ising model, J. Phys.A 50 (2017) 055002 [arXiv:1609.02428] [INSPIRE].
  29. [29]
    T. Numasawa, Scattering effect on entanglement propagation in RCFTs, JHEP12 (2016) 061 [arXiv:1610.06181] [INSPIRE].
  30. [30]
    M. Nozaki and N. Watamura, Quantum Entanglement of Locally Excited States in Maxwell Theory, JHEP12 (2016) 069 [arXiv:1606.07076] [INSPIRE].
  31. [31]
    J.R. David, S. Khetrapal and S.P. Kumar, Universal corrections to entanglement entropy of local quantum quenches, JHEP08 (2016) 127 [arXiv:1605.05987] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    P. Caputa, Y. Kusuki, T. Takayanagi and K. Watanabe, Evolution of Entanglement Entropy in Orbifold CFTs, J. Phys.A 50 (2017) 244001 [arXiv:1701.03110] [INSPIRE].
  33. [33]
    M. Nozaki and N. Watamura, Correspondence between entanglement growth and probability distribution of quasiparticles, Phys. Rev.D 96 (2017) 025019 [arXiv:1703.06589] [INSPIRE].
  34. [34]
    A. Jahn and T. Takayanagi, Holographic entanglement entropy of local quenches in AdS4/CFT3: a finite-element approach, J. Phys.A 51 (2018) 015401 [arXiv:1705.04705] [INSPIRE].
  35. [35]
    S. He, Conformal bootstrap to Ŕenyi entropy in 2D Liouville and super-Liouville CFTs, Phys. Rev.D 99 (2019) 026005 [arXiv:1711.00624] [INSPIRE].
  36. [36]
    Y. Kusuki and T. Takayanagi, Rényi entropy for local quenches in 2D CFT from numerical conformal blocks, JHEP01 (2018) 115 [arXiv:1711.09913] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    Y. Kusuki, Light Cone Bootstrap in General 2D CFTs and Entanglement from Light Cone Singularity, JHEP01 (2019) 025 [arXiv:1810.01335] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  38. [38]
    L. Apolo, S. He, W. Song, J. Xu and J. Zheng, Entanglement and chaos in warped conformal field theories, JHEP04 (2019) 009 [arXiv:1812.10456] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  39. [39]
    Y. Kusuki and M. Miyaji, Entanglement Entropy, OTOC and Bootstrap in 2D CFTs from Regge and Light Cone Limits of Multi-point Conformal Block, JHEP08 (2019) 063 [arXiv:1905.02191] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    P. Caputa, T. Numasawa, T. Shimaji, T. Takayanagi and Z. Wei, Double Local Quenches in 2D CFTs and Gravitational Force, JHEP09 (2019) 018 [arXiv:1905.08265] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    S. He and H. Shu, Correlation functions, entanglement and chaos in the T T ̄/J T ̄-deformed CFTs, arXiv:1907.12603 [INSPIRE].
  42. [42]
    Y. Kusuki and M. Miyaji, Entanglement Entropy after Double-Excitation as Interaction Measure, arXiv:1908.03351 [INSPIRE].
  43. [43]
    T. Azeyanagi, T. Nishioka and T. Takayanagi, Near Extremal Black Hole Entropy as Entanglement Entropy via AdS 2/C F T 1 , Phys. Rev.D 77 (2008) 064005 [arXiv:0710.2956] [INSPIRE].
  44. [44]
    T. Hartman, C.A. Keller and B. Stoica, Universal Spectrum of 2d Conformal Field Theory in the Large c Limit, JHEP09 (2014) 118 [arXiv:1405.5137] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  45. [45]
    N. Bao and H. Ooguri, Distinguishability of black hole microstates, Phys. Rev.D 96 (2017) 066017 [arXiv:1705.07943] [INSPIRE].
  46. [46]
    G.M. Bosyk, S. Zozor, F. Holik, M. Portesi and P.W. Lamberti, A family of generalized quantum entropies: definition and properties, Quant. Inf. Proc.15 (2016) 3393.MathSciNetCrossRefGoogle Scholar
  47. [47]
    M. Srednicki, The Approach to Thermal Equilibrium in Quantized Chaotic Systems, J. Phys.A 32 (1999) 1163 [cond-mat/9809360].
  48. [48]
    A.L. Fitzpatrick, J. Kaplan and M.T. Walters, Universality of Long-Distance AdS Physics from the CFT Bootstrap, JHEP08 (2014) 145 [arXiv:1403.6829] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Center for Gravitational Physics, Yukawa Institute for Theoretical PhysicsKyoto UniversityKyotoJapan
  2. 2.Indian Institute of TechnologyGandhinagarIndia
  3. 3.Kavli Institute for the Physics and Mathematics of the UniverseUniversity of TokyoChibaJapan

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