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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. Calabrese and J. Cardy, Entanglement entropy and conformal field theory, J. Phys. A 42 (2009) 504005 [arXiv:0905.4013] [INSPIRE].
H. Casini and M. Huerta, Entanglement entropy in free quantum field theory, J. Phys. A 42 (2009) 504007 [arXiv:0905.2562] [INSPIRE].
T. Nishioka, Entanglement entropy: holography and renormalization group, Rev. Mod. Phys. 90 (2018) 035007 [arXiv:1801.10352] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
M.A. Niesen and I.L. Chuang, Quantum Computations and Quantum Information, Cambridge University Press, (2000).
A. Almheiri, X. Dong and B. Swingle, Linearity of Holographic Entanglement Entropy, JHEP 02 (2017) 074 [arXiv:1606.04537] [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].
M. Nozaki, Notes on Quantum Entanglement of Local Operators, JHEP 10 (2014) 147 [arXiv:1405.5875] [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].
T. Shimaji, T. Takayanagi and Z. Wei, Holographic Quantum Circuits from Splitting/Joining Local Quenches, JHEP 03 (2019) 165 [arXiv:1812.01176] [INSPIRE].
T. Ugajin, Two dimensional quantum quenches and holography, arXiv:1311.2562 [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].
M. Nozaki, T. Numasawa and T. Takayanagi, Holographic Local Quenches and Entanglement Density, JHEP 05 (2013) 080 [arXiv:1302.5703] [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].
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].
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].
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. de Boer, A. Castro, E. Hijano, J.I. Jottar and P. Kraus, Higher spin entanglement and \( \mathcal{W} \)N conformal blocks, JHEP 07 (2015) 168 [arXiv:1412.7520] [INSPIRE].
W.-Z. Guo and S. He, Rényi entropy of locally excited states with thermal and boundary effect in 2D CFTs, JHEP 04 (2015) 099 [arXiv:1501.00757] [INSPIRE].
B. Chen, W.-Z. Guo, S. He and J.-q. Wu, Entanglement Entropy for Descendent Local Operators in 2D CFTs, JHEP 10 (2015) 173 [arXiv:1507.01157] [INSPIRE].
M. Nozaki, T. Numasawa and S. Matsuura, Quantum Entanglement of Fermionic Local Operators, JHEP 02 (2016) 150 [arXiv:1507.04352] [INSPIRE].
P. Caputa and A. Veliz-Osorio, Entanglement constant for conformal families, Phys. Rev. D 92 (2015) 065010 [arXiv:1507.00582] [INSPIRE].
P. Caputa, J. Sim´on, A. Štikonas, T. Takayanagi and K. Watanabe, Scrambling time from local perturbations of the eternal BTZ black hole, JHEP 08 (2015) 011 [arXiv:1503.08161] [INSPIRE].
M. Rangamani, M. Rozali and A. Vincart-Emard, Dynamics of Holographic Entanglement Entropy Following a Local Quench, JHEP 04 (2016) 069 [arXiv:1512.03478] [INSPIRE].
A. Sivaramakrishnan, Localized Excitations from Localized Unitary Operators, Annals Phys. 381 (2017) 41 [arXiv:1604.00965] [INSPIRE].
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].
T. Numasawa, Scattering effect on entanglement propagation in RCFTs, JHEP 12 (2016) 061 [arXiv:1610.06181] [INSPIRE].
M. Nozaki and N. Watamura, Quantum Entanglement of Locally Excited States in Maxwell Theory, JHEP 12 (2016) 069 [arXiv:1606.07076] [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].
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].
M. Nozaki and N. Watamura, Correspondence between entanglement growth and probability distribution of quasiparticles, Phys. Rev. D 96 (2017) 025019 [arXiv:1703.06589] [INSPIRE].
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].
S. He, Conformal bootstrap to Ŕenyi entropy in 2D Liouville and super-Liouville CFTs, Phys. Rev. D 99 (2019) 026005 [arXiv:1711.00624] [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].
Y. Kusuki, Light Cone Bootstrap in General 2D CFTs and Entanglement from Light Cone Singularity, JHEP 01 (2019) 025 [arXiv:1810.01335] [INSPIRE].
L. Apolo, S. He, W. Song, J. Xu and J. Zheng, Entanglement and chaos in warped conformal field theories, JHEP 04 (2019) 009 [arXiv:1812.10456] [INSPIRE].
Y. Kusuki and M. Miyaji, Entanglement Entropy, OTOC and Bootstrap in 2D CFTs from Regge and Light Cone Limits of Multi-point Conformal Block, JHEP 08 (2019) 063 [arXiv:1905.02191] [INSPIRE].
P. Caputa, T. Numasawa, T. Shimaji, T. Takayanagi and Z. Wei, Double Local Quenches in 2D CFTs and Gravitational Force, JHEP 09 (2019) 018 [arXiv:1905.08265] [INSPIRE].
S. He and H. Shu, Correlation functions, entanglement and chaos in the T T̄/J T̄-deformed CFTs, arXiv:1907.12603 [INSPIRE].
Y. Kusuki and M. Miyaji, Entanglement Entropy after Double-Excitation as Interaction Measure, arXiv:1908.03351 [INSPIRE].
T. Azeyanagi, T. Nishioka and T. Takayanagi, Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2 /C F T1 , Phys. Rev. D 77 (2008) 064005 [arXiv:0710.2956] [INSPIRE].
T. Hartman, C.A. Keller and B. Stoica, Universal Spectrum of 2d Conformal Field Theory in the Large c Limit, JHEP 09 (2014) 118 [arXiv:1405.5137] [INSPIRE].
N. Bao and H. Ooguri, Distinguishability of black hole microstates, Phys. Rev. D 96 (2017) 066017 [arXiv:1705.07943] [INSPIRE].
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.
M. Srednicki, The Approach to Thermal Equilibrium in Quantized Chaotic Systems, J. Phys. A 32 (1999) 1163 [cond-mat/9809360].
A.L. Fitzpatrick, J. Kaplan and M.T. Walters, Universality of Long-Distance AdS Physics from the CFT Bootstrap, JHEP 08 (2014) 145 [arXiv:1403.6829] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1909.04680
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
Bhattacharyya, A., Takayanagi, T. & Umemoto, K. Universal local operator quenches and entanglement entropy. J. High Energ. Phys. 2019, 107 (2019). https://doi.org/10.1007/JHEP11(2019)107
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2019)107