Abstract
In this paper we discuss the scattering effect on entanglement propagation in RCFTs. In our setup, we consider the time evolution of excited states created by the insertion of many local operators. Our results show that because of the finiteness of quantum dimension, entanglement is not changed after the scattering in RCFTs. In this mean, entanglement is conserved after the scattering event in RCFTs, which reflects the integrability of the system. Our results are also consistent with the free quasiparticle picture after the global quenches.
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References
J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
G. ’t Hooft, Dimensional reduction in quantum gravity, Salamfest 0284 (1993) 296 [gr-qc/9310026] [INSPIRE].
L. Susskind, The World as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].
S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].
D.A. Roberts and D. Stanford, Two-dimensional conformal field theory and the butterfly effect, Phys. Rev. Lett. 115 (2015) 131603 [arXiv:1412.5123] [INSPIRE].
J.M. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].
P. Caputa, J. Simón, 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. Miyaji, Butterflies from Information Metric, JHEP 09 (2016) 002 [arXiv:1607.01467] [INSPIRE].
A.I. Larkin and Y.N. Ovchinnikov, Quasiclassical method in the theory of superconductivity, JETP 28 (1969) 1200.
A. Kitaev, A simple model of quantum holography (part 1), talk given at Entanglement in Strongly-Correlated Quantum Matter, KITP, Santa Barbara, California, U.S.A., April 7-July 2 2015.
A. Kitaev, A simple model of quantum holography (part 2), talk given at Entanglement in Strongly-Correlated Quantum Matter, KITP, Santa Barbara, California, U.S.A., April 7-July 2 2015.
J. Polchinski, Chaos in the black hole S-matrix, arXiv:1505.08108 [INSPIRE].
G. Turiaci and H. Verlinde, On CFT and Quantum Chaos, arXiv:1603.03020 [INSPIRE].
E. Perlmutter, Bounding the Space of Holographic CFTs with Chaos, JHEP 10 (2016) 069 [arXiv:1602.08272] [INSPIRE].
P. Caputa, T. Numasawa and A. Veliz-Osorio, Scrambling without chaos in RCFT, arXiv:1602.06542 [INSPIRE].
Y. Gu and X.-L. Qi, Fractional Statistics and the Butterfly Effect, JHEP 08 (2016) 129 [arXiv:1602.06543] [INSPIRE].
J.L. Karczmarek, J.M. Maldacena and A. Strominger, Black hole non-formation in the matrix model, JHEP 01 (2006) 039 [hep-th/0411174] [INSPIRE].
J.M. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [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].
C.T. Asplund, A. Bernamonti, F. Galli and T. Hartman, Entanglement Scrambling in 2d Conformal Field Theory, JHEP 09 (2015) 110 [arXiv:1506.03772] [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].
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, Notes on Quantum Entanglement of Local Operators, JHEP 10 (2014) 147 [arXiv:1405.5875] [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].
P. Caputa, M. Nozaki and T. Takayanagi, Entanglement of local operators in large-N conformal field theories, Prog. Theor. Exp. Phys. 2014 (2014) 093B06 [arXiv:1405.5946] [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].
H. Casini, H. Liu and M. Mezei, Spread of entanglement and causality, JHEP 07 (2016) 077 [arXiv:1509.05044] [INSPIRE].
P. Caputa and A. Veliz-Osorio, Entanglement constant for conformal families, Phys. Rev. D 92 (2015) 065010 [arXiv:1507.00582] [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].
T. Hartman, S. Jain and S. Kundu, Causality Constraints in Conformal Field Theory, JHEP 05 (2016) 099 [arXiv:1509.00014] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
P. Di Francesco, P. Mathieu and D. Sénéchal, Conformal Field Theory, Springer-Verlag (1997).
P. Caputa and M.M. Rams, Quantum dimensions from local operator excitations in the Ising model, arXiv:1609.02428 [INSPIRE].
G.W. Moore and N. Seiberg, Classical and Quantum Conformal Field Theory, Commun. Math. Phys. 123 (1989) 177 [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Minimal Model Holography, J. Phys. A 46 (2013) 214002 [arXiv:1207.6697] [INSPIRE].
T. Anous, T. Hartman, A. Rovai and J. Sonner, Black Hole Collapse in the 1/c Expansion, JHEP 07 (2016) 123 [arXiv:1603.04856] [INSPIRE].
M. Nozaki, T. Numasawa and T. Takayanagi, Holographic Local Quenches and Entanglement Density, JHEP 05 (2013) 080 [arXiv:1302.5703] [INSPIRE].
J.J. Friess, S.S. Gubser, G. Michalogiorgakis and S.S. Pufu, Expanding plasmas and quasinormal modes of anti-de Sitter black holes, JHEP 04 (2007) 080 [hep-th/0611005] [INSPIRE].
P. Figueras, V.E. Hubeny, M. Rangamani and S.F. Ross, Dynamical black holes and expanding plasmas, JHEP 04 (2009) 137 [arXiv:0902.4696] [INSPIRE].
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Numasawa, T. Scattering effect on entanglement propagation in RCFTs. J. High Energ. Phys. 2016, 61 (2016). https://doi.org/10.1007/JHEP12(2016)061
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DOI: https://doi.org/10.1007/JHEP12(2016)061