Dynamics of entanglement in expanding quantum fields

Berges, Jurgen; Floerchinger, Stefan; Venugopalan, Raju

doi:10.1007/JHEP04(2018)145

Title: Dynamics of entanglement in expanding quantum fields

Journal Article · Fri Apr 27 00:00:00 EDT 2018 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP04(2018)145· OSTI ID:1462428

Berges, Jurgen ^[1]; Floerchinger, Stefan ^[1]; Venugopalan, Raju ^[2]

Univ. Heidelberg, Heidelberg (Germany)
Brookhaven National Lab. (BNL), Upton, NY (United States)

Here, we develop a novel real-time approach to computing the entanglement between spatial regions for Gaussian states in quantum field theory. The entanglement entropy is characterized in terms of local correlation functions on space-like Cauchy hypersurfaces. The framework is applied to explore an expanding light cone geometry in the particular case of the Schwinger model for quantum electrodynamics in 1+1 space-time dimensions. We observe that the entanglement entropy becomes extensive in rapidity at early times and that the corresponding local reduced density matrix is a thermal density matrix for excitations around a coherent field with a time dependent temperature. Since the Schwinger model successfully describes many features of multiparticle production in e⁺e^- collisions, our results provide an attractive explanation in this framework for the apparent thermal nature of multiparticle production even in the absence of significant final state scattering.

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Research Organization:: Brookhaven National Lab. (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0012704

OSTI ID:: 1462428

Report Number(s):: BNL-207867-2018-JAAM; TRN: US1902170

Journal Information:: Journal of High Energy Physics (Online), Vol. 2018, Issue 4; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

References (79)

Entanglement and Fast Quantum Thermalization in Heavy Ion Collisions Ho, Chiu Man; Hsu, Stephen D. H. arXiv https://doi.org/10.48550/arxiv.1506.03696	text	January 2015
Entanglement entropy and entropy production in the color glass condensate framework Kovner, Alex; Lublinsky, Michael Physical Review D, Vol. 92, Issue 3 https://doi.org/10.1103/PhysRevD.92.034016	journal	August 2015
Aspects of Holographic Entanglement Entropy Ryu, Shinsei; Takayanagi, Tadashi arXiv https://doi.org/10.48550/arxiv.hep-th/0605073	text	January 2006
Entanglement entropy in free quantum field theory Casini, H.; Huerta, M. Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue 50 https://doi.org/10.1088/1751-8113/42/50/504007	journal	December 2009
Thermal Hadronization and Hawking-Unruh Radiation in QCD Castorina, P.; Kharzeev, D.; Satz, H. arXiv https://doi.org/10.48550/arxiv.0704.1426	text	January 2007
Entanglement entropy and conformal field theory Calabrese, Pasquale; Cardy, John Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue 50 https://doi.org/10.1088/1751-8113/42/50/504005	journal	December 2009
Spacetime Entanglement Entropy in 1+1 Dimensions Saravani, Mehdi; Sorkin, Rafael D.; Yazdi, Yasaman K. arXiv https://doi.org/10.48550/arxiv.1311.7146	text	January 2013
Quantum quenches in 1 + 1 dimensional conformal field theories Calabrese, Pasquale; Cardy, John Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, Issue 6 https://doi.org/10.1088/1742-5468/2016/06/064003	journal	June 2016
Real-time dynamics of string breaking Hebenstreit, Florian; Berges, Jürgen; Gelfand, Daniil arXiv https://doi.org/10.48550/arxiv.1307.4619	text	January 2013
Measuring entanglement entropy in a quantum many-body system Islam, Rajibul; Ma, Ruichao; Preiss, Philipp M. Nature, Vol. 528, Issue 7580 https://doi.org/10.1038/nature15750	journal	December 2015
Towards a derivation of holographic entanglement entropy Casini, Horacio; Huerta, Marina; Myers, Robert C. Journal of High Energy Physics, Vol. 2011, Issue 5 https://doi.org/10.1007/JHEP05(2011)036	journal	May 2011
Congruences and canonical forms for a positive matrix: Application to the Schweinler–Wigner extremum principle Simon, R.; Chaturvedi, S.; Srinivasan, V. Journal of Mathematical Physics, Vol. 40, Issue 7 https://doi.org/10.1063/1.532913	journal	July 1999
Thermal description of hadron production in <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math> collisions revisited Andronic, A.; Beutler, F.; Braun-Munzinger, P. Physics Letters B, Vol. 675, Issue 3-4 https://doi.org/10.1016/j.physletb.2009.04.024	journal	May 2009
Particle production in field theories coupled to strong external sources, I: Formalism and main results Gelis, François; Venugopalan, Raju Nuclear Physics A, Vol. 776, Issue 3-4 https://doi.org/10.1016/j.nuclphysa.2006.07.020	journal	October 2006
Fluctuations of the string tension and transverse mass distribution Bialas, A. Physics Letters B, Vol. 466, Issue 2-4 https://doi.org/10.1016/S0370-2693(99)01159-4	journal	November 1999
Hot origin of the Little Bang Akkelin, S. V. The European Physical Journal A, Vol. 53, Issue 12 https://doi.org/10.1140/epja/i2017-12432-1	journal	December 2017
Universality of Entropy Scaling in One Dimensional Gapless Models Korepin, V. E. Physical Review Letters, Vol. 92, Issue 9 https://doi.org/10.1103/PhysRevLett.92.096402	journal	March 2004
PYTHIA 6.4 physics and manual Sjöstrand, Torbjörn; Mrenna, Stephen; Skands, Peter Journal of High Energy Physics, Vol. 2006, Issue 05 https://doi.org/10.1088/1126-6708/2006/05/026	journal	May 2006
Holographic pomeron and entropy Stoffers, Alexander; Zahed, Ismail Physical Review D, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevD.88.025038	journal	July 2013
Entanglement and fast quantum thermalization in heavy ion collisions Ho, Chiu Man; Hsu, Stephen D. H. Modern Physics Letters A, Vol. 31, Issue 18 https://doi.org/10.1142/S0217732316501108	journal	June 2016
Decoherence and dynamical entropy generation in quantum field theory Koksma, Jurjen F.; Prokopec, Tomislav; Schmidt, Michael G. Physics Letters B, Vol. 707, Issue 2 https://doi.org/10.1016/j.physletb.2011.12.049	journal	January 2012
Entropy and correlators in quantum field theory Koksma, Jurjen F.; Prokopec, Tomislav; Schmidt, Michael G. Annals of Physics, Vol. 325, Issue 6 https://doi.org/10.1016/j.aop.2010.02.016	journal	June 2010
Thermal hadronization and Hawking–Unruh radiation in QCD Castorina, P.; Kharzeev, D.; Satz, H. The European Physical Journal C, Vol. 52, Issue 1 https://doi.org/10.1140/epjc/s10052-007-0368-6	journal	July 2007
Thermodynamical String Fragmentation Fischer, Nadine; Sjöstrand, Torbjörn arXiv https://doi.org/10.48550/arxiv.1610.09818	text	January 2016
A thermodynamical approach to hadron production in $e^+e^-$ collisions Becattini, F. Zeitschrift f�r Physik C Particles and Fields, Vol. 69, Issue 3 https://doi.org/10.1007/s002880050051	journal	January 1996
Entropy and Correlators in Quantum Field Theory Koksma, Jurjen F.; Prokopec, Tomislav; Schmidt, Michael G. arXiv https://doi.org/10.48550/arxiv.1002.0749	text	January 2010
Deep inelastic scattering as a probe of entanglement Kharzeev, Dmitri E.; Levin, Eugene M. Physical Review D, Vol. 95, Issue 11 https://doi.org/10.1103/PhysRevD.95.114008	journal	June 2017
Real-time dynamics of matrix quantum mechanics beyond the classical approximation Buividovich, Pavel; Hanada, Masanori; Schäfer, Andreas EPJ Web of Conferences, Vol. 175 https://doi.org/10.1051/epjconf/201817508006	journal	January 2018
Optical Coherence and Quantum Optics Mandel, Leonard; Wolf, Emil https://doi.org/10.1017/CBO9781139644105	book	January 1995
Entropy Creation in Relativistic Heavy ion Collisions MÜLler, Berndt; SchÄFer, Andreas International Journal of Modern Physics E, Vol. 20, Issue 11 https://doi.org/10.1142/S0218301311020459	journal	November 2011
Aspects of holographic entanglement entropy Ryu, Shinsei; Takayanagi, Tadashi Journal of High Energy Physics, Vol. 2006, Issue 08 https://doi.org/10.1088/1126-6708/2006/08/045	journal	August 2006
Measuring multipartite entanglement through dynamic susceptibilities Hauke, Philipp; Heyl, Markus; Tagliacozzo, Luca Nature Physics, Vol. 12, Issue 8 https://doi.org/10.1038/nphys3700	journal	March 2016
Gaussian pure states in quantum mechanics and the symplectic group Simon, R.; Sudarshan, E. C. G.; Mukunda, N. Physical Review A, Vol. 37, Issue 8 https://doi.org/10.1103/PhysRevA.37.3028	journal	April 1988
Relative entanglement entropies in 1 + 1-dimensional conformal field theories Ruggiero, Paola; Calabrese, Pasquale Journal of High Energy Physics, Vol. 2017, Issue 2 https://doi.org/10.1007/JHEP02(2017)039	journal	February 2017
Thermodynamical string fragmentation Fischer, Nadine; Sjöstrand, Torbjörn Journal of High Energy Physics, Vol. 2017, Issue 1 https://doi.org/10.1007/JHEP01(2017)140	journal	January 2017
Continuous variable quantum information: Gaussian states and beyond Adesso, Gerardo; Ragy, Sammy; Lee, Antony R. arXiv https://doi.org/10.48550/arxiv.1401.4679	text	January 2014
A comparative analysis of statistical hadron production Becattini, F.; Castorina, P.; Milov, A. arXiv https://doi.org/10.48550/arxiv.0911.3026	text	January 2009
Decoherence and Dynamical Entropy Generation in Quantum Field Theory Koksma, Jurjen F.; Prokopec, Tomislav; Schmidt, Michael G. arXiv https://doi.org/10.48550/arxiv.1101.5323	text	January 2011
Field theories on conformally related space-times: Some global considerations Candelas, P.; Dowker, J. S. Physical Review D, Vol. 19, Issue 10 https://doi.org/10.1103/PhysRevD.19.2902	journal	May 1979
Numerical study of entanglement entropy in lattice gauge theory Buividovich, P. V.; Polikarpov, M. I. Nuclear Physics B, Vol. 802, Issue 3 https://doi.org/10.1016/j.nuclphysb.2008.04.024	journal	October 2008
Modular Hamiltonian for Excited States in Conformal Field Theory Lashkari, Nima Physical Review Letters, Vol. 117, Issue 4 https://doi.org/10.1103/PhysRevLett.117.041601	journal	July 2016
A brief introduction to PYTHIA 8.1 Sjöstrand, Torbjörn; Mrenna, Stephen; Skands, Peter Computer Physics Communications, Vol. 178, Issue 11 https://doi.org/10.1016/j.cpc.2008.01.036	journal	June 2008
The role of relative entropy in quantum information theory Vedral, V. Reviews of Modern Physics, Vol. 74, Issue 1 https://doi.org/10.1103/RevModPhys.74.197	journal	March 2002
Geometric and renormalized entropy in conformal field theory Holzhey, Christoph; Larsen, Finn; Wilczek, Frank Nuclear Physics B, Vol. 424, Issue 3 https://doi.org/10.1016/0550-3213(94)90402-2	journal	August 1994
Real-Time Dynamics of String Breaking Hebenstreit, F.; Berges, J.; Gelfand, D. Physical Review Letters, Vol. 111, Issue 20 https://doi.org/10.1103/PhysRevLett.111.201601	journal	November 2013
Analytic results on the geometric entropy for free fields Casini, H.; Huerta, M. arXiv https://doi.org/10.48550/arxiv.0707.1300	text	January 2007
Entanglement entropy in gauge theories and the holographic principle for electric strings Buividovich, P. V.; Polikarpov, M. I. Physics Letters B, Vol. 670, Issue 2 https://doi.org/10.1016/j.physletb.2008.10.032	journal	December 2008
Parton fragmentation and string dynamics Andersson, B.; Gustafson, G.; Ingelman, G. Physics Reports, Vol. 97, Issue 2-3 https://doi.org/10.1016/0370-1573(83)90080-7	journal	July 1983
Real-time dynamics of matrix quantum mechanics beyond the classical approximation Buividovich, Pavel; Hanada, Masanori; Schäfer, Andreas arXiv https://doi.org/10.48550/arxiv.1711.05556	text	January 2017
Entropy, quantum decoherence and pointer states scalar “parton” fields Elze, Hans-Thomas Physics Letters B, Vol. 369, Issue 3-4 https://doi.org/10.1016/0370-2693(95)01538-8	journal	February 1996
Continuous Variable Quantum Information: Gaussian States and Beyond Adesso, Gerardo; Ragy, Sammy; Lee, Antony R. Open Systems & Information Dynamics, Vol. 21, Issue 01n02 https://doi.org/10.1142/S1230161214400010	journal	March 2014
Towards a derivation of holographic entanglement entropy Casini, Horacio; Huerta, Marina; Myers, Robert C. arXiv https://doi.org/10.48550/arxiv.1102.0440	text	January 2011
Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence Ryu, Shinsei; Takayanagi, Tadashi Physical Review Letters, Vol. 96, Issue 18 https://doi.org/10.1103/PhysRevLett.96.181602	journal	May 2006
Entanglement in Quantum Critical Phenomena Vidal, G.; Latorre, J. I.; Rico, E. Physical Review Letters, Vol. 90, Issue 22 https://doi.org/10.1103/PhysRevLett.90.227902	journal	June 2003
Expressing entropy globally in terms of (4D) field-correlations Sorkin, R. D. Journal of Physics: Conference Series, Vol. 484 https://doi.org/10.1088/1742-6596/484/1/012004	journal	March 2014
Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Einstein, A.; Podolsky, B.; Rosen, N. Physical Review, Vol. 47, Issue 10 https://doi.org/10.1103/PhysRev.47.777	journal	May 1935
Entanglement and alpha entropies for a massive scalar field in two dimensions Casini, H.; Huerta, M. Journal of Statistical Mechanics: Theory and Experiment, Vol. 2005, Issue 12 https://doi.org/10.1088/1742-5468/2005/12/P12012	journal	December 2005
Quantum decoherence, entropy and thermalization in strong interactions at high energy. (I). Noisy and dissipative vacuum effects in toy models Elze, Hans-Thomas Nuclear Physics B, Vol. 436, Issue 1-2 https://doi.org/10.1016/0550-3213(94)00523-H	journal	February 1995
Entropy and area Srednicki, Mark Physical Review Letters, Vol. 71, Issue 5 https://doi.org/10.1103/PhysRevLett.71.666	journal	August 1993
Charge shielding and quark confinement in the massive schwinger model Coleman, Sidney; Jackiw, R.; Susskind, Leonard Annals of Physics, Vol. 93, Issue 1-2 https://doi.org/10.1016/0003-4916(75)90212-2	journal	September 1975
Particle production in field theories coupled to strong external sources, II: Generating functions Gelis, François; Venugopalan, Raju Nuclear Physics A, Vol. 779 https://doi.org/10.1016/j.nuclphysa.2006.08.015	journal	November 2006
A comparative analysis of statistical hadron production Becattini, F.; Castorina, P.; Milov, A. The European Physical Journal C, Vol. 66, Issue 3-4 https://doi.org/10.1140/epjc/s10052-010-1265-y	journal	February 2010
Entanglement entropy in ’t Hooft model Goykhman, Mikhail Physical Review D, Vol. 92, Issue 2 https://doi.org/10.1103/PhysRevD.92.025048	journal	July 2015
Notes on black-hole evaporation Unruh, W. G. Physical Review D, Vol. 14, Issue 4 https://doi.org/10.1103/PhysRevD.14.870	journal	August 1976
Evolution of entanglement entropy in one-dimensional systems Calabrese, Pasquale; Cardy, John Journal of Statistical Mechanics: Theory and Experiment, Vol. 2005, Issue 04 https://doi.org/10.1088/1742-5468/2005/04/P04010	journal	April 2005
On geometric entropy Callan, Curtis; Wilczek, Frank Physics Letters B, Vol. 333, Issue 1-2 https://doi.org/10.1016/0370-2693(94)91007-3	journal	July 1994
Analytic results on the geometric entropy for free fields Casini, H.; Huerta, M. Journal of Statistical Mechanics: Theory and Experiment, Vol. 2008, Issue 01 https://doi.org/10.1088/1742-5468/2008/01/P01012	journal	January 2008
Entropy Creation in Relativistic Heavy Ion Collisions Müller, Berndt; Schäfer, Andreas arXiv https://doi.org/10.48550/arxiv.1110.2378	text	January 2011
Particle creation by black holes Hawking, S. W. Communications In Mathematical Physics, Vol. 43, Issue 3 https://doi.org/10.1007/BF02345020	journal	August 1975
Hot origin of the Little Bang Akkelin, S. V. arXiv https://doi.org/10.48550/arxiv.1608.00472	text	January 2016
Spacetime entanglement entropy in 1 + 1 dimensions Saravani, Mehdi; Sorkin, Rafael D.; Yazdi, Yasaman K. Classical and Quantum Gravity, Vol. 31, Issue 21 https://doi.org/10.1088/0264-9381/31/21/214006	journal	October 2014
Relative Entropies in Conformal Field Theory Lashkari, Nima Physical Review Letters, Vol. 113, Issue 5 https://doi.org/10.1103/PhysRevLett.113.051602	journal	July 2014
Capacity of quantum Gaussian channels Holevo, A. S.; Sohma, M.; Hirota, O. Physical Review A, Vol. 59, Issue 3 https://doi.org/10.1103/PhysRevA.59.1820	journal	March 1999
Local temperatures and local terms in modular Hamiltonians Arias, Raúl E.; Blanco, David D.; Casini, Horacio Physical Review D, Vol. 95, Issue 6 https://doi.org/10.1103/PhysRevD.95.065005	journal	March 2017
Entanglement and correlation functions following a local quench: a conformal field theory approach Calabrese, Pasquale; Cardy, John Journal of Statistical Mechanics: Theory and Experiment, Vol. 2007, Issue 10 https://doi.org/10.1088/1742-5468/2007/10/P10004	journal	October 2007
Thermal excitation spectrum from entanglement in an expanding quantum string Berges, Jürgen; Floerchinger, Stefan; Venugopalan, Raju Physics Letters B, Vol. 778 https://doi.org/10.1016/j.physletb.2018.01.068	journal	March 2018
Particle production in field theories coupled to strong external sources. II: Generating functions Gelis, Francois; Venugopalan, Raju arXiv https://doi.org/10.48550/arxiv.hep-ph/0605246	text	January 2006
Quantum tomography for collider physics: illustrations with lepton-pair production Martens, John C.; Ralston, John P.; Takaki, J. D. Tapia The European Physical Journal C, Vol. 78, Issue 1 https://doi.org/10.1140/epjc/s10052-017-5455-8	journal	December 2017
Lpm Effect as the Origin of jet Fragmentation Scaling in Heavy ion Collisions Loshaj, FrashËR; Kharzeev, Dmitri E. International Journal of Modern Physics E, Vol. 21, Issue 10 https://doi.org/10.1142/S0218301312500887	journal	October 2012

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