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We look at two relevant phenomena: first, we analyze the stability of the Dirac vacuum with respect to particle\/antiparticle pair production, both spontaneous and induced by an external electric field; then, we examine the string breaking mechanism. We observe a strong effect of confinement, which acts by suppressing both spontaneous pair production and string breaking into quark\/antiquark pairs, indicating that the system dynamics displays a number of out-of-equilibrium features.<\/jats:p>","DOI":"10.22331\/q-2020-06-15-281","type":"journal-article","created":{"date-parts":[[2020,6,15]],"date-time":"2020-06-15T11:53:56Z","timestamp":1592222036000},"page":"281","source":"Crossref","is-referenced-by-count":119,"title":["Real Time Dynamics and Confinement in the <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mi mathvariant=\"double-struck\">Z<\/mml:mi><\/mml:mrow><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:math> Schwinger-Weyl lattice model for 1+1 QED"],"prefix":"10.22331","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7280-445X","authenticated-orcid":false,"given":"Giuseppe","family":"Magnifico","sequence":"first","affiliation":[{"name":"Dipartimento di Fisica e Astronomia dell'Universit\u00e0 di Bologna, I-40127 Bologna, Italy"},{"name":"INFN, Sezione di Bologna, I-40127 Bologna, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5338-4181","authenticated-orcid":false,"given":"Marcello","family":"Dalmonte","sequence":"additional","affiliation":[{"name":"Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy"},{"name":"SISSA, Via Bonomea 265, I-34136 Trieste, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9152-6515","authenticated-orcid":false,"given":"Paolo","family":"Facchi","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica and MECENAS, Universit\u00e0 di Bari, I-70126 Bari, Italy"},{"name":"INFN, Sezione di Bari, I-70126 Bari, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7214-5685","authenticated-orcid":false,"given":"Saverio","family":"Pascazio","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica and MECENAS, Universit\u00e0 di Bari, I-70126 Bari, Italy"},{"name":"INFN, Sezione di Bari, I-70126 Bari, Italy"},{"name":"Istituto Nazionale di Ottica (INO-CNR), I-50125 Firenze, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7407-063X","authenticated-orcid":false,"given":"Francesco V.","family":"Pepe","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica and MECENAS, Universit\u00e0 di Bari, I-70126 Bari, Italy"},{"name":"INFN, Sezione di Bari, I-70126 Bari, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6801-5976","authenticated-orcid":false,"given":"Elisa","family":"Ercolessi","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica e Astronomia dell'Universit\u00e0 di Bologna, I-40127 Bologna, Italy"},{"name":"INFN, Sezione di Bologna, I-40127 Bologna, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2020,6,15]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"H. Kleinert, Gauge Fields in Condensed Matter (World Scientific, Singapore 1989). DOI: 10.1142\/0356.","DOI":"10.1142\/0356"},{"key":"1","doi-asserted-by":"publisher","unstructured":"E. Fradkin, Field Theories of Condensed Matter Physics (Cambridge University Press, Cambridge 2013). DOI: 10.1017\/CBO9781139015509.","DOI":"10.1017\/CBO9781139015509"},{"key":"2","doi-asserted-by":"publisher","unstructured":"M. Creutz, L. Jacobs, C. Rebbi, Monte Carlo computations in lattice gauge theories, Phys. Rep. 95, 203 (1983). DOI: 10.1016\/0370-1573(83)90016-9.","DOI":"10.1016\/0370-1573(83)90016-9"},{"key":"3","doi-asserted-by":"publisher","unstructured":"H. J. Rothe, Lattice gauge theories (World Scientific, Singapore, 1992). DOI: 10.1142\/1268.","DOI":"10.1142\/1268"},{"key":"4","doi-asserted-by":"publisher","unstructured":"I. Montvay and G. M\u00fcnster, Quantum Fields on a Lattice (Cambridge University Press, Cambridge, 1994). DOI: 10.1017\/CBO9780511470783.","DOI":"10.1017\/CBO9780511470783"},{"key":"5","doi-asserted-by":"publisher","unstructured":"K. G. Wilson, Confinement of quarks, Phys. Rev. D 10, 2445 (1974). DOI: 10.1103\/PhysRevD.10.2445.","DOI":"10.1103\/PhysRevD.10.2445"},{"key":"6","doi-asserted-by":"publisher","unstructured":"J. B. Kogut and L. Susskind, Hamiltonian formulation of Wilson's lattice gauge theories, Phys. Rev. D 11, 395 (1975). DOI: 10.1103\/PhysRevD.11.395.","DOI":"10.1103\/PhysRevD.11.395"},{"key":"7","doi-asserted-by":"publisher","unstructured":"L. Susskind, Lattice fermions, Phys. Rev. D 16, 3031 (1977). DOI: 10.1103\/PhysRevD.16.3031.","DOI":"10.1103\/PhysRevD.16.3031"},{"key":"8","doi-asserted-by":"publisher","unstructured":"J. B. Kogut, An introduction to lattice gauge theory and spin systems, Rev. Mod. Phys. 51, 659 (1979). DOI: 10.1103\/RevModPhys.51.659.","DOI":"10.1103\/RevModPhys.51.659"},{"key":"9","doi-asserted-by":"publisher","unstructured":"U. Schollw\u00f6ck, The density-matrix renormalization group, Rev. Mod. Phys. 77, 259 (2005). DOI: 10.1103\/RevModPhys.77.259.","DOI":"10.1103\/RevModPhys.77.259"},{"key":"10","doi-asserted-by":"publisher","unstructured":"R. Orus, A practical introduction to tensor networks: Matrix product states and projected entangled pair states, Ann. Phys. (N.Y.) 349, 117 (2014). DOI: 10.1016\/j.aop.2014.06.013.","DOI":"10.1016\/j.aop.2014.06.013"},{"key":"11","doi-asserted-by":"publisher","unstructured":"R. P. Feynman, Simulating Physics with Computers, Int. J. Theor. Phys. 21, 467 (1982). DOI: 10.1007\/BF02650179.","DOI":"10.1007\/BF02650179"},{"key":"12","doi-asserted-by":"publisher","unstructured":"I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008). DOI: 10.1103\/RevModPhys.80.885.","DOI":"10.1103\/RevModPhys.80.885"},{"key":"13","doi-asserted-by":"publisher","unstructured":"M. Lewenstein, A. Sanpera and V. Ahufinger, Ultracold Atoms in Optical Lattices: Simulating Quantum Many-Body Systems (Oxford University Press, New York, 2012). DOI: 10.1093\/acprof:oso\/9780199573127.001.0001.","DOI":"10.1093\/acprof:oso\/9780199573127.001.0001"},{"key":"14","doi-asserted-by":"publisher","unstructured":"J. I. Cirac and P. Zoller, Goals and opportunities in quantum simulation, Nat. Phys. 8, 264 (2012). DOI: 10.1038\/nphys2275.","DOI":"10.1038\/nphys2275"},{"key":"15","doi-asserted-by":"publisher","unstructured":"I. Bloch, J. Dalibard, and S. Nascimb\u00e8ne, Quantum simulations with ultracold quantum gases, Nat. Phys. 8, 267 (2012). DOI: 10.1038\/nphys2259.","DOI":"10.1038\/nphys2259"},{"key":"16","doi-asserted-by":"publisher","unstructured":"R. Blatt and C. F. Roos, Quantum simulations with trapped ions, Nat. Phys. 8, 277 (2012). DOI: 10.1038\/nphys2252.","DOI":"10.1038\/nphys2252"},{"key":"17","doi-asserted-by":"publisher","unstructured":"E. Kapit and E. Mueller, Optical-lattice Hamiltonians for relativistic quantum electrodynamics, Phys. Rev. A 83, 033625 (2011). DOI: 10.1103\/PhysRevA.83.033625.","DOI":"10.1103\/PhysRevA.83.033625"},{"key":"18","doi-asserted-by":"publisher","unstructured":"E. Zohar, J. I. Cirac, and B. Reznik, Simulating Compact Quantum Electrodynamics with Ultracold Atoms: Probing Confinement and Nonperturbative Effects, Phys. Rev. Lett. 109, 125302 (2012). DOI: 10.1103\/PhysRevLett.109.125302.","DOI":"10.1103\/PhysRevLett.109.125302"},{"key":"19","doi-asserted-by":"publisher","unstructured":"L. Tagliacozzo, A. Celi, P. Orland, and M. Lewenstein, Simulation of non-Abelian gauge theories with optical lattices, Nat. Commun. 4, 2615 (2013). DOI: 10.1038\/ncomms3615.","DOI":"10.1038\/ncomms3615"},{"key":"20","doi-asserted-by":"publisher","unstructured":"K. Kasamatsu, I. Ichinose, and T. Matsui, Atomic Quantum Simulation of the Lattice Gauge-Higgs Model: Higgs Couplings and Emergence of Exact Local Gauge Symmetry, Phys. 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DOI: 10.1103\/PhysRevA.88.023617.","DOI":"10.1103\/PhysRevA.88.023617"},{"key":"24","doi-asserted-by":"publisher","unstructured":"K. Stannigel, P. Hauke, D. Marcos, M. Hafezi, S. Diehl, M. Dalmonte, and P. Zoller, Constrained Dynamics via the Zeno Effect in Quantum Simulation: Implementing Non-Abelian Lattice Gauge Theories with Cold Atoms, Phys. Rev. Lett. 112, 120406 (2014). DOI: 10.1103\/PhysRevLett.112.120406.","DOI":"10.1103\/PhysRevLett.112.120406"},{"key":"25","doi-asserted-by":"publisher","unstructured":"E. Zohar, J. I. Cirac, and B. Reznik, Quantum simulations of lattice gauge theories using ultracold atoms in optical lattices., Rep. Prog. Phys. 79, 014401 (2016). DOI: 10.1088\/0034-4885\/79\/1\/014401.","DOI":"10.1088\/0034-4885\/79\/1\/014401"},{"key":"26","doi-asserted-by":"publisher","unstructured":"E. A. Martinez, C. A. Muschik, P. Schindler, D. Nigg, A. Erhard, M. Heyl, P. Hauke, M. Dalmonte, T. Monz, P. Zoller, and R. 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F\u00f6lling, Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions, Nat. Phys. 10, 779 (2014). DOI: 10.1038\/nphys3061.","DOI":"10.1038\/nphys3061"},{"key":"30","doi-asserted-by":"publisher","unstructured":"M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, L. Fallani, Observation of chiral edge states with neutral fermions in synthetic Hall ribbons., Science 349, 1510 (2015). DOI: 10.1126\/science.aaa8736.","DOI":"10.1126\/science.aaa8736"},{"key":"31","doi-asserted-by":"publisher","unstructured":"L. F. Livi, G. Cappellini, M. Diem, L. Franchi, C. Clivati, M. Frittelli, F. Levi, D. Calonico, J. Catani, M. Inguscio, L. Fallani, Synthetic Dimensions and Spin-Orbit Coupling with an Optical Clock Transition, Phys. Rev. Lett. 117, 220401 (2016). DOI: 10.1103\/PhysRevLett.117.220401.","DOI":"10.1103\/PhysRevLett.117.220401"},{"key":"32","doi-asserted-by":"publisher","unstructured":"J. Schwinger, On Gauge Invariance and Vacuum Polarization, Phys. Rev. 82, 664 (1951). DOI: 10.1103\/PhysRev.82.664.","DOI":"10.1103\/PhysRev.82.664"},{"key":"33","doi-asserted-by":"publisher","unstructured":"F. A. Wilczek, Nobel Lecture: Asymptotic freedom: From paradox to paradigm, Rev. Mod. Phys. 77, 857 (2005). DOI: 10.1103\/RevModPhys.77.857.","DOI":"10.1103\/RevModPhys.77.857"},{"key":"34","doi-asserted-by":"publisher","unstructured":"R. Nandkishore and D. A. Huse, Many-Body Localization and Thermalization in Quantum Statistical Mechanics, Annu. Rev. Condens. Matter Phys. 6, 15 (2015). DOI: 10.1146\/annurev-conmatphys-031214-014726.","DOI":"10.1146\/annurev-conmatphys-031214-014726"},{"key":"35","doi-asserted-by":"publisher","unstructured":"F. Alet and N. Laflorencie, Many-body localization: An introduction and selected topics, C. R. Phys. 19, 498 (2018). DOI: 10.1016\/j.crhy.2018.03.003.","DOI":"10.1016\/j.crhy.2018.03.003"},{"key":"36","doi-asserted-by":"publisher","unstructured":"C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papi\u0107, Weak ergodicity breaking from quantum many-body scars, Nat. Phys. 14, 745 (2018) DOI: 10.1038\/s41567-018-0137-5; Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations, Phys. Rev. B 98, 155134 (2018). DOI: 10.1103\/PhysRevB.98.155134.","DOI":"10.1103\/PhysRevB.98.155134"},{"key":"37","doi-asserted-by":"publisher","unstructured":"V. Khemani, C. R. Laumann, and A. Chandran, Signatures of integrability in the dynamics of Rydberg-blockaded chains, Phys. Rev. B 99, 161101 (2019). DOI: 10.1103\/PhysRevB.99.161101.","DOI":"10.1103\/PhysRevB.99.161101"},{"key":"38","doi-asserted-by":"publisher","unstructured":"P. Hauke, D. Marcos, M. Dalmonte, and P. Zoller, Quantum Simulation of a Lattice Schwinger Model in a Chain of Trapped Ions, Phys. Rev. X 3, 041018 (2013). DOI: 10.1103\/PhysRevX.3.041018.","DOI":"10.1103\/PhysRevX.3.041018"},{"key":"39","doi-asserted-by":"publisher","unstructured":"S. K\u00fchn, J. I. Cirac, and M.C. Ba\u00f1uls, Quantum simulation of the Schwinger model: A study of feasibility, Phys. Rev. A 90, 042305 (2014). DOI: 10.1103\/PhysRevA.90.042305.","DOI":"10.1103\/PhysRevA.90.042305"},{"key":"40","doi-asserted-by":"publisher","unstructured":"S. Notarnicola, E. Ercolessi, P. Facchi, G. Marmo, S. Pascazio and F. V. Pepe, Discrete Abelian gauge theories for quantum simulations of QED, J. Phys. A: Math. Theor. 48, 30FT01 (2015). DOI: 10.1088\/1751-8113\/48\/30\/30FT01.","DOI":"10.1088\/1751-8113\/48\/30\/30FT01"},{"key":"41","doi-asserted-by":"publisher","unstructured":"V. Kasper, F. Hebenstreit, F. Jendrzejewski, M K Oberthaler, and J. Berges, Implementing quantum electrodynamics with ultracold atomic systems, New J. Phys. 19, 023030 (2017). DOI: 10.1088\/1367-2630\/aa54e0.","DOI":"10.1088\/1367-2630\/aa54e0"},{"key":"42","doi-asserted-by":"publisher","unstructured":"S. Notarnicola, M. Collura, and S. Montangero, Real time dynamics quantum simulation of (1+1)-D lattice QED with Rydberg atoms, Phys. Rev. Research 2, 013288 (2020). DOI: 10.1103\/PhysRevResearch.2.013288.","DOI":"10.1103\/PhysRevResearch.2.013288"},{"key":"43","doi-asserted-by":"publisher","unstructured":"F. M. Surace, P. P. Mazza, G. Giudici, A. Lerose, A. Gambassi, and Marcello Dalmonte, Lattice gauge theories and string dynamics in Rydberg atom quantum simulators, Phys. Rev. X 10, 021041 (2020). DOI: 10.1103\/PhysRevX.10.021041.","DOI":"10.1103\/PhysRevX.10.021041"},{"key":"44","doi-asserted-by":"publisher","unstructured":"D. Banerjee, M. Dalmonte, M. M\u00fcller, E. Rico, P. Stebler, U. J. Wiese, and P. Zoller, Atomic Quantum Simulation of Dynamical Gauge Fields Coupled to Fermionic Matter: From String Breaking to Evolution after a Quench, Phys. Rev. Lett. 109, 175302 (2012). DOI: 10.1103\/PhysRevLett.109.175302.","DOI":"10.1103\/PhysRevLett.109.175302"},{"key":"45","doi-asserted-by":"publisher","unstructured":"E. Rico, T. Pichler, M. Dalmonte, P. Zoller, and S. Montangero, Tensor Networks for Lattice Gauge Theories and Atomic Quantum Simulation, Phys. Rev. Lett. 112, 201601 (2014). DOI: 10.1103\/PhysRevLett.112.201601.","DOI":"10.1103\/PhysRevLett.112.201601"},{"key":"46","doi-asserted-by":"publisher","unstructured":"D. Horn, Finite Matrix Models With Continuous Local Gauge Invariance, Phys. Lett. 100B, 149 (1981). DOI: 10.1016\/0370-2693(81)90763-2.","DOI":"10.1016\/0370-2693(81)90763-2"},{"key":"47","doi-asserted-by":"publisher","unstructured":"P. Orland and D. Rohrlich, Lattice gauge magnets: Local isospin from spin, Nucl. Phys. B 338, 647 (1990). DOI: 10.1016\/0550-3213(90)90646-U.","DOI":"10.1016\/0550-3213(90)90646-U"},{"key":"48","doi-asserted-by":"publisher","unstructured":"S. Chandrasekharan and U. J. Wiese, Quantum Link Models: A Discrete Approach to Gauge Theories, Nucl. Phys. B 492, 455 (1997). DOI: 10.1016\/S0550-3213(97)80041-7.","DOI":"10.1016\/S0550-3213(97)80041-7"},{"key":"49","doi-asserted-by":"publisher","unstructured":"U. J. Wiese, Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories, Ann. Phys. (Berl.) 525, 777 (2013). DOI: 10.1002\/andp.201300104.","DOI":"10.1002\/andp.201300104"},{"key":"50","doi-asserted-by":"publisher","unstructured":"B. Buyens, S. Montangero, J. Haegeman, F. Verstraete and K. Van Acoleyen, Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks, Phys. Rev. D 95, 094509 (2017). DOI: 10.1103\/PhysRevD.95.094509.","DOI":"10.1103\/PhysRevD.95.094509"},{"key":"51","doi-asserted-by":"publisher","unstructured":"M.C. Ba\u00f1uls, K. Cichy, K. Jansen, J.I. Cirac, The mass spectrum of the Schwinger model with matrix product states, J. High Energy Phys. 11, 158 (2013). DOI: 10.1007\/JHEP11(2013)158.","DOI":"10.1007\/JHEP11(2013)158"},{"key":"52","doi-asserted-by":"publisher","unstructured":"T. Pichler, M. Dalmonte, E. Rico, P. Zoller, and S. Montangero, Real-Time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks, Phys. Rev. X 6, 011023 (2016). DOI: 10.1103\/PhysRevX.6.011023.","DOI":"10.1103\/PhysRevX.6.011023"},{"key":"53","doi-asserted-by":"publisher","unstructured":"B. Buyens, J. Haegeman, F. Hebenstreit, F. Verstraete and K. Van Acoleyen, Real-time simulation of the Schwinger effect with matrix product states, Phys. Rev. D 96, 114501 (2017). DOI: 10.1103\/PhysRevD.96.114501.","DOI":"10.1103\/PhysRevD.96.114501"},{"key":"54","doi-asserted-by":"publisher","unstructured":"B. Buyens, J. Haegeman, H. Verschelde, F. Verstraete, K. Van Acoleyen, Confinement and String Breaking for $QED_2$ in the Hamiltonian Picture, Phys. Rev. X 6, 041040 (2016). DOI: 10.1103\/PhysRevX.6.041040.","DOI":"10.1103\/PhysRevX.6.041040"},{"key":"55","doi-asserted-by":"publisher","unstructured":"Y. Kuno, S. Sakane, K. Kasamatsu, I. Ichinose, and Tetsuo Matsui, Quantum simulation of (1+1)-dimensional U(1) gauge-Higgs model on a lattice by cold Bose gases, Phys. Rev. D 95, 094507 (2017). DOI: 10.1103\/PhysRevD.95.094507.","DOI":"10.1103\/PhysRevD.95.094507"},{"key":"56","doi-asserted-by":"publisher","unstructured":"J. Park, Y. Kuno, and I. Ichinose, Glassy dynamics from quark confinement: Atomic quantum simulation of the gauge-Higgs model on a lattice, Phys. Rev. A 100, 013629 (2019). DOI: 10.1103\/PhysRevA.100.013629.","DOI":"10.1103\/PhysRevA.100.013629"},{"key":"57","doi-asserted-by":"publisher","unstructured":"E. Ercolessi, P. Facchi, G. Magnifico, S. Pascazio, and F. V. Pepe, Phase transitions in $Z_n$ gauge models: Towards quantum simulations of the Schwinger-Weyl QED, Phys. Rev. D 98, 074503 (2018). DOI: 10.1103\/PhysRevD.98.074503.","DOI":"10.1103\/PhysRevD.98.074503"},{"key":"58","doi-asserted-by":"publisher","unstructured":"J. Schwinger, Gauge Invariance and Mass. II, Phys. Rev. 128, 2425 (1962). DOI: 10.1103\/PhysRev.128.2425.","DOI":"10.1103\/PhysRev.128.2425"},{"key":"59","doi-asserted-by":"publisher","unstructured":"G. Magnifico, D. Vodola, E. Ercolessi, S. P. Kumar, M. M\u00fcller, and A. Bermudez, Symmetry-protected topological phases in lattice gauge theories: Topological $QED_2$, Phys. Rev. D 99, 014503 (2019). DOI: 10.1103\/PhysRevD.99.014503.","DOI":"10.1103\/PhysRevD.99.014503"},{"key":"60","doi-asserted-by":"publisher","unstructured":"G. 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Doyon, Entanglement Entropy in Extended Quantum Systems Special Issue, Journal of Physics A 42 (2009). DOI: 10.1088\/1751-8121\/42\/50\/500301.","DOI":"10.1088\/1751-8121\/42\/50\/500301"},{"key":"68","unstructured":"S. Rachel, M. Haque, A. Bernevug, A. Laeuchli and E. Fradkin (Guest Editors), Quantum Entanglement in Condensed Matter Physics, Special Issue, J. Stat. Mech. (2015). Link: https:\/\/iopscience.iop.org\/journal\/1742-5468\/page\/extra.special4."},{"key":"69","doi-asserted-by":"publisher","unstructured":"P. Calabrese and J. L. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech. 2005, P04010 (2005). DOI: 10.1088\/1742-5468\/2005\/04\/P04010.","DOI":"10.1088\/1742-5468\/2005\/04\/P04010"},{"key":"70","doi-asserted-by":"publisher","unstructured":"E. H. Lieb and D. W. Robinson, The finite group velocity of quantum spin systems, Commun. Math. Phys. 28, 251 (1972). DOI: 10.1007\/BF01645779.","DOI":"10.1007\/BF01645779"},{"key":"71","doi-asserted-by":"publisher","unstructured":"A. Laeuchli and C. Kollath, Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model, J. Stat. Mech. 2008, P05018 (2008). DOI: 10.1088\/1742-5468\/2008\/05\/P05018.","DOI":"10.1088\/1742-5468\/2008\/05\/P05018"},{"key":"72","doi-asserted-by":"publisher","unstructured":"S. R. Manmana, S. Wessel, R. M. Noack, and A. Muramatsu, Time evolution of correlations in strongly interacting fermions after a quantum quench, Phys. Rev. B 79, 155104 (2009). DOI: 10.1103\/PhysRevB.79.155104.","DOI":"10.1103\/PhysRevB.79.155104"},{"key":"73","doi-asserted-by":"publisher","unstructured":"H. Kim and D. A. Huse, Ballistic Spreading of Entanglement in a Diffusive Nonintegrable System, Phys. Rev. Lett. 111, 127205 (2013). DOI: 10.1103\/PhysRevLett.111.127205.","DOI":"10.1103\/PhysRevLett.111.127205"},{"key":"74","doi-asserted-by":"publisher","unstructured":"P. Barmettler, D. Poletti, M. Cheneau, and C. Kollath, Propagation front of correlations in an interacting Bose gas, Phys. Rev. A 85, 053625 (2012). DOI: 10.1103\/PhysRevA.85.053625.","DOI":"10.1103\/PhysRevA.85.053625"},{"key":"75","doi-asserted-by":"publisher","unstructured":"G. Carleo, F. Becca, L. Sanchez-Palencia, S. Sorella, and M. Fabrizio, Light-cone effect and supersonic correlations in one- and two-dimensional bosonic superfluids, Phys. Rev. A 89, 031602 (2014). DOI: 10.1103\/PhysRevA.89.031602.","DOI":"10.1103\/PhysRevA.89.031602"},{"key":"76","doi-asserted-by":"publisher","unstructured":"L. Bonnes, F. H. L. Essler, and A. M. Lauchli, ``Light-Cone'' Dynamics After Quantum Quenches in Spin Chains, Phys. Rev. Lett. 113, 187203 (2014). DOI: 10.1103\/PhysRevLett.113.187203.","DOI":"10.1103\/PhysRevLett.113.187203"},{"key":"77","doi-asserted-by":"publisher","unstructured":"R. Geiger, T. Langen, I. E. Mazets, and J. Schmiedmayer, Local relaxation and light-cone-like propagation of correlations in a trapped one-dimensional Bose gas, New J. Phys. 16, 053034 (2014). DOI: 10.1088\/1367-2630\/16\/5\/053034.","DOI":"10.1088\/1367-2630\/16\/5\/053034"},{"key":"78","unstructured":"Compare for example our Fig. 8(a) with Fig. 6 of Ref. [62]."},{"key":"79","doi-asserted-by":"publisher","unstructured":"H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuleti\u0107, M. D. Lukin, Probing many-body dynamics on a 51-atom quantum simulator, Nature 551, 579 (2017). DOI: 10.1038\/nature24622.","DOI":"10.1038\/nature24622"},{"key":"80","doi-asserted-by":"publisher","unstructured":"P. Calabrese and J. Cardy, Time Dependence of Correlation Functions Following a Quantum Quench, Phys. Rev. Lett. 96, 136801 (2006) DOI: 10.1103\/PhysRevLett.96.136801; Quantum quenches in extended systems, J. Stat. Mech. 2007 P06008 (2007). DOI: 10.1088\/1742-5468\/2007\/06\/P06008.","DOI":"10.1103\/PhysRevLett.96.136801"},{"key":"81","doi-asserted-by":"publisher","unstructured":"F. Hebenstreit, R. Alkofer, and H. Gies, Schwinger pair production in space- and time-dependent electric fields: Relating the Wigner formalism to quantum kinetic theory, Phys. Rev. D 82, 105026 (2010). DOI: 10.1103\/PhysRevD.82.105026.","DOI":"10.1103\/PhysRevD.82.105026"},{"key":"82","doi-asserted-by":"publisher","unstructured":"F. Hebenstreit, J. Berges, and D. Gelfand, Simulating fermion production in 1+1 dimensional QED, Phys. Rev. D 87, 105006 (2013). DOI: 10.1103\/PhysRevD.87.105006.","DOI":"10.1103\/PhysRevD.87.105006"},{"key":"83","doi-asserted-by":"publisher","unstructured":"F. Liu, R. Lundgren, P. Titum, G. Pagano, J. 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