1Dipartimento di Fisica e Astronomia dell’Università di Bologna, I-40127 Bologna, Italy
2INFN, Sezione di Bologna, I-40127 Bologna, Italy
3Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
4SISSA, Via Bonomea 265, I-34136 Trieste, Italy
5Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari, Italy
6INFN, Sezione di Bari, I-70126 Bari, Italy
7Istituto Nazionale di Ottica (INO-CNR), I-50125 Firenze, Italy
Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.
Abstract
We study the out-of-equilibrium properties of $1+1$ dimensional quantum electrodynamics (QED), discretized via the staggered-fermion Schwinger model with an Abelian $mathbb{Z}_{n}$ gauge group. 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.
Featured image: Particle production after a quantum quench in Z5 lattice gauge theories as a function of time (x-axis) and mass (y-axis).
Popular summary
In recent years, several approaches leveraging on quantum information have enabled controlled simulations of such theories in real-time. These novel tools, based on a class of wave-functions known as tensor networks, offer unique opportunities to understand the spreading of quantum correlations, and in particular entanglement, in gauge theories.
We study here the Schwinger-Weyl lattice model, in which both space and the gauge degree of freedom are discretized, in such a way that standard quantum electrodynamics in 1+1 dimensions is reproduced in the continuum limit.
We analyze the stability of the Dirac vacuum, the mechanism of pair (particle/antiparticle) production, as well as the intriguing string breaking mechanism. Strings behave very differently, depending on the particle mass and charge (coupling), and their dynamics leaves characteristics footprints in the entanglement evolution. A number of out-of-equilibrium features are unhearted and scrutinized.
► BibTeX data
► References
[1] H. Kleinert, Gauge Fields in Condensed Matter (World Scientific, Singapore 1989). DOI: 10.1142/0356.
https://doi.org/10.1142/0356
[2] E. Fradkin, Field Theories of Condensed Matter Physics (Cambridge University Press, Cambridge 2013). DOI: 10.1017/CBO9781139015509.
https://doi.org/10.1017/CBO9781139015509
[3] 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.
https://doi.org/10.1016/0370-1573(83)90016-9
[4] H. J. Rothe, Lattice gauge theories (World Scientific, Singapore, 1992). DOI: 10.1142/1268.
https://doi.org/10.1142/1268
[5] I. Montvay and G. Münster, Quantum Fields on a Lattice (Cambridge University Press, Cambridge, 1994). DOI: 10.1017/CBO9780511470783.
https://doi.org/10.1017/CBO9780511470783
[6] K. G. Wilson, Confinement of quarks, Phys. Rev. D 10, 2445 (1974). DOI: 10.1103/PhysRevD.10.2445.
https://doi.org/10.1103/PhysRevD.10.2445
[7] 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.
https://doi.org/10.1103/PhysRevD.11.395
[8] L. Susskind, Lattice fermions, Phys. Rev. D 16, 3031 (1977). DOI: 10.1103/PhysRevD.16.3031.
https://doi.org/10.1103/PhysRevD.16.3031
[9] J. B. Kogut, An introduction to lattice gauge theory and spin systems, Rev. Mod. Phys. 51, 659 (1979). DOI: 10.1103/RevModPhys.51.659.
https://doi.org/10.1103/RevModPhys.51.659
[10] U. Schollwöck, The density-matrix renormalization group, Rev. Mod. Phys. 77, 259 (2005). DOI: 10.1103/RevModPhys.77.259.
https://doi.org/10.1103/RevModPhys.77.259
[11] 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.
https://doi.org/10.1016/j.aop.2014.06.013
[12] R. P. Feynman, Simulating Physics with Computers, Int. J. Theor. Phys. 21, 467 (1982). DOI: 10.1007/BF02650179.
https://doi.org/10.1007/BF02650179
[13] 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.
https://doi.org/10.1103/RevModPhys.80.885
[14] 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.
https://doi.org/10.1093/acprof:oso/9780199573127.001.0001
[15] J. I. Cirac and P. Zoller, Goals and opportunities in quantum simulation, Nat. Phys. 8, 264 (2012). DOI: 10.1038/nphys2275.
https://doi.org/10.1038/nphys2275
[16] I. Bloch, J. Dalibard, and S. Nascimbène, Quantum simulations with ultracold quantum gases, Nat. Phys. 8, 267 (2012). DOI: 10.1038/nphys2259.
https://doi.org/10.1038/nphys2259
[17] R. Blatt and C. F. Roos, Quantum simulations with trapped ions, Nat. Phys. 8, 277 (2012). DOI: 10.1038/nphys2252.
https://doi.org/10.1038/nphys2252
[18] E. Kapit and E. Mueller, Optical-lattice Hamiltonians for relativistic quantum electrodynamics, Phys. Rev. A 83, 033625 (2011). DOI: 10.1103/PhysRevA.83.033625.
https://doi.org/10.1103/PhysRevA.83.033625
[19] 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.
https://doi.org/10.1103/PhysRevLett.109.125302
[20] 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.
https://doi.org/10.1038/ncomms3615
[21] 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. Rev. Lett. 111, 115303 (2013). DOI: 10.1103/PhysRevLett.111.115303.
https://doi.org/10.1103/PhysRevLett.111.115303
[22] D. Banerjee, M. Bögli, M. Dalmonte, E. Rico, P. Stebler, U. J. Wiese, and P. Zoller, Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories, Phys. Rev. Lett. 110, 125303 (2013). DOI: 10.1103/PhysRevLett.110.125303.
https://doi.org/10.1103/PhysRevLett.110.125303
[23] L. Tagliacozzo, A. Celi, A. Zamora, and M. Lewenstein, Optical Abelian lattice gauge theories, Ann. Phys. (N.Y.) 330, 160 (2013). DOI: 10.1016/j.aop.2012.11.009.
https://doi.org/10.1016/j.aop.2012.11.009
[24] E. Zohar, J. I. Cirac, and B. Reznik, Quantum simulations of gauge theories with ultracold atoms: Local gauge invariance from angular-momentum conservation, Phys. Rev. A 88, 023617 (2013). DOI: 10.1103/PhysRevA.88.023617.
https://doi.org/10.1103/PhysRevA.88.023617
[25] 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.
https://doi.org/10.1103/PhysRevLett.112.120406
[26] 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.
https://doi.org/10.1088/0034-4885/79/1/014401
[27] E. A. Martinez, C. A. Muschik, P. Schindler, D. Nigg, A. Erhard, M. Heyl, P. Hauke, M. Dalmonte, T. Monz, P. Zoller, and R. Blatt, Real-time dynamics of lattice gauge theories with a few-qubit quantum computer, Nature 534, 516-519 (2016). DOI: 10.1038/nature18318.
https://doi.org/10.1038/nature18318
[28] A. Celi, P. Massignan, J. Ruseckas, N. Goldman, I. B. Spielman, G. Juzeliūnas, and M. Lewenstein, Synthetic Gauge Fields in Synthetic Dimensions, Phys. Rev. Lett. 112, 043001 (2014). DOI: 10.1103/PhysRevLett.112.043001.
https://doi.org/10.1103/PhysRevLett.112.043001
[29] G. Pagano, M. Mancini, G. Cappellini, P. Lombardi, F. Schäfer, H. Hu, X.-J. Liu, J. Catani, C. Sias, M. Inguscio, and L. Fallani, A one-dimensional liquid of fermions with tunable spin, Nat. Phys. 10, 198 (2014). DOI: 10.1038/nphys2878.
https://doi.org/10.1038/nphys2878
[30] F. Scazza, C. Hofrichter, M. Höfer, P. C. De Groot, I. Bloch, and S. Fölling, Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions, Nat. Phys. 10, 779 (2014). DOI: 10.1038/nphys3061.
https://doi.org/10.1038/nphys3061
[31] 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.
https://doi.org/10.1126/science.aaa8736
[32] 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.
https://doi.org/10.1103/PhysRevLett.117.220401
[33] J. Schwinger, On Gauge Invariance and Vacuum Polarization, Phys. Rev. 82, 664 (1951). DOI: 10.1103/PhysRev.82.664.
https://doi.org/10.1103/PhysRev.82.664
[34] F. A. Wilczek, Nobel Lecture: Asymptotic freedom: From paradox to paradigm, Rev. Mod. Phys. 77, 857 (2005). DOI: 10.1103/RevModPhys.77.857.
https://doi.org/10.1103/RevModPhys.77.857
[35] 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.
https://doi.org/10.1146/annurev-conmatphys-031214-014726
[36] 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.
https://doi.org/10.1016/j.crhy.2018.03.003
[37] C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papić, 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.
https://doi.org/10.1103/PhysRevB.98.155134
[38] 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.
https://doi.org/10.1103/PhysRevB.99.161101
[39] 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.
https://doi.org/10.1103/PhysRevX.3.041018
[40] S. Kühn, J. I. Cirac, and M.C. Bañuls, Quantum simulation of the Schwinger model: A study of feasibility, Phys. Rev. A 90, 042305 (2014). DOI: 10.1103/PhysRevA.90.042305.
https://doi.org/10.1103/PhysRevA.90.042305
[41] 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.
https://doi.org/10.1088/1751-8113/48/30/30FT01
[42] 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.
https://doi.org/10.1088/1367-2630/aa54e0
[43] 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.
https://doi.org/10.1103/PhysRevResearch.2.013288
[44] 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.
https://doi.org/10.1103/PhysRevX.10.021041
[45] D. Banerjee, M. Dalmonte, M. Müller, 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.
https://doi.org/10.1103/PhysRevLett.109.175302
[46] 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.
https://doi.org/10.1103/PhysRevLett.112.201601
[47] D. Horn, Finite Matrix Models With Continuous Local Gauge Invariance, Phys. Lett. 100B, 149 (1981). DOI: 10.1016/0370-2693(81)90763-2.
https://doi.org/10.1016/0370-2693(81)90763-2
[48] 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.
https://doi.org/10.1016/0550-3213(90)90646-U
[49] 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.
https://doi.org/10.1016/S0550-3213(97)80041-7
[50] 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.
https://doi.org/10.1002/andp.201300104
[51] 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.
https://doi.org/10.1103/PhysRevD.95.094509
[52] M.C. Bañuls, 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.
https://doi.org/10.1007/JHEP11(2013)158
[53] 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.
https://doi.org/10.1103/PhysRevX.6.011023
[54] 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.
https://doi.org/10.1103/PhysRevD.96.114501
[55] 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.
https://doi.org/10.1103/PhysRevX.6.041040
[56] 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.
https://doi.org/10.1103/PhysRevD.95.094507
[57] 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.
https://doi.org/10.1103/PhysRevA.100.013629
[58] 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.
https://doi.org/10.1103/PhysRevD.98.074503
[59] J. Schwinger, Gauge Invariance and Mass. II, Phys. Rev. 128, 2425 (1962). DOI: 10.1103/PhysRev.128.2425.
https://doi.org/10.1103/PhysRev.128.2425
[60] G. Magnifico, D. Vodola, E. Ercolessi, S. P. Kumar, M. Müller, 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.
https://doi.org/10.1103/PhysRevD.99.014503
[61] G. Magnifico, D. Vodola, E. Ercolessi, S. P. Kumar, M. Müller, and A. Bermudez, $mathbb{Z}_N$ gauge theories coupled to topological fermions: $QED_2$ with a quantum-mechanical $theta$ angle, Phys. Rev. B 100, 115152 (2019). DOI: 10.1103/PhysRevB.100.115152.
https://doi.org/10.1103/PhysRevB.100.115152
[62] M. Kormos, M. Collura, G. Takacs, and P. Calabrese, Real time confinement following a quantum quench to a non-integrable model, Nat. Phys. 13 246, (2017). DOI: 10.1038/nphys3934.
https://doi.org/10.1038/nphys3934
[63] H. Weyl, The Theory of Groups and Quantum Mechanics (Dover Publications, New York, Dover Publications, 1950).
[64] J. Schwinger and B. G. Englert, Quantum Mechanics: Symbolism of Atomic Measurements (Springer, Berlin, 2001). DOI: 10.1007/978-3-662-04589-3.
https://doi.org/10.1007/978-3-662-04589-3
[65] M. Dalmonte and S. Montangero, Contemp. Lattice gauge theories simulations in the quantum information era, Phys. 57, 388 (2016). DOI: 10.1080/00107514.2016.1151199.
https://doi.org/10.1080/00107514.2016.1151199
[66] E. Zohar and J.I. Cirac, Removing staggered fermionic matter in U(N) and SU(N) lattice gauge theories, Phys. Rev. D 99, 114511 (2019). DOI: 10.1103/PhysRevD.99.114511.
https://doi.org/10.1103/PhysRevD.99.114511
[67] B. M. McCoy and T. T. Wu, Two-dimensional Ising field theory in a magnetic field: Breakup of the cut in the two-point function, Phys. Rev. D 18, 1259 (1978). DOI: 10.1103/PhysRevD.18.1259.
https://doi.org/10.1103/PhysRevD.18.1259
[68] P. Calabrese, J. cardy and B. Doyon, Entanglement Entropy in Extended Quantum Systems Special Issue, Journal of Physics A 42 (2009). DOI: 10.1088/1751-8121/42/50/500301.
https://doi.org/10.1088/1751-8121/42/50/500301
[69] 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.
https://iopscience.iop.org/journal/1742-5468/page/extra.special4
[70] 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.
https://doi.org/10.1088/1742-5468/2005/04/P04010
[71] 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.
https://doi.org/10.1007/BF01645779
[72] 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.
https://doi.org/10.1088/1742-5468/2008/05/P05018
[73] 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.
https://doi.org/10.1103/PhysRevB.79.155104
[74] 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.
https://doi.org/10.1103/PhysRevLett.111.127205
[75] 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.
https://doi.org/10.1103/PhysRevA.85.053625
[76] 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.
https://doi.org/10.1103/PhysRevA.89.031602
[77] 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.
https://doi.org/10.1103/PhysRevLett.113.187203
[78] 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.
https://doi.org/10.1088/1367-2630/16/5/053034
[79] Compare for example our Fig. 8(a) with Fig. 6 of Ref. [62].
[80] H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, M. D. Lukin, Probing many-body dynamics on a 51-atom quantum simulator, Nature 551, 579 (2017). DOI: 10.1038/nature24622.
https://doi.org/10.1038/nature24622
[81] 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.
https://doi.org/10.1103/PhysRevLett.96.136801
[82] 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.
https://doi.org/10.1103/PhysRevD.82.105026
[83] 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.
https://doi.org/10.1103/PhysRevD.87.105006
[84] F. Liu, R. Lundgren, P. Titum, G. Pagano, J. Zhang, C. Monroe, and A. V. Gorshkov, Confined Quasiparticle Dynamics in Long-Range Interacting Quantum Spin Chains, Phys. Rev. Lett. 122, 150601 (2019). DOI: 10.1103/PhysRevLett.122.150601.
https://doi.org/10.1103/PhysRevLett.122.150601
[85] O. Pomponio, L. Pristyák, and G. Takács, Quasi-particle spectrum and entanglement generation after a quench in the quantum Potts spin chain, J. Stat. Mech. (2019) 013104. DOI: 10.1088/1742-5468/aafa80.
https://doi.org/10.1088/1742-5468/aafa80
[86] U. Schollwöck and S. R. White, Methods for Time Dependence in DMRG, AIP Conf. Proc. 816, 155 (2006). DOI: 10.1063/1.2178041.
https://doi.org/10.1063/1.2178041
Cited by
[1] Thomas Iadecola and Michael Schecter, “Quantum many-body scar states with emergent kinetic constraints and finite-entanglement revivals”, Physical Review B 101 2, 024306 (2020).
[2] Titas Chanda, Jakub Zakrzewski, Maciej Lewenstein, and Luca Tagliacozzo, “Confinement and Lack of Thermalization after Quenches in the Bosonic Schwinger Model”, Physical Review Letters 124 18, 180602 (2020).
[3] Umberto Borla, Ruben Verresen, Fabian Grusdt, and Sergej Moroz, “Confined Phases of One-Dimensional Spinless Fermions Coupled to Z<SUB>2</SUB> Gauge Theory”, Physical Review Letters 124 12, 120503 (2020).
[4] Roberto Verdel, Fangli Liu, Seth Whitsitt, Alexey V. Gorshkov, and Markus Heyl, “Real-time dynamics of string breaking in quantum spin chains”, arXiv:1911.11382.
[5] Dmitri E. Kharzeev and Yuta Kikuchi, “Real-time chiral dynamics from a digital quantum simulation”, arXiv:2001.00698.
[6] Bipasha Chakraborty, Masazumi Honda, Taku Izubuchi, Yuta Kikuchi, and Akio Tomiya, “Digital Quantum Simulation of the Schwinger Model with Topological Term via Adiabatic State Preparation”, arXiv:2001.00485.
[7] Olalla A. Castro-Alvaredo, Máté Lencsés, István M. Szécsényi, and Jacopo Viti, “Entanglement Oscillations near a Quantum Critical Point”, arXiv:2001.10007.
[8] Riccardo Javier Valencia Tortora, Pasquale Calabrese, and Mario Collura, “Relaxation of the order-parameter statistics and dynamical confinement”, arXiv:2005.01679.
[9] Flavia B. Ramos, Mate Lencses, J. C. Xavier, and Rodrigo G. Pereira, “Confinement and bound states of bound states in a transverse-field two-leg Ising ladder”, arXiv:2005.03145.
[10] Gianluca Lagnese, Federica Maria Surace, Márton Kormos, and Pasquale Calabrese, “Confinement in the spectrum of a Heisenberg-Ising spin ladder”, arXiv:2005.03131.
[11] Yannick Meurice, “Discrete aspects of continuous symmetries in the tensorial formulation of Abelian gauge theories”, arXiv:2003.10986.
[12] Titas Chanda, Ruixiao Yao, and Jakub Zakrzewski, “Coexistence of localized and extended phases: Many-body localization in a harmonic trap”, arXiv:2004.00954.
[13] Piotr Sierant, Maciej Lewenstein, and Jakub Zakrzewski, “Polynomially filtered exact diagonalization approach to many-body localization”, arXiv:2005.09534.
[14] Zhi-Cheng Yang, Fangli Liu, Alexey V. Gorshkov, and Thomas Iadecola, “Hilbert-Space Fragmentation from Strict Confinement”, Physical Review Letters 124 20, 207602 (2020).
[15] Yao-Tai Kang, Chung-Yu Lo, Shuai Yin, and Pochung Chen, “Kibble-Zurek mechanism in a quantum link model”, Physical Review A 101 2, 023610 (2020).
[16] Nouman Butt, Simon Catterall, Yannick Meurice, Ryo Sakai, and Judah Unmuth-Yockey, “Tensor network formulation of the massless Schwinger model with staggered fermions”, Physical Review D 101 9, 094509 (2020).
[17] Ana Hudomal, Ivana Vasić, Nicolas Regnault, and Zlatko Papić, “Quantum scars of bosons with correlated hopping”, Communications Physics 3 1, 99 (2020).
The above citations are from SAO/NASA ADS (last updated successfully 2020-06-19 07:00:56). The list may be incomplete as not all publishers provide suitable and complete citation data.
On Crossref’s cited-by service no data on citing works was found (last attempt 2020-06-19 07:00:55).
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.
Source: https://quantum-journal.org/papers/q-2020-06-15-281/
