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  • Letter
  • Open Access

Weak ergodicity breaking in the Schwinger model

Jean-Yves Desaules1, Debasish Banerjee2,3, Ana Hudomal1,4, Zlatko Papić1, Arnab Sen5, and Jad C. Halimeh6,7,*

  • 1School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
  • 2Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata 700064, India
  • 3Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai 400094, India
  • 4Institute of Physics Belgrade, University of Belgrade, 11080 Belgrade, Serbia
  • 5School of Physical Sciences, Indian Association for the Cultivation of Science, Kolkata 700032, India
  • 6Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
  • 7Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, D-80799 München, Germany

  • *jad.halimeh@physik.lmu.de

Phys. Rev. B 107, L201105 – Published 5 May, 2023

DOI: https://doi.org/10.1103/PhysRevB.107.L201105

Abstract

As a paradigm of weak ergodicity breaking in disorder-free nonintegrable models, quantum many-body scars (QMBS) can offer deep insights into the thermalization dynamics of gauge theories. Having been first discovered in a spin-12 quantum link formulation of the Schwinger model, it is a fundamental question as to whether QMBS persist for S>12 since such theories converge to the lattice Schwinger model in the large-S limit, which is the appropriate version of lattice QED in one spatial dimension. In this work, we address this question by exploring QMBS in spin-SU(1) quantum link models (QLMs) with staggered fermions. We find that QMBS persist at S>12, with the resonant scarring regime, which occurs for a zero-mass quench, arising from simple high-energy gauge-invariant initial product states. We furthermore find evidence of detuned scarring regimes, which occur for finite-mass quenches starting in the physical vacua and the charge-proliferated state. Our results conclusively show that QMBS exist in a wide class of lattice gauge theories in one spatial dimension represented by spin-S QLMs coupled to dynamical fermions, and our findings can be tested on near-term cold-atom quantum simulators of these models.

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Prominent quantum many-body scars in a truncated Schwinger model

Jean-Yves Desaules, Ana Hudomal, Debasish Banerjee, Arnab Sen, Zlatko Papić, and Jad C. Halimeh
Phys. Rev. B 107, 205112 (2023)

Article Text

References (73)

  1. H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, Probing many-body dynamics on a 51-atom quantum simulator, Nature (London) 551, 579 (2017).
  2. S. Moudgalya, S. Rachel, B. A. Bernevig, and N. Regnault, Exact excited states of nonintegrable models, Phys. Rev. B 98, 235155 (2018).
  3. H. Zhao, J. Vovrosh, F. Mintert, and J. Knolle, Quantum Many-Body Scars in Optical Lattices, Phys. Rev. Lett. 124, 160604 (2020).
  4. H. Zhao, A. Smith, F. Mintert, and J. Knolle, Orthogonal Quantum Many-Body Scars, Phys. Rev. Lett. 127, 150601 (2021).
  5. D. Bluvstein, A. Omran, H. Levine, A. Keesling, G. Semeghini, S. Ebadi, T. T. Wang, A. A. Michailidis, N. Maskara, W. W. Ho, S. Choi, M. Serbyn, M. Greiner, V. Vuletić, and M. D. Lukin, Controlling quantum many-body dynamics in driven Rydberg atom arrays, Science 371, 1355 (2021).
  6. P. N. Jepsen, Y. K.-E. Lee, H. Lin, I. Dimitrova, Y. Margalit, W. W. Ho, and W. Ketterle, Long-lived phantom helix states in Heisenberg quantum magnets, Nat. Phys. 18, 899 (2022).
  7. G.-X. Su, H. Sun, A. Hudomal, J.-Y. Desaules, Z.-Y. Zhou, B. Yang, J. C. Halimeh, Z.-S. Yuan, Z. Papić, and J.-W. Pan, Observation of many-body scarring in a Bose-Hubbard quantum simulator, Phys. Rev. Res. 5, 023010 (2023).
  8. P. Zhang, H. Dong, Y. Gao, L. Zhao, J. Hao, J.-Y. Desaules, Q. Guo, J. Chen, J. Deng, B. Liu, W. Ren, Y. Yao, X. Zhang, S. Xu, K. Wang, F. Jin, X. Zhu, B. Zhang, H. Li, C. Song et al., Many-body Hilbert space scarring on a superconducting processor, Nat. Phys. 19, 120 (2022).
  9. S. Moudgalya, N. Regnault, and B. A. Bernevig, Entanglement of exact excited states of Affleck-Kennedy-Lieb-Tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization hypothesis, Phys. Rev. B 98, 235156 (2018).
  10. C.-J. Lin and O. I. Motrunich, Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain, Phys. Rev. Lett. 122, 173401 (2019).
  11. 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).
  12. M. Schecter and T. Iadecola, Weak Ergodicity Breaking and Quantum many-body Scars in Spin-1 XY Magnets, Phys. Rev. Lett. 123, 147201 (2019).
  13. W. W. Ho, S. Choi, H. Pichler, and M. D. Lukin, Periodic Orbits, Entanglement, and Quantum Many-Body Scars in Constrained Models: Matrix Product State Approach, Phys. Rev. Lett. 122, 040603 (2019).
  14. C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papić, Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations, Phys. Rev. B 98, 155134 (2018).
  15. M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50, 888 (1994).
  16. J. M. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A 43, 2046 (1991).
  17. M. Rigol, V. Dunjko, and M. Olshanii, Thermalization and its mechanism for generic isolated quantum systems, Nature (London) 452, 854 (2008).
  18. J. Eisert, M. Friesdorf, and C. Gogolin, Quantum many-body systems out of equilibrium, Nat. Phys. 11, 124 (2015).
  19. L. D'Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics, Adv. Phys. 65, 239 (2016).
  20. J. M. Deutsch, Eigenstate thermalization hypothesis, Rep. Prog. Phys. 81, 082001 (2018).
  21. D. K. Mark, C.-J. Lin, and O. I. Motrunich, Unified structure for exact towers of scar states in the Affleck-Kennedy-Lieb-Tasaki and other models, Phys. Rev. B 101, 195131 (2020).
  22. S. Moudgalya, N. Regnault, and B. A. Bernevig, η-pairing in Hubbard models: From spectrum generating algebras to quantum many-body scars, Phys. Rev. B 102, 085140 (2020).
  23. N. O'Dea, F. Burnell, A. Chandran, and V. Khemani, From tunnels to towers: Quantum scars from Lie algebras and q-deformed Lie algebras, Phys. Rev. Res. 2, 043305 (2020).
  24. K. Pakrouski, P. N. Pallegar, F. K. Popov, and I. R. Klebanov, Many-Body Scars as a Group Invariant Sector of Hilbert Space, Phys. Rev. Lett. 125, 230602 (2020).
  25. N. Shiraishi and T. Mori, Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis, Phys. Rev. Lett. 119, 030601 (2017).
  26. M. Serbyn, D. A. Abanin, and Z. Papić, Quantum many-body scars and weak breaking of ergodicity, Nat. Phys. 17, 675 (2021).
  27. S. Moudgalya, B. A. Bernevig, and N. Regnault, Quantum many-body scars and Hilbert space fragmentation: A review of exact results, Rep. Prog. Phys. 85, 086501 (2022).
  28. A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, Generation and manipulation of Schrödinger cat states in Rydberg atom arrays, Science 365, 570 (2019).
  29. S. Dooley, Robust quantum sensing in strongly interacting systems with many-body scars, PRX Quantum 2, 020330 (2021).
  30. J.-Y. Desaules, F. Pietracaprina, Z. Papić, J. Goold, and S. Pappalardi, Extensive Multipartite Entanglement from su(2) Quantum Many-Body Scars, Phys. Rev. Lett. 129, 020601 (2022).
  31. S. Dooley, S. Pappalardi, and J. Goold, Entanglement enhanced metrology with quantum many-body scars, Phys. Rev. B 107, 035123 (2023).
  32. M. Brenes, M. Dalmonte, M. Heyl, and A. Scardicchio, Many-Body Localization Dynamics from Gauge Invariance, Phys. Rev. Lett. 120, 030601 (2018).
  33. F. M. Surace, P. P. Mazza, G. Giudici, A. Lerose, A. Gambassi, and M. Dalmonte, Lattice Gauge Theories and String Dynamics in Rydberg Atom Quantum Simulators, Phys. Rev. X 10, 021041 (2020).
  34. D. Banerjee and A. Sen, Quantum Scars from Zero Modes in an Abelian Lattice Gauge Theory on Ladders, Phys. Rev. Lett. 126, 220601 (2021).
  35. A. S. Aramthottil, U. Bhattacharya, D. González-Cuadra, M. Lewenstein, L. Barbiero, and J. Zakrzewski, Scar states in deconfined Z2 lattice gauge theories, Phys. Rev. B 106, L041101 (2022).
  36. S. Biswas, D. Banerjee, and A. Sen, Scars from protected zero modes and beyond in U(1) quantum link and quantum dimer models, SciPost Phys. 12, 148 (2022).
  37. S. Weinberg, The Quantum Theory of Fields, Vol. 2: Modern Applications (Cambridge University Press, Cambridge, 1995).
  38. C. Gattringer and C. Lang, Quantum Chromodynamics on the Lattice: An Introductory Presentation, Lecture Notes in Physics (Springer, Berlin, 2009).
  39. A. Zee, Quantum Field Theory in a Nutshell (Princeton University Press, Princeton, NJ, 2003).
  40. R. P. Feynman and P. Cziffra, Quantum Electrodynamics, A Lecture Note and Reprint Series (Basic Books, New York, 1962).
  41. 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 (London) 534, 516 (2016).
  42. C. Muschik, M. Heyl, E. Martinez, T. Monz, P. Schindler, B. Vogell, M. Dalmonte, P. Hauke, R. Blatt, and P. Zoller, U(1) Wilson lattice gauge theories in digital quantum simulators, New J. Phys. 19, 103020 (2017).
  43. N. Klco, E. F. Dumitrescu, A. J. McCaskey, T. D. Morris, R. C. Pooser, M. Sanz, E. Solano, P. Lougovski, and M. J. Savage, Quantum-classical computation of Schwinger model dynamics using quantum computers, Phys. Rev. A 98, 032331 (2018).
  44. A. Keesling, A. Omran, H. Levine, H. Bernien, H. Pichler, S. Choi, R. Samajdar, S. Schwartz, P. Silvi, S. Sachdev, P. Zoller, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator, Nature (London) 568, 207 (2019).
  45. C. Kokail, C. Maier, R. van Bijnen, T. Brydges, M. K. Joshi, P. Jurcevic, C. A. Muschik, P. Silvi, R. Blatt, C. F. Roos, and P. Zoller, Self-verifying variational quantum simulation of lattice models, Nature (London) 569, 355 (2019).
  46. F. Görg, K. Sandholzer, J. Minguzzi, R. Desbuquois, M. Messer, and T. Esslinger, Realization of density-dependent Peierls phases to engineer quantized gauge fields coupled to ultracold matter, Nat. Phys. 15, 1161 (2019).
  47. C. Schweizer, F. Grusdt, M. Berngruber, L. Barbiero, E. Demler, N. Goldman, I. Bloch, and M. Aidelsburger, Floquet approach to Z2 lattice gauge theories with ultracold atoms in optical lattices, Nat. Phys. 15, 1168 (2019).
  48. A. Mil, T. V. Zache, A. Hegde, A. Xia, R. P. Bhatt, M. K. Oberthaler, P. Hauke, J. Berges, and F. Jendrzejewski, A scalable realization of local U(1) gauge invariance in cold atomic mixtures, Science 367, 1128 (2020).
  49. N. Klco, M. J. Savage, and J. R. Stryker, SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers, Phys. Rev. D 101, 074512 (2020).
  50. B. Yang, H. Sun, R. Ott, H.-Y. Wang, T. V. Zache, J. C. Halimeh, Z.-S. Yuan, P. Hauke, and J.-W. Pan, Observation of gauge invariance in a 71-site Bose–Hubbard quantum simulator, Nature (London) 587, 392 (2020).
  51. Z.-Y. Zhou, G.-X. Su, J. C. Halimeh, R. Ott, H. Sun, P. Hauke, B. Yang, Z.-S. Yuan, J. Berges, and J.-W. Pan, Thermalization dynamics of a gauge theory on a quantum simulator, Science 377, 311 (2022).
  52. I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).
  53. W. S. Bakr, J. I. Gillen, A. Peng, S. Fölling, and M. Greiner, A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice, Nature (London) 462, 74 (2009).
  54. U.-J. Wiese, Ultracold quantum gases and lattice systems: Quantum simulation of lattice gauge theories, Ann. Phys. (Berlin) 525, 777 (2013).
  55. M. C. Bañuls, R. Blatt, J. Catani, A. Celi, J. I. Cirac, M. Dalmonte, L. Fallani, K. Jansen, M. Lewenstein, S. Montangero, C. A. Muschik, B. Reznik, E. Rico, L. Tagliacozzo, K. Van Acoleyen, F. Verstraete, U.-J. Wiese, M. Wingate, J. Zakrzewski, and P. Zoller, Simulating lattice gauge theories within quantum technologies, Eur. Phys. J. D 74, 165 (2020).
  56. Y. Alexeev, D. Bacon, K. R. Brown, R. Calderbank, L. D. Carr, F. T. Chong, B. DeMarco, D. Englund, E. Farhi, B. Fefferman, A. V. Gorshkov, A. Houck, J. Kim, S. Kimmel, M. Lange, S. Lloyd, M. D. Lukin, D. Maslov, P. Maunz, C. Monroe et al., Quantum computer systems for scientific discovery, PRX Quantum 2, 017001 (2021).
  57. M. Aidelsburger, L. Barbiero, A. Bermudez, T. Chanda, A. Dauphin, D. González-Cuadra, P. R. Grzybowski, S. Hands, F. Jendrzejewski, J. Jünemann, G. Juzeliūnas, V. Kasper, A. Piga, S.-J. Ran, M. Rizzi, G. Sierra, L. Tagliacozzo, E. Tirrito, T. V. Zache, J. Zakrzewski et al., Cold atoms meet lattice gauge theory, Philos. Trans. R. Soc. A 380, 20210064 (2022).
  58. E. Zohar, Quantum simulation of lattice gauge theories in more than one space dimension: Requirements, challenges and methods, Philos. Trans. R. Soc. A 380, 20210069 (2022).
  59. N. Klco, A. Roggero, and M. J. Savage, Standard model physics and the digital quantum revolution: Thoughts about the interface, Rep. Prog. Phys. 85, 064301 (2022).
  60. L. Homeier, C. Schweizer, M. Aidelsburger, A. Fedorov, and F. Grusdt, Z2 lattice gauge theories and Kitaev's toric code: A scheme for analog quantum simulation, Phys. Rev. B 104, 085138 (2021).
  61. S Chandrasekharan and U.-J Wiese, Quantum link models: A discrete approach to gauge theories, Nucl. Phys. B 492, 455 (1997).
  62. J. Schwinger, Gauge invariance and mass. II, Phys. Rev. 128, 2425 (1962).
  63. S. Coleman, R. Jackiw, and L. Susskind, Charge shielding and quark confinement in the massive Schwinger model, Ann. Phys. 93, 267 (1975).
  64. 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).
  65. 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).
  66. B. Mukherjee, Z. Cai, and W. V. Liu, Constraint-induced breaking and restoration of ergodicity in spin-1 PXP models, Phys. Rev. Res. 3, 033201 (2021).
  67. J.-Y. Desaules, A. Hudomal, D. Banerjee, A. Sen, Z. Papić, and J. C. Halimeh, Prominent quantum many-body scars in a truncated Schwinger model, Phys. Rev. B 107, 205112 (2023).
  68. T. V. Zache, M. V. Damme, J. C. Halimeh, P. Hauke, and D. Banerjee, Toward the continuum limit of a (1+1)D quantum link Schwinger model, Phys. Rev. D 106, L091502 (2022).
  69. U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Phys. 326, 96 (2011).
  70. S. Choi, C. J. Turner, H. Pichler, W. W. Ho, A. A. Michailidis, Z. Papić, M. Serbyn, M. D. Lukin, and D. A. Abanin, Emergent SU(2) Dynamics and Perfect Quantum Many-Body Scars, Phys. Rev. Lett. 122, 220603 (2019).
  71. 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).
  72. M. C. Bañuls and K. Cichy, Review on novel methods for lattice gauge theories, Rep. Prog. Phys. 83, 024401 (2020).
  73. J. C. Halimeh, M. V. Damme, T. V. Zache, D. Banerjee, and P. Hauke, Achieving the quantum field theory limit in far-from-equilibrium quantum link models, Quantum 6, 878 (2021).

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