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Constraint-induced breaking and restoration of ergodicity in spin-1 PXP models

Bhaskar Mukherjee1,2,*, Zi Cai1,3,4,†, and W. Vincent Liu2,1,5,4,6,‡

  • 1Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
  • 2Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
  • 3Key Laboratory of Artificial Structures and Quantum Control, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
  • 4Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
  • 5T. D. Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
  • 6Department of Physics and Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China

  • *bhaskarmukherjee1991@gmail.com
  • †zcai@sjtu.edu.cn
  • ‡wvliu@pitt.edu
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Phys. Rev. Research 3, 033201 – Published 31 August, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.033201

Abstract

Eigenstate thermalization hypothesis (ETH) has played a pivotal role in understanding ergodicity and its breaking in isolated quantum many-body systems. The recent experiment on 51-atom Rydberg quantum simulator by Bernien et al. [Nature (London) 551, 579 (2017)] and subsequent theoretical analysis have shown that hardcore kinetic constraint can lead to weak ergodicity breaking. In this work, we demonstrate, using 1d spin-1 PXP models, that miscellaneous type of ergodicity can be realized by adjusting the hardcore constraints between different components of nearest-neighbor spins. This includes ETH violation due to emergent shattering of Hilbert space into exponentially many subsectors of various sizes, a novel form of nonintegrability with an extensive number of local conserved quantities and strong ergodicity. We analyze these different forms of ergodicity and study their impact on the nonequilibrium dynamics of a Z2 initial state. We use forward-scattering approximation to understand the amount of Z2 oscillation present in these models. Our work shows that not only ergodicity breaking but an appropriate choice of constraints can lead to restoration of ergodicity as well.

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References (58)

  1. 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).
  2. J. M. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A 43, 2046 (1991).
  3. M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50, 888 (1994).
  4. M. Srednicki, The approach to thermal equilibrium in quantized chaotic systems, J. Phys. A 32, 1163 (1999).
  5. M. Rigol, V. Dunjko, and M. Olshanii, Thermalization and its mechanism for generic isolated quantum systems, Nature (Lond.) 452, 854 (2008).
  6. B. Sutherland, Beautiful Models: 70 Years of Exactly Solved Quantum Many-body Problems (World Scientific, River Edge, NJ, 2004).
  7. Subir Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, UK, 1999).
  8. M. Basko, I. L. Aleiner, and B. L. Altshuler, Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states, Ann. Phys. 321, 1126 (2006).
  9. V. Oganesyan and D. A. Huse, Localization of interacting fermions at high temperature, Phys. Rev. B 75, 155111 (2007).
  10. A. Pal and D. A. Huse, Many-body localization phase transition, Phys. Rev. B 82, 174411 (2010).
  11. D. A. Huse, R. Nandkishore, V. Oganesyan, A. Pal, and S. L. Sondhi, Localization-protected quantum order, Phys. Rev. B 88, 014206 (2013).
  12. M. Serbyn, Z. Papic, and D. A. Abanin, Local Conservation Laws and the Structure of the Many-Body Localized States, Phys. Rev. Lett. 111, 127201 (2013).
  13. H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin, Probing many-body dynamics on a 51-atom quantum simulator, Nature (Lond.) 551, 579 (2017).
  14. C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papic, Weak ergodicity breaking from quantum many-body scars, Nat. Phys. 14, 745 (2018).
  15. C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papic, Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations, Phys. Rev. B 98, 155134 (2018).
  16. C.-J. Lin and Olexei I. Motrunich, Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain, Phys. Rev. Lett. 122, 173401 (2019).
  17. N. Shiraishi, Connection between quantum-many-body scars and the Affleck-Kennedy-Lieb-Tasaki model from the viewpoint of embedded Hamiltonians, J. Stat. Mech. (2019) 083103.
  18. V. Khemani, C. R. Laumann, and A. Chandran, Signatures of integrability in the dynamics of Rydberg-blockaded chains, Phys. Rev. B 99, 161101(R) (2019).
  19. 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).
  20. N. Shiraishi and T. Mori, Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis, Phys. Rev. Lett. 119, 030601 (2017)
  21. M. Schecter and T. Iadecola, Weak Ergodicity Breaking and Quantum Many-Body Scars in Spin-1 XY Magnets, Phys. Rev. Lett. 123, 147201 (2019).
  22. S. Moudgalya, S. Rachel, B. A. Bernevig, and N. Regnault, Exact excited states of nonintegrable models, Phys. Rev. B 98, 235155 (2018).
  23. S. Maudgalya, 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)
  24. D. K. Mark and O. I. Motrunich, η-pairing states as true scars in an extended Hubbard model, Phys. Rev. B 102, 075132 (2020).
  25. 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).
  26. 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).
  27. K. Bull, I. Martin, and Z. Papic, Systematic Construction of Scarred Many-Body Dynamics in 1D Lattice Models, Phys. Rev. Lett. 123, 030601 (2019).
  28. S. Pai and M. Pretko, Dynamical Scar States in Driven Fracton Systems, Phys. Rev. Lett. 123, 136401 (2019).
  29. B. Mukherjee, S. Nandy, A. Sen, D. Sen, and K. Sengupta, Collapse and revival of quantum many-body scars via Floquet engineering, Phys. Rev. B 101, 245107 (2020).
  30. B. Mukherjee, A. Sen, D. Sen, and K. Sengupta, Restoring coherence via aperiodic drives in a many-body quantum system, Phys. Rev. B 102, 014301 (2020).
  31. B. Mukherjee, A. Sen, D. Sen, and K. Sengupta, Dynamics of the vacuum state in a periodically driven Rydberg chain, Phys. Rev. B 102, 075123 (2020).
  32. S. Sugiura, T. Kuwahara, and K. Saito, Many-body scar state intrinsic to periodically driven system, Phys. Rev. Res. 3, L012010 (2021).
  33. K. Mizuta, K. Takasan, and Norio Kawakami, Exact Floquet quantum many-body scars under Rydberg blockade, Phys. Rev. Res. 2, 033284 (2020).
  34. N. Shibata, N. Yoshioka, and H. Katsura, Onsager's Scars in Disordered Spin Chains, Phys. Rev. Lett. 124, 180604 (2020).
  35. S. Maudgalya, N. Regnault, and B. A. Bernevig, Quantum many-body scars in a Landau level on a thin torus, Phys. Rev. B 102, 195150 (2020).
  36. S. Ok, K. Choo, C. Mudry, C. Castelnovo, C. Chamon, and T. Neupert, Topological many-body scar states in dimensions one, two, and three, Phys. Rev. Res. 1, 033144 (2019).
  37. C.-J. Lin, V. Calvera, and T. H. Hsieh, Quantum many-body scar states in two-dimensional Rydberg atom arrays, Phys. Rev. B 101, 220304(R) (2020).
  38. A. A. Michailidis, C. J. Turner, Z. Papić, D. A. Abanin, and M. Serbyn, Stabilizing two-dimensional quantum scars by deformation and synchronization, Phys. Rev. Res. 2, 022065(R) (2020).
  39. K. Lee, R. Melendrez, A. Pal, and H. J. Changlani, Exact three-colored quantum scars from geometric frustration, Phys. Rev. B 101, 241111(R) (2020).
  40. N. S. Srivatsa, J. Wildeboer, A. Seidel, and A. E. B. Nielsen, Quantum many-body scars with chiral topological order in two dimensions and critical properties in one dimension, Phys. Rev. B 102, 235106 (2020).
  41. J. Wildeboer, A. Seidel, N. S. Srivatsa, A. E. B. Nielsen, and O. Erten, Topological quantum many-body scars in quantum dimer models on the Kagome lattice, arXiv:2009.00022.
  42. A. J. A. James, R. M. Konik, and N. J. Robinson, Symmetry Breaking Bias and the Dynamics of a Quantum Phase Transition, Phys. Rev. Lett. 122, 130603 (2019).
  43. 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).
  44. G. Magnifico, M. Dalmonte, P. Facchi, S. Pascazio, F. V Pepe, and E. Ercolessi, Real time dynamics and confinement in the Zn Schwinger-Weyl lattice model for 1+1 QED, Quantum 4, 281 (2020).
  45. B. Mukherjee, D. Banerjee, K. Sengupta, and A. Sen, A minimal model for Hilbert space fragmentation with local constraints, arXiv:2106.14897v2.
  46. T. Iadecola, M. Schecter, and S. Xu, Quantum many-body scars from magnon condensation, Phys. Rev. B 100, 184312 (2019).
  47. D. Banerjee and A. Sen, Quantum Scars from Zero Modes in an Abelian Lattice Gauge Theory, Phys. Rev. Lett. 126, 220601 (2021).
  48. V. Karle, M. Serbyn, and A. A. Michailidis, Area-Law Entangled Eigenstates from Nullspaces of Local Hamiltonians, Phys. Rev. Lett. 127, 060602 (2021).
  49. V. Khemani, M. Hermele, and R. M. Nandkishore, Localization from Hilbert space shattering: From theory to physical realizations, Phys. Rev. B 101, 174204 (2020).
  50. P. Sala, T. Rakovszky, R. Verresen, M. Knap, and F. Pollmann, Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians, Phys. Rev. X 10, 011047 (2020).
  51. T. Iadecola and M. Schecter, Quantum many-body scar states with emergent kinetic constraints and finite-entanglement revivals, Phys. Rev. B 101, 024306 (2020).
  52. Z. C. Yang, F. Liu, A. V. Gorshkov, and T. Iadecola, Hilbert-Space Fragmentation from Strict Confinement, Phys. Rev. Lett. 124, 207602 (2020).
  53. K. Lee, A. Pal, and H. J. Changlani, Frustration-induced emergent Hilbert space fragmentation, Phys. Rev. B 103, 235133 (2021).
  54. D. Hahn, P. A. McClarty, and D. J. Luitz, Information dynamics in a model with Hilbert space fragmentation, arxiv:2104.00692v4.
  55. S. Roy and A. Lazarides, Strong ergodicity breaking due to local constraints in a quantum system, Phys. Rev. Res. 2, 023159 (2020).
  56. S. Scherg, T. Kohlert, P. Sala, F. Pollmann, B. H. Madhusudhana, I. Bloch, and M. Aidelsburger, Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains, Nat. Commun. 12, 4490 (2021).
  57. A. Signoles, T. Franz, R. Ferracini Alves, M. Gärttner, S. Whitlock, G. Zü, and M. Weidemüller, Observation of Glassy Dynamics in a Disordered Quantum Spin System, Phys. Rev. X 11, 011011 (2021).
  58. B. Nienhuis, M. Campostrini, and P. Calabrese, Entanglement, combinatorics and finite-size effects in spin-chains, J. Stat. Mech. (2009) P02063.

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Phys. Rev. Research 3, 033201– Published 31 August, 2021
  • Received 23 April 2021
  • Revised 10 August 2021
  • Accepted 11 August 2021
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