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  • Letter
  • Open Access

Many-body scar state intrinsic to periodically driven system

Sho Sugiura1,2, Tomotaka Kuwahara3,4, and Keiji Saito5

  • 1Physics and Informatics Laboratories, NTT Research, Inc., 940 Stewart Drive, Sunnyvale, California 94085, USA
  • 2Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
  • 3Mathematical Science Team, RIKEN Center for Advanced Intelligence Project (AIP),1-4-1 Nihonbashi, Chuo-ku, Tokyo 103-0027, Japan
  • 4Interdisciplinary Theoretical & Mathematical Sciences Program (iTHEMS) RIKEN 2-1, Hirosawa, Wako, Saitama 351-0198, Japan
  • 5Department of Physics, Keio University, Yokohama 223-8522, Japan

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Phys. Rev. Research 3, L012010 – Published 2 February, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L012010

Abstract

The violation of the Floquet version of the eigenstate thermalization hypothesis is rigorously discussed with realistic Hamiltonians. Our model is based on the PXP-type interactions without disorder. We rigorously prove the existence of many-body scar states in the Floquet eigenstates that appear only at specific periods of driving by showing the explicit expressions of the wave functions. This is equivalently the first rigorous proof of the breakdown of the Floquet eigenstate thermalization hypothesis. Through the exact expression of the scar states, the underlying physical mechanism is clarified. Using the underlying mechanism, various driven Hamiltonians with Floquet-scar states can be systematically engineered. We then discuss Floquet-scar states that can be checked through time evolution of observables in a chain of Rydberg atoms.

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References (53)

  1. S. Popescu, A. J. Short, and A. Winter, Entanglement and the foundations of statistical mechanics, Nat. Phys. 2, 754 (2006).
  2. S. Goldstein, J. L. Lebowitz, R. Tumulka, and N. Zanghì, Canonical Typicality, Phys. Rev. Lett. 96, 050403 (2006).
  3. J. Goold, M. Huber, A. Riera, L. del Rio, and P. Skrzypczyk, The role of quantum information in thermodynamics—A topical review, J. Phys. A: Math. Theor. 49, 143001 (2016).
  4. V. Yukalov, Equilibration and thermalization in finite quantum systems, Laser Phys. Lett. 8, 485 (2011).
  5. R. Nandkishore and D. A. Huse, Many-body localization and thermalization in quantum statistical mechanics, Annu. Rev. Condens. Matter Phys. 6, 15 (2015).
  6. 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).
  7. C. Gogolin and J. Eisert, Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems, Rep. Prog. Phys. 79, 056001 (2016).
  8. T. Mori, T. N. Ikeda, E. Kaminishi, and M. Ueda, Thermalization and prethermalization in isolated quantum systems: A theoretical overview, J. Phys. B: At., Mol. Opt. Phys. 51, 112001 (2018).
  9. P. Reimann, Eigenstate thermalization: Deutsch's approach and beyond, New J. Phys. 17, 055025 (2015).
  10. J. M. Deutsch, Eigenstate thermalization hypothesis, Rep. Prog. Phys. 81, 082001 (2018).
  11. J. M. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A 43, 2046 (1991).
  12. M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50, 888 (1994).
  13. L. D'Alessio and A. Polkovnikov, Many-body energy localization transition in periodically driven systems, Ann. Phys. 333, 19 (2013).
  14. L. D'Alessio and M. Rigol, Long-Time Behavior of Isolated Periodically Driven Interacting Lattice Systems, Phys. Rev. X 4, 041048 (2014).
  15. A. Lazarides, A. Das, and R. Moessner, Equilibrium states of generic quantum systems subject to periodic driving, Phys. Rev. E 90, 012110 (2014).
  16. T. Kuwahara, T. Mori, and K. Saito, Floquet–Magnus theory and generic transient dynamics in periodically driven many-body quantum systems, Ann. Phys. 367, 96 (2016).
  17. T. Mori, T. Kuwahara, and K. Saito, Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems, Phys. Rev. Lett. 116, 120401 (2016).
  18. H. Kim, T. N. Ikeda, and D. A. Huse, Testing whether all eigenstates obey the eigenstate thermalization hypothesis, Phys. Rev. E 90, 052105 (2014).
  19. R. Mondaini, K. R. Fratus, M. Srednicki, and M. Rigol, Eigenstate thermalization in the two-dimensional transverse field Ising model, Phys. Rev. E 93, 032104 (2016).
  20. R. Mondaini and M. Rigol, Eigenstate thermalization in the two-dimensional transverse field ising model. II. Off-diagonal matrix elements of observables, Phys. Rev. E 96, 012157 (2017).
  21. A. Haldar, D. Sen, R. Moessner, and A. Das, Scars in strongly driven Floquet matter: Resonance vs emergent conservation laws, arXiv:1909.04064 (2019).
  22. P. Ponte, Z. Papić, F. Huveneers, and D. A. Abanin, Many-Body Localization in Periodically Driven Systems, Phys. Rev. Lett. 114, 140401 (2015).
  23. P. Ponte, A. Chandran, Z. Papić, and D. A. Abanin, Periodically driven ergodic and many-body localized quantum systems, Ann. Phys. 353, 196 (2015).
  24. 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).
  25. 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).
  26. S. Moudgalya, S. Rachel, B. A. Bernevig, and N. Regnault, Exact excited states of nonintegrable models, Phys. Rev. B 98, 235155 (2018).
  27. 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).
  28. 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).
  29. A. J. A. James, R. M. Konik, and N. J. Robinson, Nonthermal States Arising from Confinement in One and Two Dimensions, Phys. Rev. Lett. 122, 130603 (2019).
  30. 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).
  31. 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).
  32. H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner et al., Probing many-body dynamics on a 51-atom quantum simulator, Nature (London) 551, 579 (2017).
  33. 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).
  34. N. Shiraishi and T. Mori, Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis, Phys. Rev. Lett. 119, 030601 (2017).
  35. 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).
  36. M. Schecter and T. Iadecola, Weak Ergodicity Breaking and Quantum Many-Body Scars in Spin-1 xy Magnets, Phys. Rev. Lett. 123, 147201 (2019).
  37. S. Chattopadhyay, H. Pichler, M. D. Lukin, and W. W. Ho, Quantum many-body scars from virtual entangled pairs, Phys. Rev. B 101, 174308 (2020).
  38. T. Iadecola and M. Schecter, Quantum many-body scar states with emergent kinetic constraints and finite-entanglement revivals, Phys. Rev. B 101, 024306 (2020).
  39. We note the recent numerical works on the Fracton dynamics where the unitary operator was randomly assigned to the finite unitary circuits and localized circuit states are discussed [43, 44]. The localization is induced by effective conserved quantities depending on specific configurations, and the number of such circuit states increases exponentially with the system size. These properties are different from typical scar states in the static Hamiltonians [24, 25, 26].
  40. P. Schauß, J. Zeiher, T. Fukuhara, S. Hild, M. Cheneau, T. Macrì, T. Pohl, I. Bloch, and C. Gross, Crystallization in Ising quantum magnets, Science 347, 1455 (2015).
  41. H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrì, T. Lahaye, and A. Browaeys, Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models, Nature (London) 534, 667 (2016).
  42. T. M. Graham, M. Kwon, B. Grinkemeyer, Z. Marra, X. Jiang, M. T. Lichtman, Y. Sun, M. Ebert, and M. Saffman, Rydberg Mediated Entanglement in a Two-Dimensional Neutral Atom Qubit Array, Phys. Rev. Lett. 123, 230501 (2019).
  43. S. Pai and M. Pretko, Phys. Rev. Lett. 123, 136401 (2019).
  44. V. Khemani and R. Nandkishore, Phys. Rev. B 101, 174204 (2020).
  45. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L012010 for details of the generic aspect.
  46. I.-D. Potirniche, A. C. Potter, M. Schleier-Smith, A. Vishwanath, and N. Y. Yao, Floquet Symmetry-Protected Topological Phases in Cold-Atom Systems, Phys. Rev. Lett. 119, 123601 (2017).
  47. D. N. Page, Average Entropy of a Subsystem, Phys. Rev. Lett. 71, 1291 (1993).
  48. A. Dymarsky, N. Lashkari, and H. Liu, Subsystem eigenstate thermalization hypothesis, Phys. Rev. E 97, 012140 (2018).
  49. Y. O. Nakagawa, M. Watanabe, H. Fujita, and S. Sugiura, Universality in volume-law entanglement of scrambled pure quantum states, Nat. Commun. 9, 1635 (2018).
  50. T.-C. Lu and T. Grover, Renyi entropy of chaotic eigenstates, Phys. Rev. E 99, 032111 (2019).
  51. SN/2=ln|HN/2|−0.5135⋯ where |HN/2| is the number of Hilbert space for the size N/2. The subtracted term −0.5135⋯ in the PXP model is slightly different from the value in unconstrained models, −0.5 [52].
  52. S. C. Morampudi, A. Chandran, and C. R. Laumann, Phys. Rev. Lett. 124, 050602 (2020).
  53. In the case of the periodic boundary condition setting V1=PNX1P2 and V2=PN−1XNP1 in the Hamiltonians, one can obtain only one Floquet-intrinsic scar state for the period T=22πm. With (11), the state is given by FS=↓N↓1⊗|Φ̃2,N/2−1〉⊗|↓〉N/2|↓〉N/2+1⊗|Φ̃N/2+2,N−1〉.The entanglement entropy for the subsystem consisting of the sites i=1,⋯,N/2 is zero from the structure.

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Phys. Rev. Research 3, L012010– Published 2 February, 2021
  • Received 28 November 2019
  • Accepted 18 January 2021
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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