Skip to main content
SpringerLink
Log in

Quantum critical behaviour at the many-body localization transition

  • Letter
  • Published:

From Nature

View current issue Submit your manuscript

Abstract

Phase transitions are driven by collective fluctuations of a system’s constituents that emerge at a critical point1. This mechanism has been extensively explored for classical and quantum systems in equilibrium, whose critical behaviour is described by the general theory of phase transitions. Recently, however, fundamentally distinct phase transitions have been discovered for out-of-equilibrium quantum systems, which can exhibit critical behaviour that defies this description and is not well understood1. A paradigmatic example is the many-body localization (MBL) transition, which marks the breakdown of thermalization in an isolated quantum many-body system as its disorder increases beyond a critical value2,3,4,5,6,7,8,9,10,11. Characterizing quantum critical behaviour in an MBL system requires probing its entanglement over space and time4,5,7, which has proved experimentally challenging owing to stringent requirements on quantum state preparation and system isolation. Here we observe quantum critical behaviour at the MBL transition in a disordered Bose–Hubbard system and characterize its entanglement via its multi-point quantum correlations. We observe the emergence of strong correlations, accompanied by the onset of anomalous diffusive transport throughout the system, and verify their critical nature by measuring their dependence on the system size. The correlations extend to high orders in the quantum critical regime and appear to form via a sparse network of many-body resonances that spans the entire system12,13. Our results connect the macroscopic phenomenology of the transition to the system’s microscopic structure of quantum correlations, and they provide an essential step towards understanding criticality and universality in non-equilibrium systems1,7,13.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1: Microscopy of the many-body localization transition.
Fig. 2: Quantum critical dynamics at the MBL transition.
Fig. 3: Sparse network of resonances.
Fig. 4: Many-body correlations in the quantum critical regime.

Similar content being viewed by others

Data availability

The data that support the findings of this study are available in the Dataverse repository at https://doi.org/10.7910/DVN/E2ROXU.

References

  1. Täuber, U. C. Phase transitions and scaling in systems far from equilibrium. Annu. Rev. Condens. Matter Phys. 8, 185–210 (2017).

    Article  ADS  Google Scholar 

  2. Basko, D. M., Aleiner, I. L. & Altshuler, B. L. On the problem of many-body localization. Ann. Phys. 321, 1126 (2006).

    Article  CAS  ADS  Google Scholar 

  3. Pal, A. & Huse, D. A. Many-body localization phase transition. Phys. Rev. B 82, 174411 (2010).

    Article  ADS  Google Scholar 

  4. Serbyn, M., Papic, Z. & Abanin, D. A. Local conservation laws and the structure of the many-body localized states. Phys. Rev. Lett. 111, 127201 (2013).

    Article  ADS  Google Scholar 

  5. Huse, D. A., Nandkishore, R. & Oganesyan, V. Phenomenology of fully many- body-localized systems. Phys. Rev. B 90, 174202 (2014).

    Article  ADS  Google Scholar 

  6. D’Alessio, L., Kafri, Y., Polkovnikov, A. & Rigol, M. From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239–362 (2016).

    Article  ADS  Google Scholar 

  7. Abanin, D. A., Altman, E., Bloch, I. & Serbyn, M. Ergodicity, entanglement and many-body localization. Preprint at https://arxiv.org/abs/1804.11065 (2018).

  8. Schreiber, M. et al. Observation of many-body localization of interacting fermions in a quasirandom optical lattice. Science 349, 842–845 (2015).

    Article  CAS  ADS  MathSciNet  Google Scholar 

  9. Smith, J. et al. Many-body localization in a quantum simulator with programmable random disorder. Nat. Phys. 12, 907–911 (2016).

    Article  CAS  Google Scholar 

  10. Choi, J. et al. Exploring the many-body localization transition in two dimensions. Science 352, 1547–1552 (2016).

    MathSciNet  MATH  Google Scholar 

  11. Lukin, A. et al. Probing entanglement in a many-body–localized system. Science 364, 256–260 (2019).

    CAS  ADS  PubMed  Google Scholar 

  12. Potter, A. C., Vasseur, R. & Parameswaran, S. A. Universal properties of many-body delocalization transitions. Phys. Rev. X 5, 031033 (2015).

    Google Scholar 

  13. Khemani, V., Lim, S. P., Sheng, D. N. & Huse, D. A. Critical properties of the many-body localization transition. Phys. Rev. X 7, 021013 (2017).

    Google Scholar 

  14. Neill, C. et al. Ergodic dynamics and thermalization in an isolated quantum system. Nat. Phys. 12, 1037–1041 (2016).

    Article  CAS  Google Scholar 

  15. Kaufman, A. M. et al. Quantum thermalization through entanglement in an isolated many-body system. Science 353, 794–800 (2016).

    Article  CAS  ADS  Google Scholar 

  16. Agarwal, K., Gopalakrishnan, S., Knap, M., Müller, M. & Demler, E. Anomalous diffusion and Griffiths effects near the many-body localization transition. Phys. Rev. Lett. 114, 160401 (2015).

    Article  ADS  Google Scholar 

  17. Setiawan, F., Dong, L. D. & Pixley, J. H. Transport properties across the many-body localization transition in quasiperiodic and random systems. Phys. Rev. B 96, 104205 (2017).

    Article  ADS  Google Scholar 

  18. Vosk, R., Huse, D. A. & Altman, E. Theory of the many-body localization transition in one-dimensional systems. Phys. Rev. X 5, 031032 (2015).

    Google Scholar 

  19. Dumitrescu, P. T., Vasseur, R. & Potter, A. C. Scaling theory of entanglement at the many-body localization transition. Phys. Rev. Lett. 119, 110604 (2017).

    Article  ADS  Google Scholar 

  20. Goremykina, A., Vasseur, R. & Serbyn, M. Analytically solvable renormalization group for the many-body localization transition. Preprint at https://arxiv.org/abs/1807.04285 (2018).

  21. Lüschen, H. P. et al. Observation of slow dynamics near the many-body local- ization transition in one-dimensional quasiperiodic systems. Phys. Rev. Lett. 119, 260401 (2017).

    Article  ADS  Google Scholar 

  22. Bordia, P. et al. Probing slow relaxation and many-body localization in two-dimensional quasiperiodic systems. Phys. Rev. X 7, 041047 (2017).

    Google Scholar 

  23. Luitz, D. J., Laflorencie, N. & Alet, F. Extended slow dynamical regime close to the many-body localization transition. Phys. Rev. B 93, 060201 (2016).

    Article  ADS  Google Scholar 

  24. Nandkishore, R., Gopalakrishnan, S. & Huse, D. A. Spectral features of a many-body-localized system weakly coupled to a bath. Phys. Rev. B 90, 064203 (2014).

    Article  ADS  Google Scholar 

  25. Lüschen, H. P. et al. Signatures of many-body localization in a controlled open quantum system. Phys. Rev. X 7, 011034 (2017).

    Google Scholar 

  26. De Roeck, W. & Huveneers, F. Stability and instability towards delocalization in many-body localization systems. Phys. Rev. B 95, 155129 (2017).

    Article  ADS  Google Scholar 

  27. Nandkishore, R. & Gopalakrishnan, S. Many body localized systems weakly cou-pled to baths. Ann. Phys. 529, 1600181 (2017).

    Article  Google Scholar 

  28. Agarwal, K. et al. Rare-region effects and dynamics near the many-body localization transition. Ann. Phys. 529, 1600326 (2017).

    Article  MathSciNet  Google Scholar 

  29. Lucioni, E. et al. Observation of subdiffusion in a disordered interacting system. Phys. Rev. Lett. 106, 230403 (2011).

    Article  CAS  ADS  Google Scholar 

  30. Liu, H.-C. High-order correlation of chaotic bosons and fermions. Phys. Rev. A 94, 023827 (2016).

    Article  ADS  Google Scholar 

  31. Schweigler, T. et al. Experimental characterization of a many-body system via higher-order correlations. Nature 545, 323–326 (2017).

    Article  CAS  ADS  Google Scholar 

  32. Hodgman, S. S., Khakimov, R. I., Truscott, A. G. & Kheruntsyan, K. V. Solving the quantum many-body problem via correlations measured with a momentum microscope. Phys. Rev. Lett. 118, 240402 (2017).

    Article  CAS  ADS  Google Scholar 

  33. Grover, T. Certain general constraints on the many-body localization transition. Preprint at https://arxiv.org/abs/1405.1471 (2014).

Download references

Acknowledgements

We acknowledge discussions with D. Abanin, E. Altman, H. Bernien, C. Chiu, S. Choi, E. Demler, A. Hébert, W. W. Ho, V. Kasper, V. Khemani, J. Kwan, L. Santos and J. Schmiedmayer. We were supported by grants from the National Science Foundation, the Gordon and Betty Moore Foundations EPiQS Initiative, an Air Force Office of Scientific Research MURI programme, an Army Research Office MURI programme and the NSF Graduate Research Fellowship Program. J.L. acknowledges support from the Swiss National Science Foundation.

Author information

Authors and Affiliations

  1. Department of Physics, Harvard University, Cambridge, MA, USA

    Matthew Rispoli, Alexander Lukin, Robert Schittko, Sooshin Kim, M. Eric Tai, Julian Léonard & Markus Greiner

Authors
  1. Matthew Rispoli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexander Lukin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Robert Schittko
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sooshin Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. M. Eric Tai
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Julian Léonard
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Markus Greiner
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed extensively to the construction of the experiment, the collection and analysis of the data, and the writing of the manuscript. M.G. supervised the work.

Corresponding author

Correspondence to Markus Greiner.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Peer review information Nature thanks Maksym Serbyn and Jean-Philippe Brantut for their contribution to the peer review of this work.

Supplementary information

Supplementary Information

Supplementary Sections 1–9, including Supplementary Figs. 1–7 and Supplementary Table 1.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rispoli, M., Lukin, A., Schittko, R. et al. Quantum critical behaviour at the many-body localization transition. Nature 573, 385–389 (2019). https://doi.org/10.1038/s41586-019-1527-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-019-1527-2

  • Springer Nature Limited

This article is cited by

Search

Navigation