- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

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
  • Letter
  • Open Access

Disorder-free localization transition in a two-dimensional lattice gauge theory

Nilotpal Chakraborty1,*, Markus Heyl1,2, Petr Karpov1, and Roderich Moessner1

  • 1Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, D-01187 Dresden, Germany
  • 2Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, D-86135 Augsburg, Germany

  • *Corresponding author: nilotpal@pks.mpg.de
PDF

Phys. Rev. B 106, L060308 – Published 26 August, 2022

DOI: https://doi.org/10.1103/PhysRevB.106.L060308

Abstract

Disorder-free localization has been proposed as a mechanism for ergodicity breaking in lattice gauge theories (LGTs) which can even occur in two spatial dimensions (2D). It has been shown that the U(1) quantum link model (QLM) can localize due to an emergent classical percolation transition fragmenting the system into disconnected real-space clusters. While the nature of the quantum localization transition (QLT) is still debated for conventional many-body localization, here we provide a comprehensive characterization of the QLT for the QLM in 2D for a disorder-free case. In this Letter we find compelling evidence that the QLT in the 2D QLM is continuous and we determine its universality class. We base our considerations on a spectral analysis of finite-size clusters in the percolation problem which exhibits two regimes—one in which large clusters effectively behave nonergodically, a result naturally accounted for as an interference phenomenon in configuration space, and the other in which all large clusters behave ergodically. Our analysis can also be applied to other 2D U(1) LGTs potentially including also matter degrees of freedom.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (37)

  1. P. W. Anderson, Phys. Rev. 109, 1492 (1958).
  2. E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).
  3. D. M. Basko, I. L. Aleiner, and B. L. Altshuler, Ann. Phys. 321, 1126 (2006).
  4. J. Z. Imbrie, J. Stat. Phys. 163, 998 (2016).
  5. W. De Roeck and F. Huveneers, Phys. Rev. B 95, 155129 (2017).
  6. I.-D. Potirniche, S. Banerjee, and E. Altman, Phys. Rev. B 99, 205149 (2019).
  7. V. Oganesyan and D. A. Huse, Phys. Rev. B 75, 155111 (2007).
  8. A. Pal and D. A. Huse, Phys. Rev. B 82, 174411 (2010).
  9. J. Šuntajs, J. Bonča, T. Prosen, and L. Vidmar, Phys. Rev. E 102, 062144 (2020).
  10. A. Morningstar, L. Colmenarez, V. Khemani, D. J. Luitz, and D. A. Huse, Phys. Rev. B 105, 174205 (2022).
  11. D. Abanin, J. H. Bardarson, G. De Tomasi, S. Gopalakrishnan, V. Khemani, S. Parameswaran, F. Pollmann, A. Potter, M. Serbyn, and R. Vasseur, Ann. Phys. 427, 168415 (2021).
  12. A. Smith, J. Knolle, D. L. Kovrizhin, and R. Moessner, Phys. Rev. Lett. 118, 266601 (2017).
  13. M. Brenes, M. Dalmonte, M. Heyl, and A. Scardicchio, Phys. Rev. Lett. 120, 030601 (2018).
  14. I. Papaefstathiou, A. Smith, and J. Knolle, Phys. Rev. B 102, 165132 (2020).
  15. J. C. Halimeh, L. Homeier, H. Zhao, A. Bohrdt, F. Grusdt, P. Hauke, and J. Knolle, PRX Quantum 3, 020345 (2022).
  16. J. C. Halimeh, H. Zhao, P. Hauke, and J. Knolle, arXiv:2111.02427.
  17. W.-H. Li, X. Deng, and L. Santos, Phys. Rev. Lett. 127, 260601 (2021).
  18. T. Hodson, J. Willsher, and J. Knolle, Phys. Rev. B 104, 045116 (2021).
  19. P. Karpov, R. Verdel, Y.-P. Huang, M. Schmitt, and M. Heyl, Phys. Rev. Lett. 126, 130401 (2021).
  20. R. Verdel, M. Schmitt, Y.-P. Huang, P. Karpov, and M. Heyl, Phys. Rev. B 103, 165103 (2021).
  21. U.-J. Wiese, Ann. Phys. 525, 777 (2013).
  22. S. Chandrasekharan and U.-J. Wiese, Nucl. Phys. B 492, 455 (1997).
  23. D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988).
  24. A. Y. Kitaev, Ann. Phys. 303, 2 (2003).
  25. M. Hermele, M. P. A. Fisher, and L. Balents, Phys. Rev. B 69, 064404 (2004).
  26. N. Shannon, G. Misguich, and K. Penc, Phys. Rev. B 69, 220403(R) (2004).
  27. R. Moessner and S. L. Sondhi, Phys. Rev. B 63, 224401 (2001).
  28. A. W. Glaetzle, M. Dalmonte, R. Nath, I. Rousochatzakis, R. Moessner, and P. Zoller, Phys. Rev. X 4, 041037 (2014).
  29. A. Celi, B. Vermersch, O. Viyuela, H. Pichler, M. D. Lukin, and P. Zoller, Phys. Rev. X 10, 021057 (2020).
  30. G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kalinowski, R. Samajdar et al., Science 374, 1242 (2021).
  31. D. Banerjee and A. Sen, Phys. Rev. Lett. 126, 220601 (2021).
  32. M. E. J. Newman and R. M. Ziff, Phys. Rev. E 64, 016706 (2001).
  33. D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor & Francis, London, 2018).
  34. S. Roy and D. E. Logan, Phys. Rev. B 101, 134202 (2020).
  35. N. Macé, F. Alet, and N. Laflorencie, Phys. Rev. Lett. 123, 180601 (2019).
  36. S. D. Pace, S. C. Morampudi, R. Moessner, and C. R. Laumann, Phys. Rev. Lett. 127, 117205 (2021).
  37. N. Chakraborty, M. Heyl, P. Karpov, and R. Moessner, Zenodo (2022).

Outline

Information

Phys. Rev. B 106, L060308– Published 26 August, 2022
  • Received 28 March 2022
  • Revised 15 August 2022
  • Accepted 16 August 2022
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. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation