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  • Letter
  • Open Access

Ergodic inclusions in many-body localized systems

Luis Colmenarez1,2,3,*, David J. Luitz4,†, and Wojciech De Roeck5,‡

  • 1Institute for Quantum Information, RWTH Aachen University, 52056 Aachen, Germany
  • 2Institute for Theoretical Nanoelectronics (PGI-2), Forschungszentrum Jülich, 52428 Jülich, Germany
  • 3Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187-Dresden, Germany
  • 4Institute of Physics, University of Bonn, Nußallee 12, 53115 Bonn, Germany
  • 5KU Leuven, 3001 Leuven, Belgium

  • *colmenarez@physik.rwth-aachen.de
  • †dluitz@uni-bonn.de
  • ‡wojciech.deroeck@kuleuven.be
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Phys. Rev. B 109, L081117 – Published 28 February, 2024

DOI: https://doi.org/10.1103/PhysRevB.109.L081117

Abstract

We investigate the effect of ergodic inclusions in putative many-body localized systems. We consider the random field Heisenberg chain, which is many-body localized at strong disorder and we couple it to an ergodic bubble, modeled by a random matrix Hamiltonian. Recent theoretical work suggests that localized systems are unstable to ergodic bubbles, driving the delocalization transition. We tentatively confirm this by numerically analyzing the response of the on-site purities to the insertion of the bubble. For a range of intermediate disorder strengths, this response decays very slowly, or not at all, with increasing distance to the bubble. This suggests that at those disorder strengths, the system is actually delocalized in the thermodynamic limit. However, the signal is quite weak and artefacts in the numerics cannot be ruled out conclusively.

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References (80)

  1. P. W. Anderson, Phys. Rev. 109, 1492 (1958).
  2. L. Fleishman and P. W. Anderson, Phys. Rev. B 21, 2366 (1980).
  3. I. V. Gornyi, A. D. Mirlin, and D. G. Polyakov, Phys. Rev. Lett. 95, 206603 (2005).
  4. D. M. Basko, I. L. Aleiner, and B. L. Altshuler, Ann. Phys. 321, 1126 (2006).
  5. V. Oganesyan and D. A. Huse, Phys. Rev. B 75, 155111 (2007).
  6. J. Z. Imbrie, J. Stat. Phys. 163, 998 (2016).
  7. J. Z. Imbrie, Phys. Rev. Lett. 117, 027201 (2016).
  8. M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Lüschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, and I. Bloch, Science 349, 842 (2015).
  9. H. P. Lüschen, P. Bordia, S. S. Hodgman, M. Schreiber, S. Sarkar, A. J. Daley, M. H. Fischer, E. Altman, I. Bloch, and U. Schneider, Phys. Rev. X 7, 011034 (2017).
  10. J. Smith, A. Lee, P. Richerme, B. Neyenhuis, P. W. Hess, P. Hauke, M. Heyl, D. A. Huse, and C. Monroe, Nat. Phys. 12, 907 (2016).
  11. J. M. Deutsch, Phys. Rev. A 43, 2046 (1991).
  12. M. Srednicki, Phys. Rev. E 50, 888 (1994).
  13. M. Rigol, V. Dunjko, and M. Olshanii, Nature (London) 452, 854 (2008).
  14. L. D'Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, Adv. Phys. 65, 239 (2016).
  15. R. Nandkishore and D. A. Huse, Annu. Rev. Condens. Matter Phys. 6, 15 (2015).
  16. R. Vosk, D. A. Huse, and E. Altman, Phys. Rev. X 5, 031032 (2015).
  17. D. A. Abanin and Z. Papić, Ann. Phys. 529, 1700169 (2017).
  18. J. Z. Imbrie, V. Ros, and A. Scardicchio, Ann. Phys. 529, 1600278 (2017).
  19. D. J. Luitz and Y. B. Lev, Ann. Phys. 529, 1600350 (2017).
  20. K. Agarwal, E. Altman, E. Demler, S. Gopalakrishnan, D. A. Huse, and M. Knap, Ann. Phys. 529, 1600326 (2017).
  21. F. Alet and N. Laflorencie, C. R. Phys. 19, 498 (2018).
  22. D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Rev. Mod. Phys. 91, 021001 (2019).
  23. M. Serbyn, Z. Papić, and D. A. Abanin, Phys. Rev. Lett. 111, 127201 (2013).
  24. D. A. Huse, R. Nandkishore, and V. Oganesyan, Phys. Rev. B 90, 174202 (2014).
  25. B. Bauer and C. Nayak, J. Stat. Mech. (2013) P09005.
  26. D. J. Luitz, Phys. Rev. B 93, 134201 (2016).
  27. X. Yu, D. J. Luitz, and B. K. Clark, Phys. Rev. B 94, 184202 (2016).
  28. G. D. Chiara, S. Montangero, P. Calabrese, and R. Fazio, J. Stat. Mech. (2006) P03001.
  29. M. Žnidarič, T. Prosen, and P. Prelovšek, Phys. Rev. B 77, 064426 (2008).
  30. J. H. Bardarson, F. Pollmann, and J. E. Moore, Phys. Rev. Lett. 109, 017202 (2012).
  31. M. Serbyn, Z. Papić, and D. A. Abanin, Phys. Rev. Lett. 110, 260601 (2013).
  32. D. A. Abanin, J. H. Bardarson, G. De Tomasi, S. Gopalakrishnan, V. Khemani, S. A. Parameswaran, F. Pollmann, A. C. Potter, M. Serbyn, and R. Vasseur, Ann. Phys. 427, 168415 (2021).
  33. R. K. Panda, A. Scardicchio, M. Schulz, S. R. Taylor, and M. Žnidarič, Europhys. Lett. 128, 67003 (2020).
  34. R. Ghosh and M. Žnidarič, Phys. Rev. B 105, 144203 (2022).
  35. M. Kiefer-Emmanouilidis, R. Unanyan, M. Fleischhauer, and J. Sirker, Phys. Rev. B 103, 024203 (2021).
  36. D. J. Luitz and Y. B. Lev, Phys. Rev. B 102, 100202 (2020).
  37. A. Morningstar, L. Colmenarez, V. Khemani, D. J. Luitz, and D. A. Huse, Phys. Rev. B 105, 174205 (2022).
  38. D. Sels, Phys. Rev. B 106, L020202 (2022).
  39. D. Sels and A. Polkovnikov, Phys. Rev. E 104, 054105 (2021).
  40. D. Sels and A. Polkovnikov, Phys. Rev. X 13, 011041 (2023).
  41. P. Sierant, D. Delande, and J. Zakrzewski, Phys. Rev. Lett. 124, 186601 (2020).
  42. J. Šuntajs, J. Bonča, T. Prosen, and L. Vidmar, Phys. Rev. B 102, 064207 (2020).
  43. J. Šuntajs, J. Bonča, T. Prosen, and L. Vidmar, Phys. Rev. E 102, 062144 (2020).
  44. P. Sierant, M. Lewenstein, and J. Zakrzewski, Phys. Rev. Lett. 125, 156601 (2020).
  45. P. Sierant and J. Zakrzewski, Phys. Rev. B 105, 224203 (2022).
  46. F. Weiner, F. Evers, and S. Bera, Phys. Rev. B 100, 104204 (2019).
  47. P. Crowley and A. Chandran, SciPost Phys. 12, 201 (2022).
  48. E. V. H. Doggen, F. Schindler, K. S. Tikhonov, A. D. Mirlin, T. Neupert, D. G. Polyakov, and I. V. Gornyi, Phys. Rev. B 98, 174202 (2018).
  49. F. Evers, I. Modak, and S. Bera, Phys. Rev. B 108, 134204 (2023).
  50. S. Kondov, W. McGehee, W. Xu, and B. DeMarco, Phys. Rev. Lett. 114, 083002 (2015).
  51. M. Gong, G. D. de Moraes Neto, C. Zha, Y. Wu, H. Rong, Y. Ye, S. Li, Q. Zhu, S. Wang, Y. Zhao, F. Liang, J. Lin, Y. Xu, C.-Z. Peng, H. Deng, A. Bayat, X. Zhu, and J.-W. Pan, Phys. Rev. Res. 3, 033043 (2021).
  52. Y. Bar Lev, G. Cohen, and D. R. Reichman, Phys. Rev. Lett. 114, 100601 (2015).
  53. K. Agarwal, S. Gopalakrishnan, M. Knap, M. Müller, and E. Demler, Phys. Rev. Lett. 114, 160401 (2015).
  54. D. J. Luitz, N. Laflorencie, and F. Alet, Phys. Rev. B 93, 060201 (2016).
  55. H. P. Lüschen, P. Bordia, S. Scherg, F. Alet, E. Altman, U. Schneider, and I. Bloch, Phys. Rev. Lett. 119, 260401 (2017).
  56. T. L. M. Lezama, S. Bera, and J. H. Bardarson, Phys. Rev. B 99, 161106 (2019).
  57. D. J. Luitz and Y. Bar Lev, Phys. Rev. Lett. 117, 170404 (2016).
  58. S. Roy, Y. B. Lev, and D. J. Luitz, Phys. Rev. B 98, 060201 (2018).
  59. L. A. Colmenarez, P. A. McClarty, M. Haque, and D. J. Luitz, SciPost Phys. 7, 064 (2019).
  60. M. Žnidarič, A. Scardicchio, and V. K. Varma, Phys. Rev. Lett. 117, 040601 (2016).
  61. S. Gopalakrishnan, K. Agarwal, E. A. Demler, D. A. Huse, and M. Knap, Phys. Rev. B 93, 134206 (2016).
  62. A. C. Potter, R. Vasseur, and S. Parameswaran, Phys. Rev. X 5, 031033 (2015).
  63. Y. B. Lev, D. M. Kennes, C. Klöckner, D. R. Reichman, and C. Karrasch, Europhys. Lett. 119, 37003 (2017).
  64. D. M. Long, P. J. D. Crowley, V. Khemani, and A. Chandran, Phys. Rev. Lett. 131, 106301 (2023).
  65. W. De Roeck and F. Huveneers, Phys. Rev. B 95, 155129 (2017).
  66. W. De Roeck and J. Z. Imbrie, Philos. Trans. R. Soc. A 375, 20160422 (2017).
  67. T. Thiery, F. Huveneers, M. Müller, and W. De Roeck, Phys. Rev. Lett. 121, 140601 (2018).
  68. D. J. Luitz, F. Huveneers, and W. De Roeck, Phys. Rev. Lett. 119, 150602 (2017).
  69. P. J. D. Crowley and A. Chandran, Phys. Rev. Res. 2, 033262 (2020).
  70. P. Ponte, C. R. Laumann, D. A. Huse, and A. Chandran, Philos. Trans. R. Soc. A 375, 20160428 (2017).
  71. I.-D. Potirniche, S. Banerjee, and E. Altman, Phys. Rev. B 99, 205149 (2019).
  72. M. Goihl, J. Eisert, and C. Krumnow, Phys. Rev. B 99, 195145 (2019).
  73. G. De Tomasi, I. M. Khaymovich, F. Pollmann, and S. Warzel, Phys. Rev. B 104, 024202 (2021).
  74. Y.-T. Tu, D. Vu, and S. Das Sarma, Phys. Rev. B 107, 014203 (2023).
  75. Y.-T. Tu, D. Vu, and S. D. Sarma, Phys. Rev. B 108, 064313 (2023).
  76. A. Rubio-Abadal, J.-Y. Choi, J. Zeiher, S. Hollerith, J. Rui, I. Bloch, and C. Gross, Phys. Rev. X 9, 041014 (2019).
  77. J. Léonard, S. Kim, M. Rispoli, A. Lukin, R. Schittko, J. Kwan, E. Demler, D. Sels, and M. Greiner, Nat. Phys. 19, 481 (2023).
  78. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.109.L081117 for details about the numerical calculations, analysis on additional data, details about the avalanche theory prediction in our model and analytical calculation of the purity correlaton in the infinite disorder limit.
  79. D. J. Luitz, N. Laflorencie, and F. Alet, Phys. Rev. B 91, 081103 (2015).
  80. F. Pietracaprina, N. Macé, D. J. Luitz, and F. Alet, SciPost Phys. 5, 045 (2018).

Outline

Information

Phys. Rev. B 109, L081117– Published 28 February, 2024
  • Received 23 August 2023
  • Revised 15 January 2024
  • Accepted 31 January 2024
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