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Annual Review of Condensed Matter Physics

Volume 15, 2024

Superdiffusion from Nonabelian Symmetries in Nearly Integrable Systems

Abstract

The Heisenberg spin chain is a canonical integrable model. As such, it features stable ballistically propagating quasiparticles, but spin transport is subballistic at any nonzero temperature: An initially localized spin fluctuation spreads in time to a width 2/3. This exponent as well as the functional form of the dynamical spin correlation function suggest that spin transport is in the Kardar–Parisi–Zhang (KPZ) universality class. However, the full counting statistics of magnetization is manifestly incompatible with KPZ scaling. A simple two-mode hydrodynamic description, derivable from microscopic principles, captures both the KPZ scaling of the correlation function and the coarse features of the full counting statistics, but remains to be numerically validated. These results generalize to any integrable spin chain invariant under a continuous nonabelian symmetry and are surprisingly robust against moderately strong integrability-breaking perturbations that respect the nonabelian symmetry.

Keyword(s): anomalous transport, hydrodynamics, quantum spin chains
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2024-03-11
2024-10-13
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Literature Cited

  1. 1.
    Bloch I, Dalibard J, Zwerger W. 2008. Rev. Mod. Phys. 80:3885–964
     [Google Scholar]
  2. 2.
    Prosen T, Žnidarič M. 2009. J. Stat. Mech.: Theory Exp. 2009:02P02035
     [Google Scholar]
  3. 3.
    Žnidarič M. 2011. J. Stat. Mech.: Theory Exp. 2011:12P12008
     [Google Scholar]
  4. 4.
    Steinigeweg R, Gemmer J. 2009. Phys. Rev. B 80:18184402
     [Google Scholar]
  5. 5.
    Ljubotina M, Žnidarič M, Prosen T. 2017. Nat. Commun. 8:16117
     [Google Scholar]
  6. 6.
    Bertini B, Heidrich-Meisner F, Karrasch C, Prosen T, Steinigeweg R, Znidarič M. 2021. Rev. Mod. Phys. 93:2025003
     [Google Scholar]
  7. 7.
    Prosen T. 2011. Phys. Rev. Lett. 106:21217206
     [Google Scholar]
  8. 8.
    Ilievski E, De Nardis J, Wouters B, Caux JS, Essler FHL, Prosen T. 2015. Phys. Rev. Lett. 115:15157201
     [Google Scholar]
  9. 9.
    Castro-Alvaredo OA, Doyon B, Yoshimura T. 2016. Phys. Rev. X 6:4041065
     [Google Scholar]
  10. 10.
    Bertini B, Collura M, De Nardis J, Fagotti M. 2016. Phys. Rev. Lett. 117:20207201
     [Google Scholar]
  11. 11.
    Doyon B. 2020. 2018-08: Integrability in Atomic and Condensed Matter Physics, Les Houches Summer School Lecture Notes, SciPost Phys. Lect. Notes 18
    [Google Scholar]
  12. 12.
    Bastianello A, Bertini B, Doyon B, Vasseur R. 2022. J. Stat. Mech.: Theory Exp. 2022:014001
     [Google Scholar]
  13. 13.
    Doyon B, Yoshimura T. 2017. SciPost Phys. 2:2014
     [Google Scholar]
  14. 14.
    Ilievski E, De Nardis J. 2017. Phys. Rev. Lett. 119:2020602
     [Google Scholar]
  15. 15.
    Bulchandani VB, Vasseur R, Karrasch C, Moore JE. 2017. Phys. Rev. Lett. 119:22220604
     [Google Scholar]
  16. 16.
    Bulchandani VB, Vasseur R, Karrasch C, Moore JE. 2018. Phys. Rev. B 97:4045407
     [Google Scholar]
  17. 17.
    Piroli L, De Nardis J, Collura M, Bertini B, Fagotti M. 2017. Phys. Rev. B 96:11115124
     [Google Scholar]
  18. 18.
    Doyon B, Spohn H. 2017. SciPost Phys. 3:6039
     [Google Scholar]
  19. 19.
    Doyon B, Spohn H. 2017. J. Stat. Mech.: Theory Exp. 2017:7073210
     [Google Scholar]
  20. 20.
    Doyon B, Yoshimura T, Caux JS. 2018. Phys. Rev. Lett. 120:4045301
     [Google Scholar]
  21. 21.
    Doyon B, Dubail J, Konik R, Yoshimura T. 2017. Phys. Rev. Lett. 119:19195301
     [Google Scholar]
  22. 22.
    Ilievski E, De Nardis J. 2017. Phys. Rev. B 96:8081118
     [Google Scholar]
  23. 23.
    Collura M, De Luca A, Viti J. 2018. Phys. Rev. B 97:8081111
     [Google Scholar]
  24. 24.
    Alba V, Calabrese P. 2017. PNAS 114:307947–51
     [Google Scholar]
  25. 25.
    Bertini B, Piroli L, Calabrese P. 2018. Phys. Rev. Lett. 120:17176801
     [Google Scholar]
  26. 26.
    De Nardis J, Bernard D, Doyon B. 2018. Phys. Rev. Lett. 121:16160603
     [Google Scholar]
  27. 27.
    Gopalakrishnan S, Huse DA, Khemani V, Vasseur R. 2018. Phys. Rev. B 98:22220303
     [Google Scholar]
  28. 28.
    De Nardis J, Bernard D, Doyon B. 2019. SciPost Phys. 6:449
     [Google Scholar]
  29. 29.
    Bertini B, Piroli L, Kormos M. 2019. Phys. Rev. B 100:3035108
     [Google Scholar]
  30. 30.
    Schemmer M, Bouchoule I, Doyon B, Dubail J. 2019. Phys. Rev. Lett. 122:9090601
     [Google Scholar]
  31. 31.
    Bastianello A, Alba V, Caux JS. 2019. Phys. Rev. Lett. 123:13130602
     [Google Scholar]
  32. 32.
    Pozsgay B. 2020. SciPost Phys. 8:216
     [Google Scholar]
  33. 33.
    Borsi M, Pozsgay B, Pristyák L. 2020. Phys. Rev. X 10:011054
     [Google Scholar]
  34. 34.
    Yoshimura T, Spohn H. 2020. SciPost Phys. 9:040
     [Google Scholar]
  35. 35.
    Pozsgay B. 2020. Phys. Rev. Lett. 125:7070602
     [Google Scholar]
  36. 36.
    Møller FS, Schmiedmayer J. 2020. SciPost Phys. 8:341
     [Google Scholar]
  37. 37.
    Gopalakrishnan S, Vasseur R. 2019. Phys. Rev. Lett. 122:12127202
     [Google Scholar]
  38. 38.
    Medenjak M, De Nardis J, Yoshimura T. 2020. SciPost Phys. 9:075
     [Google Scholar]
  39. 39.
    Doyon B. 2022. J. Stat. Phys. 186:25
     [Google Scholar]
  40. 40.
    Sánchez RJ, Varma VK, Oganesyan V. 2018. Phys. Rev. B 98:5054415
     [Google Scholar]
  41. 41.
    Ilievski E, De Nardis J, Medenjak M, Prosen T. 2018. Phys. Rev. Lett. 121:23230602
     [Google Scholar]
  42. 42.
    Gopalakrishnan S, Vasseur R, Ware B. 2019. PNAS 116:3316250–55
     [Google Scholar]
  43. 43.
    De Nardis J, Medenjak M, Karrasch C, Ilievski E. 2019. Phys. Rev. Lett. 123:18186601
     [Google Scholar]
  44. 44.
    Ljubotina M, Znidarič M, Prosen T. 2019. Phys. Rev. Lett. 122:21210602
     [Google Scholar]
  45. 45.
    Das A, Kulkarni M, Spohn H, Dhar A. 2019. Phys. Rev. E 100:4042116
     [Google Scholar]
  46. 46.
    Agrawal U, Gopalakrishnan S, Vasseur R, Ware B. 2020. Phys. Rev. B 101:22224415
     [Google Scholar]
  47. 47.
    Bulchandani VB. 2020. Phys. Rev. B 101:4041411
     [Google Scholar]
  48. 48.
    Krajnik Z, Ilievski E, Prosen T. 2020. SciPost Phys. 9:038
     [Google Scholar]
  49. 49.
    De Nardis J, Gopalakrishnan S, Ilievski E, Vasseur R. 2020. Phys. Rev. Lett. 125:7070601
     [Google Scholar]
  50. 50.
    Fava M, Ware B, Gopalakrishnan S, Vasseur R, Parameswaran SA. 2020. Phys. Rev. B 102:11115121
     [Google Scholar]
  51. 51.
    Ilievski E, De Nardis J, Gopalakrishnan S, Vasseur R, Ware B. 2021. Phys. Rev. X 11:3031023
     [Google Scholar]
  52. 52.
    Kardar M, Parisi G, Zhang YC. 1986. Phys. Rev. Lett. 56:9889–92
     [Google Scholar]
  53. 53.
    Prähofer M, Spohn H. 2004. 1151/2255–79
  54. 54.
    Quastel J. 2014. XVIIth International Congress on Mathematical Physics A Jensen 113–33 Singapore: World Sci.
     [Google Scholar]
  55. 55.
    Scheie A, Sherman NE, Dupont M, Nagler SE, Stone MB et al. 2021. Nat. Phys. 17:6726–30
     [Google Scholar]
  56. 56.
    Wei D, Rubio-Abadal A, Ye B, Machado F, Kemp J et al. 2022. Science 376:6594716–20
     [Google Scholar]
  57. 57.
    Krajnik Ž, Prosen T. 2020. J. Stat. Phys. 179:110–30
     [Google Scholar]
  58. 58.
    Ye B, Machado F, Kemp J, Hutson RB, Yao NY. 2022. Phys. Rev. Lett. 129:23230602
     [Google Scholar]
  59. 59.
    Krajnik Z, Ilievski E, Prosen T. 2022. Phys. Rev. Lett. 128:9090604
     [Google Scholar]
  60. 60.
    De Nardis J, Gopalakrishnan S, Vasseur R. 2022. arXiv:2212.03696
  61. 61.
    Bulchandani VB, Gopalakrishnan S, Ilievski E. 2021. J. Stat. Mech.: Theory Exp. 2021:8084001
     [Google Scholar]
  62. 62.
    Gopalakrishnan S, Vasseur R. 2022. Rep. Prog. Phys. 86:036502
     [Google Scholar]
  63. 63.
    Takahashi M. 1999. Thermodynamics of One-Dimensional Solvable Models Cambridge, UK: Cambridge Univ. Press
     [Google Scholar]
  64. 64.
    Dugave M, Göhmann F, Kozlowski KK, Suzuki J. 2016. J. Phys. A: Math. Theor. 49:39394001
     [Google Scholar]
  65. 65.
    Ilievski E, Quinn E, De Nardis J, Brockmann M. 2016. J. Stat. Mech.: Theory Exp. 2016:6063101
     [Google Scholar]
  66. 66.
    Prosen T, Ilievski E. 2013. Phys. Rev. Lett. 111:5057203
     [Google Scholar]
  67. 67.
    Zadnik L, Bidzhiev K, Fagotti M. 2021. SciPost Phys. 10:599
     [Google Scholar]
  68. 68.
    Fagotti M. 2014. J. Stat. Mech.: Theory Exp. 2014:3P03016
     [Google Scholar]
  69. 69.
    Pozsgay B, Eisler V. 2016. J. Stat. Mech.: Theory Exp. 2016:5053107
     [Google Scholar]
  70. 70.
    De Nardis J, Gopalakrishnan S, Vasseur R, Ware B. 2022. PNAS 119:34e2202823119
     [Google Scholar]
  71. 71.
    Gopalakrishnan S, Morningstar A, Vasseur R, Khemani V. 2022. arXiv:2203.09526
  72. 72.
    Cecile G, De Nardis J, Ilievski E. 2022. arXiv:2303.08832
  73. 73.
    Damle K, Sachdev S. 2005. Phys. Rev. Lett. 95:18187201
     [Google Scholar]
  74. 74.
    Damle K, Sachdev S. 1998. Phys. Rev. B 57:148307–39
     [Google Scholar]
  75. 75.
    Ljubotina M, Zadnik L, Prosen T. 2019. Phys. Rev. Lett. 122:15150605
     [Google Scholar]
  76. 76.
    Corwin I. 2011. arXiv:1106.1596
  77. 77.
    Spohn H. 2014. J. Stat. Phys. 154:51191–227
     [Google Scholar]
  78. 78.
    Nahum A, Ruhman J, Vijay S, Haah J. 2017. Phys. Rev. X 7:3031016
     [Google Scholar]
  79. 79.
    Fontaine Q, Squizzato D, Baboux F, Amelio I, Lemaître A et al. 2022. Nature 608:7924687–91
     [Google Scholar]
  80. 80.
    Jin T, Krajenbrink A, Bernard D. 2020. Phys. Rev. Lett. 125:4040603
     [Google Scholar]
  81. 81.
    Jin T, Martin DG. 2022. Phys. Rev. Lett. 129:260603
     [Google Scholar]
  82. 82.
    Bernard D, Doussal PL. 2020. Europhys. Lett. 131:10007
     [Google Scholar]
  83. 83.
    Diessel OK, Diehl S, Chiocchetta A. 2022. Phys. Rev. Lett. 128:7070401
     [Google Scholar]
  84. 84.
    Delacrétaz LV, Glorioso P. 2020. Phys. Rev. Lett. 124:23236802
     [Google Scholar]
  85. 85.
    Sasamoto T, Spohn H. 2010. Phys. Rev. Lett. 104:23230602
     [Google Scholar]
  86. 86.
    Amir G, Corwin I, Quastel J. 2011. Commun. Pure Appl. Math. 64:4466–537
     [Google Scholar]
  87. 87.
    Calabrese P, Le Doussal P 2011. Phys. Rev. Lett. 106:25250603
     [Google Scholar]
  88. 88.
    Imamura T, Sasamoto T. 2013. J. Stat. Phys. 150:908–39
     [Google Scholar]
  89. 89.
    Bertini L, De Sole A, Gabrielli D, Jona-Lasinio G, Landim C. 2015. Rev. Mod. Phys. 87:2593–636
     [Google Scholar]
  90. 90.
    McCulloch E, De Nardis J, Gopalakrishnan S, Vasseur R. 2023. arXiv:2302.01355
  91. 91.
    Lakshmanan M, Ruijgrok TW, Thompson C. 1976. Phys. A: Stat. Mech. Appl. 84:3577–90
     [Google Scholar]
  92. 92.
    Theodorakopoulos N, Bacalis NC. 1991. Phys. Rev. Lett. 67:213018–21
     [Google Scholar]
  93. 93.
    De Nardis J, Gopalakrishnan S, Vasseur R, Ware B. 2021. Phys. Rev. Lett. 127:5057201
     [Google Scholar]
  94. 94.
    Dupont M, Sherman NE, Moore JE. 2021. Phys. Rev. Lett. 127:10107201
     [Google Scholar]
  95. 95.
    Dupont M, Moore JE. 2020. Phys. Rev. B 101:12121106
     [Google Scholar]
  96. 96.
    Baik J, Rains EM. 2000. J. Stat. Phys. 100:3523–41
     [Google Scholar]
  97. 97.
    Cecile G, Gopalakrishnan S, Vasseur R, De Nardis J. 2023. Phys. Rev. B 108:075135
     [Google Scholar]
  98. 98.
    Gamayun O, Miao Y, Ilievski E. 2019. Phys. Rev. B 99:14140301
     [Google Scholar]
  99. 99.
    Stéphan JM. 2017. J. Stat. Mech.: Theory Exp. 2017:10103108
     [Google Scholar]
  100. 100.
    Hild S, Fukuhara T, Schauß P, Zeiher J, Knap M et al. 2014. Phys. Rev. Lett. 113:14147205
     [Google Scholar]
  101. 101.
    Jepsen PN, Amato-Grill J, Dimitrova I, Ho WW, Demler E, Ketterle W. 2020. Nature 588:7838403–7
     [Google Scholar]
  102. 102.
    Basko D. 2011. Ann. Phys. 326:71577–655
     [Google Scholar]
  103. 103.
    Roy D, Dhar A, Spohn H, Kulkarni M. 2023. Phys. Rev. B 107:L100413
     [Google Scholar]
  104. 104.
    McRoberts AJ, Bilitewski T, Haque M, Moessner R. 2022. Phys. Rev. B 105:10L100403
     [Google Scholar]
  105. 105.
    McRoberts AJ, Bilitewski T, Haque M, Moessner R. 2022. Phys. Rev. E 106:6L062202
     [Google Scholar]
  106. 106.
    Claeys PW, Lamacraft A, Herzog-Arbeitman J. 2022. Phys. Rev. Lett. 128:24246603
     [Google Scholar]
  107. 107.
    Glorioso P, Delacrétaz LV, Chen X, Nandkishore RM, Lucas A. 2021. SciPost Phys. 10:015
     [Google Scholar]
  108. 108.
    Friedman AJ, Gopalakrishnan S, Vasseur R. 2022. Phys. Rev. B 101:18180302
     [Google Scholar]
  109. 109.
    Bastianello A, De Nardis J, De Luca A. 2020. Phys. Rev. B 102:16161110
     [Google Scholar]
  110. 110.
    Durnin J, Bhaseen MJ, Doyon B. 2021. Phys. Rev. Lett. 127:13130601
     [Google Scholar]
  111. 111.
    Bastianello A, Luca AD, Vasseur R. 2021. J. Stat. Mech.: Theory Exp. 2021:11114003
     [Google Scholar]
  112. 112.
    Kurlov DV, Malikis S, Gritsev V. 2022. Phys. Rev. B 105:10104302
     [Google Scholar]
  113. 113.
    Szász-Schagrin D, Pozsgay B, Takacs G. 2021. SciPost Phys. 11:2037
     [Google Scholar]
  114. 114.
    Surace FM, Motrunich O. 2023. Phys. Rev. Res. 5:043019
     [Google Scholar]
  115. 115.
    Orlov P, Tiutiakina A, Sharipov R, Petrova E, Gritsev V, Kurlov DV. 2023. Phys. Rev. B 107:184312
     [Google Scholar]
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Superdiffusion from Nonabelian Symmetries in Nearly Integrable Systems
Annual Review of Condensed Matter Physics 15, 159 (2024); https://doi.org/10.1146/annurev-conmatphys-032922-110710
/content/journals/10.1146/annurev-conmatphys-032922-110710
/content/journals/10.1146/annurev-conmatphys-032922-110710
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