- Physical Review Journals
All JournalsPhysics Magazine

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

Superdiffusive Transport in Chaotic Quantum Systems with Nodal Interactions

Yu-Peng Wang1,2,3,*, Jie Ren1,4,*, Sarang Gopalakrishnan5, and Romain Vasseur6

  • *These authors contributed equally to this work.
PDF

Phys. Rev. Lett. 135, 166303 – Published 15 October, 2025

DOI: https://doi.org/10.1103/xx9z-4j6c

Abstract

We introduce a class of interacting fermionic quantum models in d dimensions with nodal interactions that exhibit superdiffusive transport. We establish nonperturbatively that the nodal structure of the interactions gives rise to long-lived quasiparticle excitations that result in a diverging diffusion constant, even though the system is fully chaotic. Using a Boltzmann equation approach, we find that the charge mode acquires an anomalous dispersion relation at long wavelength ω(q)∼qz with dynamical exponent z=min[(2n+d)/2n,2], where n is the order of the nodal point in momentum space. We verify our predictions in one-dimensional systems using tensor-network techniques.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (83)

  1. M. Crossleyæ, P. Glorioso, and H. Liu, J. High Energy Phys. 09 (2017) 095.
  2. O. A. Castro-Alvaredo, B. Doyon, and T. Yoshimura, Phys. Rev. X 6, 041065 (2016).
  3. B. Bertini, M. Collura, J. De Nardis, and M. Fagotti, Phys. Rev. Lett. 117, 207201 (2016).
  4. A. Lucas and K. C. Fong, J. Phys. Condens. Matter 30, 053001 (2018).
  5. L. Fritz and T. Scaffidi, Annu. Rev. Condens. Matter Phys. 15, 17 (2024).
  6. M. K. Joshi, F. Kranzl, A. Schuckert, I. Lovas, C. Maier, R. Blatt, M. Knap, and C. F. Roos, Science 376, 720 (2022).
  7. D. Wei, A. Rubio-Abadal, B. Ye, F. Machado, J. Kemp, K. Srakaew, S. Hollerith, J. Rui, S. Gopalakrishnan, N. Y. Yao, I. Bloch, and J. Zeiher, Science 376, 716 (2022).
  8. J. F. Wienand, S. Karch, A. Impertro, C. Schweizer, E. McCulloch, R. Vasseur, S. Gopalakrishnan, M. Aidelsburger, and I. Bloch, Nat. Phys. 20, 1732 (2024).
  9. B. Doyon, S. Gopalakrishnan, F. Møller, J. Schmiedmayer, and R. Vasseur, Phys. Rev. X 15, 010501 (2025).
  10. T. Prosen and M. Žnidarič, Phys. Rev. B 86, 125118 (2012).
  11. C. Karrasch, J. E. Moore, and F. Heidrich-Meisner, Phys. Rev. B 89, 075139 (2014).
  12. J. Lux, J. Müller, A. Mitra, and A. Rosch, Phys. Rev. A 89, 053608 (2014).
  13. M. Žnidarič, A. Scardicchio, and V. K. Varma, Phys. Rev. Lett. 117, 040601 (2016).
  14. M. Blake, R. A. Davison, and S. Sachdev, Phys. Rev. D 96, 106008 (2017).
  15. J. De Nardis, M. Medenjak, C. Karrasch, and E. Ilievski, Phys. Rev. Lett. 124, 210605 (2020).
  16. B. Bertini, F. Heidrich-Meisner, C. Karrasch, T. Prosen, R. Steinigeweg, and M. Žnidarič, Rev. Mod. Phys. 93, 025003 (2021).
  17. A. J. Friedman, S. Gopalakrishnan, and R. Vasseur, Phys. Rev. B 101, 180302 (2020).
  18. P. W. Anderson, Phys. Rev. 109, 1492 (1958).
  19. M. Žnidarič and M. Ljubotina, Proc. Natl. Acad. Sci. U.S.A. 115, 4595 (2018).
  20. Y. Bar Lev, G. Cohen, and D. R. Reichman, Phys. Rev. Lett. 114, 100601 (2015).
  21. K. Agarwal, S. Gopalakrishnan, M. Knap, M. Müller, and E. Demler, Phys. Rev. Lett. 114, 160401 (2015).
  22. D. Basko, I. Aleiner, and B. Altshuler, Ann. Phys. (Amsterdam) 321, 1126 (2006).
  23. Y. B. Lev, D. M. Kennes, C. Klöckner, D. R. Reichman, and C. Karrasch, Europhys. Lett. 119, 37003 (2017).
  24. J. Iaconis, S. Vijay, and R. Nandkishore, Phys. Rev. B 100, 214301 (2019).
  25. J. Feldmeier, P. Sala, G. De Tomasi, F. Pollmann, and M. Knap, Phys. Rev. Lett. 125, 245303 (2020).
  26. A. Gromov, A. Lucas, and R. M. Nandkishore, Phys. Rev. Res. 2, 033124 (2020).
  27. J. Iaconis, A. Lucas, and R. Nandkishore, Phys. Rev. E 103, 022142 (2021).
  28. S. Moudgalya, A. Prem, D. A. Huse, and A. Chan, Phys. Rev. Res. 3, 023176 (2021).
  29. H. Singh, B. A. Ware, R. Vasseur, and A. J. Friedman, Phys. Rev. Lett. 127, 230602 (2021).
  30. J. Richter and A. Pal, Phys. Rev. Res. 4, L012003 (2022).
  31. A. Morningstar, V. Khemani, and D. A. Huse, Phys. Rev. B 101, 214205 (2020).
  32. C. McCarthy, H. Singh, S. Gopalakrishnan, and R. Vasseur, Phys. Rev. B 111, 184317 (2025).
  33. A. Schuckert, I. Lovas, and M. Knap, Phys. Rev. B 101, 020416 (2020).
  34. L. Borland and J. Menchero, Braz. J. Phys. 29, 169 (1999).
  35. A. D. Mirlin, Y. V. Fyodorov, F.-M. Dittes, J. Quezada, and T. H. Seligman, Phys. Rev. E 54, 3221 (1996).
  36. M. Saha, S. K. Maiti, and A. Purkayastha, Phys. Rev. B 100, 174201 (2019).
  37. J. Richter, O. Lunt, and A. Pal, Phys. Rev. Res. 5, L012031 (2023).
  38. B.-L. Cheng, S.-K. Jian, and Z.-C. Yang, Phys. Rev. Lett. 134, 156301 (2025).
  39. T. Prosen and D. K. Campbell, Phys. Rev. Lett. 84, 2857 (2000).
  40. O. Narayan and S. Ramaswamy, Phys. Rev. Lett. 89, 200601 (2002).
  41. H. Spohn, J. Stat. Phys. 154, 1191 (2014).
  42. G. Casati and T. Prosen, Phys. Rev. E 67, 015203 (2003).
  43. T. Prosen and D. K. Campbell, Chaos 15, 015117 (2005).
  44. S. Ostlund, R. Pandit, D. Rand, H. J. Schellnhuber, and E. D. Siggia, Phys. Rev. Lett. 50, 1873 (1983).
  45. M. Kohmoto, L. P. Kadanoff, and C. Tang, Phys. Rev. Lett. 50, 1870 (1983).
  46. H. Hiramoto and S. Abe, J. Phys. Soc. Jpn. 57, 230 (1988).
  47. D. H. Dunlap, H.-L. Wu, and P. W. Phillips, Phys. Rev. Lett. 65, 88 (1990).
  48. G. Cane, J. M. Bhat, A. Dhar, and C. Bernardin, J. Stat. Mech. (2021) P113204.
  49. A. Dhar, Phys. Rev. Lett. 86, 5882 (2001).
  50. R. J. Rubin and W. L. Greer, J. Math. Phys. (N.Y.) 12, 1686 (1971).
  51. S. Gattenlöhner, I. V. Gornyi, P. M. Ostrovsky, B. Trauzettel, A. D. Mirlin, and M. Titov, Phys. Rev. Lett. 117, 046603 (2016).
  52. Y.-P. Wang, J. Ren, and C. Fang, Phys. Rev. B 110, 144201 (2024).
  53. J. M. Bhat, Phys. Rev. B 110, 115405 (2024).
  54. Y.-P. Wang, C. Fang, and J. Ren, SciPost Phys. 17, 150 (2024).
  55. M. Žnidarič, Phys. Rev. B 109, 075105 (2024).
  56. M. Žnidarič, Phys. Rev. Lett. 106, 220601 (2011).
  57. M. Ljubotina, M. Žnidarič, and T. Prosen, Nat. Commun. 8, 16117 (2017).
  58. S. Gopalakrishnan and R. Vasseur, Phys. Rev. Lett. 122, 127202 (2019).
  59. M. Ljubotina, M. Žnidarič, and T. Prosen, Phys. Rev. Lett. 122, 210602 (2019).
  60. E. Ilievski, J. De Nardis, S. Gopalakrishnan, R. Vasseur, and B. Ware, Phys. Rev. X 11, 031023 (2021).
  61. P. W. Claeys, A. Lamacraft, and J. Herzog-Arbeitman, Phys. Rev. Lett. 128, 246603 (2022).
  62. S. Gopalakrishnan and R. Vasseur, Annu. Rev. Condens. Matter Phys. 15, 159 (2024).
  63. J. De Nardis, S. Gopalakrishnan, R. Vasseur, and B. Ware, Phys. Rev. Lett. 127, 057201 (2021).
  64. C. McCarthy, S. Gopalakrishnan, and R. Vasseur, Phys. Rev. B 110, L180301 (2024).
  65. A. J. McRoberts and R. Moessner, Phys. Rev. Lett. 133, 256301 (2024).
  66. M. Ljubotina, J.-Y. Desaules, M. Serbyn, and Z. Papić, Phys. Rev. X 13, 011033 (2023).
  67. P. Mazur, Physica (Amsterdam) 43, 533 (1969).
  68. V. Oganesyan and D. A. Huse, Phys. Rev. B 75, 155111 (2007).
  69. B. S. Shastry and B. Sutherland, Phys. Rev. Lett. 65, 243 (1990).
  70. D. J. Scalapino, S. R. White, and S. C. Zhang, Phys. Rev. Lett. 68, 2830 (1992).
  71. H. Kim, M. C. Bañuls, J. I. Cirac, M. B. Hastings, and D. A. Huse, Phys. Rev. E 92, 012128 (2015).
  72. See Supplemental Material at http://link.aps.org/supplemental/10.1103/xx9z-4j6c for a proof of the lower bound on the diffusion constant, for details of the Boltzmann scattering integrals, and for numerical methods.
  73. X. Cao, A. Tilloy, and A. D. Luca, SciPost Phys. 7, 024 (2019).
  74. U. Schollwöck, Ann. Phys. (Amsterdam) 326, 96 (2011).
  75. G. T. Landi, D. Poletti, and G. Schaller, Rev. Mod. Phys. 94, 045006 (2022).
  76. T. Prosen and M. Žnidarič, J. Stat. Mech. (2009) P02035.
  77. M. Žnidarič, A. Scardicchio, and V. K. Varma, Phys. Rev. Lett. 117, 040601 (2016).
  78. G. Vidal, Phys. Rev. Lett. 91, 147902 (2003).
  79. F. Verstraete, J. J. García-Ripoll, and J. I. Cirac, Phys. Rev. Lett. 93, 207204 (2004).
  80. M. Zwolak and G. Vidal, Phys. Rev. Lett. 93, 207205 (2004).
  81. C. D. White, M. Zaletel, R. S. K. Mong, and G. Refael, Phys. Rev. B 97, 035127 (2018).
  82. M. Fishman, S. R. White, and E. M. Stoudenmire, SciPost Phys. Codebases 4 (2022).
  83. Yu-Peng Wang, Zenedo (2025), 10.5281/zenodo.17192677.

Outline

Information

Phys. Rev. Lett. 135, 166303– Published 15 October, 2025
  • Received 6 February 2025
  • Accepted 23 September 2025
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