- 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

Symmetric Tensor Scars with Tunable Entanglement from Volume to Area Law

Bhaskar Mukherjee1,2, Christopher J. Turner2, Marcin Szyniszewski2,3, and Arijeet Pal2

PDF

Phys. Rev. Lett. 136, 090401 – Published 3 March, 2026

DOI: https://doi.org/10.1103/v8rf-p5zc

Abstract

Teleportation of quantum information over long distances requires robust entanglement on the macroscopic scale. The construction of highly energetic eigenstates with tunable long-range entanglement can provide a new medium for information transmission. Using a symmetric superposition of the antipodal triplet states, we construct polynomially many exact zero-energy eigenstates for a class of nonintegrable spin-1/2 Hamiltonians with two-body interactions. These states exhibit nonthermal correlations, and hence, are genuine quantum many-body scars. By tuning the distribution of triplets, we induce extensive, logarithmic, or area-law entanglement and can observe a second-order entanglement phase transition. Quasiparticle excitations in this manifold converge to be exact quantum many-body scars in the thermodynamic limit. This framework has a natural extension to higher dimensions, where entangled states controlled by lattice geometry and internal symmetries can result in new classes of correlated out-of-equilibrium quantum matter. Our results provide a new avenue for entanglement control and quantum state constructions.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (81)

  1. M. Rigol, V. Dunjko, and M. Olshanii, Nature (London) 452, 854 (2008).
  2. L. D’Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, Adv. Phys. 65, 239 (2016).
  3. H. Kim, T. N. Ikeda, and D. A. Huse, Phys. Rev. E 90, 052105 (2014).
  4. C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papić, Nat. Phys. 14, 745 (2018).
  5. C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papić, Phys. Rev. B 98, 155134 (2018).
  6. S. Moudgalya, S. Rachel, B. A. Bernevig, and N. Regnault, Phys. Rev. B 98, 235155 (2018).
  7. C.-J. Lin and O. I. Motrunich, Phys. Rev. Lett. 122, 173401 (2019).
  8. T. Iadecola and M. Schecter, Phys. Rev. B 101, 024306 (2020).
  9. K. Lee, R. Melendrez, A. Pal, and H. J. Changlani, Phys. Rev. B 101, 241111 (2020).
  10. J. Wildeboer, A. Seidel, N. S. Srivatsa, A. E. B. Nielsen, and O. Erten, Phys. Rev. B 104, L121103 (2021).
  11. N. S. Srivatsa, J. Wildeboer, A. Seidel, and A. E. B. Nielsen, Phys. Rev. B 102, 235106 (2020).
  12. M. Serbyn, D. A. Abanin, and Z. Papić, Nat. Phys. 17, 675 (2021).
  13. J. Richter and A. Pal, Phys. Rev. Res. 4, L012003 (2022).
  14. B. A. B. Sanjay Moudgalya and N. Regnault, Rep. Prog. Phys. 85, 086501 (2022).
  15. A. Chandran, T. Iadecola, V. Khemani, and R. Moessner, Annu. Rev. Condens. Matter Phys. 14, 443 (2023).
  16. H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin, Nature (London) 551, 579 (2017).
  17. J. Jeyaretnam, J. Richter, and A. Pal, Phys. Rev. B 104, 014424 (2021).
  18. N. Shiraishi and T. Mori, Phys. Rev. Lett. 119, 030601 (2017).
  19. C. M. Langlett, Z.-C. Yang, J. Wildeboer, A. V. Gorshkov, T. Iadecola, and S. Xu, Phys. Rev. B 105, L060301 (2022).
  20. G. Vitagliano, A. Riera, and J. I. Latorre, New J. Phys. 12, 113049 (2010).
  21. G. Ramírez, J. Rodríguez-Laguna, and G. Sierra, J. Stat. Mech. (2014) P10004.
  22. G. Ramírez, J. Rodríguez-Laguna, and G. Sierra, J. Stat. Mech. (2015) P06002.
  23. J. Maldacena, J. High Energy Phys. 04 (2003) 021.
  24. T. Hartman and J. Maldacena, J. High Energy Phys. 05 (2013) 014.
  25. K. Papadodimas and S. Raju, Phys. Rev. Lett. 115, 211601 (2015).
  26. W. Cottrell, B. Freivogel, D. M. Hofman, and S. F. Lokhande, J. High Energy Phys. 02 (2019) 058.
  27. Y. Chiba and Y. Yoneta, Phys. Rev. Lett. 133, 170404 (2024).
  28. S. Mohapatra, S. Moudgalya, and A. C. Balram, Phys. Rev. Lett. 134, 210403 (2025).
  29. A. N. Ivanov and O. I. Motrunich, Phys. Rev. Lett. 134, 050403 (2025).
  30. J. Caetano and S. Komatsu, J. Stat. Phys. 187, 1 (2022).
  31. T. Gombor, J. High Energy Phys. 10 (2022) 096.
  32. C. Ekman, arXiv:2207.12354.
  33. A. Udupa, S. Sur, S. Nandy, A. Sen, and D. Sen, Phys. Rev. B 108, 214430 (2023).
  34. N. Ishibashi, Mod. Phys. Lett. A 04, 251 (1989).
  35. C. K. Majumdar and D. K. Ghosh, J. Math. Phys. (N.Y.) 10, 1388 (1969).
  36. C. K. Majumdar and D. K. Ghosh, J. Math. Phys. (N.Y.) 10, 1399 (1969).
  37. P. W. Anderson, Mater. Res. Bull. 8, 153 (1973).
  38. P. W. Anderson, Science 235, 1196 (1987).
  39. P. W. Anderson, G. Baskaran, Z. Zou, and T. Hsu, Phys. Rev. Lett. 58, 2790 (1987).
  40. G. Baskaran, Z. Zou, and P. W. Anderson, Solid State Commun. 88, 853 (1993).
  41. D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988).
  42. S. A. Kivelson, D. S. Rokhsar, and J. P. Sethna, Phys. Rev. B 35, 8865 (1987).
  43. R. Moessner and S. L. Sondhi, Phys. Rev. Lett. 86, 1881 (2001).
  44. L. Balents, Nature (London) 464, 199 (2010).
  45. S. Liang, B. Doucot, and P. W. Anderson, Phys. Rev. Lett. 61, 365 (1988).
  46. M. Schecter and T. Iadecola, Phys. Rev. B 98, 035139 (2018).
  47. V. Karle, M. Serbyn, and A. A. Michailidis, Phys. Rev. Lett. 127, 060602 (2021).
  48. D. Banerjee and A. Sen, Phys. Rev. Lett. 126, 220601 (2021).
  49. C. J. Turner, M. Szyniszewski, B. Mukherjee, R. Melendrez, H. J. Changlani, and A. Pal, arXiv:2407.11956.
  50. N. Swain, H.-K. Tang, D. C. W. Foo, B. J. J. Khor, G. Lemarié, F. F. Assaad, P. Sengupta, and S. Adam, Phys. Rev. B 111, 224201 (2025).
  51. R. Melendrez, B. Mukherjee, M. Szyniszewski, C. J. Turner, A. Pal, and H. J. Changlani, arXiv:2501.14017.
  52. K. Hida, Phys. Rev. B 45, 2207 (1992).
  53. K. Hida, Phys. Rev. B 46, 8268 (1992).
  54. T. Kennedy and H. Tasaki, Phys. Rev. B 45, 304 (1992).
  55. H. Manaka, I. Yamada, and K. Yamaguchi, J. Phys. Soc. Jpn. 66, 564 (1997).
  56. See Supplemental Material at http://link.aps.org/supplemental/10.1103/v8rf-p5zc, which includes details of proofs related to symmetric tensor scars (Appendix A), calculation of Rényi-2 entropy (Appendix B) and correlation functions (Appendix C), details on von Neumann entropy (Appendix D), and discussion on the stability against perturbations (Appendix E). Here, we additionally refer to Refs. [57–59].
  57. V. Bergholm and J. D. Biamonte, J. Phys. A 44, 245304 (2011).
  58. R. Reuvers, Proc. R. Soc. A 474, 20180023 (2018).
  59. C.-J. Lin, A. Chandran, and O. I. Motrunich, Phys. Rev. Res. 2, 033044 (2020).
  60. K. Sanada, Y. Miao, and H. Katsura, Phys. Rev. B 108, 155102 (2023).
  61. H. K. Kazuyuki Sanada and Yuan Miao, arXiv:2411.01270.
  62. Y. Bao, S. Choi, and E. Altman, Phys. Rev. B 101, 104301 (2020).
  63. T. Zhou and A. Nahum, Phys. Rev. B 99, 174205 (2019).
  64. C.-M. Jian, Y.-Z. You, R. Vasseur, and A. W. W. Ludwig, Phys. Rev. B 101, 104302 (2020).
  65. F. Alet and N. Laflorencie, C. R. Phys. 19, 498 (2018).
  66. R. Vasseur, A. C. Potter, Y.-Z. You, and A. W. W. Ludwig, Phys. Rev. B 100, 134203 (2019).
  67. B. Skinner, J. Ruhman, and A. Nahum, Phys. Rev. X 9, 031009 (2019).
  68. Y. Li, X. Chen, and Matthew P. A. Fisher, Phys. Rev. B 98, 205136 (2018).
  69. A. Chan, R. M. Nandkishore, M. Pretko, and G. Smith, Phys. Rev. B 99, 224307 (2019).
  70. M. Szyniszewski, A. Romito, and H. Schomerus, Phys. Rev. B 100, 064204 (2019).
  71. E. Chitambar, D. Leung, L. Mančinska, M. Ozols, and A. Winter, Commun. Math. Phys. 328, 303 (2014).
  72. D. A. Huse, R. Nandkishore, V. Oganesyan, A. Pal, and S. L. Sondhi, Phys. Rev. B 88, 014206 (2013).
  73. T. Iadecola, M. Schecter, and S. Xu, Phys. Rev. B 100, 184312 (2019).
  74. J.-Y. Desaules, F. Pietracaprina, Z. Papić, J. Goold, and S. Pappalardi, Phys. Rev. Lett. 129, 020601 (2022).
  75. L. Gotta, S. Moudgalya, and L. Mazza, Phys. Rev. Lett. 131, 190401 (2023).
  76. W. W. Ho, S. Choi, H. Pichler, and M. D. Lukin, Phys. Rev. Lett. 122, 040603 (2019).
  77. C. J. Turner, J.-Y. Desaules, K. Bull, and Z. Papić, Phys. Rev. X 11, 021021 (2021).
  78. I.-C. Chen, B. Burdick, Y. Yao, P. P. Orth, and T. Iadecola, Phys. Rev. Res. 4, 043027 (2022).
  79. E. J. Gustafson, A. C. Y. Li, A. Khan, J. Kim, D. M. Kurkcuoglu, M. S. Alam, P. P. Orth, A. Rahmani, and T. Iadecola, Quantum 7, 1171 (2023).
  80. H. Dong, J.-Y. Desaules, Y. Gao, N. Wang, Z. Guo, J. Chen, Y. Zou, F. Jin, X. Zhu, P. Zhang, H. Li, Z. Wang, Q. Guo, J. Zhang, L. Ying, and Z. Papić, Sci. Adv. 9, eadj3822 (2023).
  81. B. Mukherjee, C. J. Turner, M. Szyniszewski, and A. Pal, 10.25446/oxford.31324879 (2026).

Outline

Information

Phys. Rev. Lett. 136, 090401– Published 3 March, 2026
  • Received 6 February 2025
  • Revised 9 September 2025
  • Accepted 11 February 2026
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