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Quantum many-body scars and weak breaking of ergodicity

Nature Physics volume 17, pages 675–685 (2021)Cite this article

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Abstract

Thermalization is the inevitable fate of many complex quantum systems, whose dynamics allow them to fully explore the vast configuration space regardless of the initial state—the behaviour known as quantum ergodicity. In a quest for experimental realizations of coherent long-time dynamics, efforts have focused on ergodicity-breaking mechanisms, such as integrability and localization. The recent discovery of persistent revivals in quantum simulators based on Rydberg atoms have pointed to the existence of a new type of behaviour where the system rapidly relaxes for most initial conditions, while certain initial states give rise to non-ergodic dynamics. This collective effect has been named ‘quantum many-body scarring’ by analogy with a related form of weak ergodicity breaking that occurs for a single particle inside a stadium billiard potential. In this Review, we provide a pedagogical introduction to quantum many-body scars and highlight the emerging connections with the semiclassical quantization of many-body systems. We discuss the relation between scars and more general routes towards weak violations of ergodicity due to embedded algebras and non-thermal eigenstates, and highlight possible applications of scars in quantum technology.

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Fig. 1: Origins and applications of weak ergodicity breaking.
Fig. 2: Weak breakdown of thermalization.
Fig. 3: Embeddings of scarred eigenstates in a many-body system.
Fig. 4: Mechanisms and physical realizations of weak ergodicity breaking.
Fig. 5: Many-body scarring and periodic orbits in semiclassical dynamics.

References

  1. Bloch, I., Dalibard, J. & Nascimbène, S. Quantum simulations with ultracold quantum gases. Nat. Phys. 8, 267–276 (2012).

    Article  Google Scholar 

  2. Georgescu, I. M., Ashhab, S. & Nori, F. Quantum simulation. Rev. Mod. Phys. 86, 153–185 (2014).

    Article  ADS  Google Scholar 

  3. Kinoshita, T., Wenger, T. & Weiss, D. S. A quantum Newton’s cradle. Nature 440, 900–903 (2006).

    Article  ADS  Google Scholar 

  4. Nandkishore, R. & Huse, D. A. Many-body localization and thermalization in quantum statistical mechanics. Annu. Rev. Condens. Matter Phys. 6, 15–38 (2015).

    Article  ADS  Google Scholar 

  5. Abanin, D. A., Altman, E., Bloch, I. & Serbyn, M. Colloquium: Many-body localization, thermalization, and entanglement. Rev. Mod. Phys. 91, 021001 (2019).

    Article  MathSciNet  ADS  Google Scholar 

  6. Deutsch, J. M. Quantum statistical mechanics in a closed system. Phys. Rev. A 43, 2046–2049 (1991).

    Article  ADS  Google Scholar 

  7. Srednicki, M. Chaos and quantum thermalization. Phys. Rev. E 50, 888–901 (1994).

    Article  ADS  Google Scholar 

  8. Bernien, H. et al. Probing many-body dynamics on a 51-atom quantum simulator. Nature 551, 579–584 (2017).

    Article  ADS  Google Scholar 

  9. Turner, C. J., Michailidis, A. A., Abanin, D. A., Serbyn, M. & Papić, Z. Weak ergodicity breaking from quantum many-body scars. Nat. Phys. 14, 745–749 (2018).

    Article  Google Scholar 

  10. Ho, W. W., Choi, S., Pichler, H. & Lukin, M. D. Periodic orbits, entanglement, and quantum many-body scars in constrained models: matrix product state approach. Phys. Rev. Lett. 122, 040603 (2019).

    Article  MathSciNet  ADS  Google Scholar 

  11. Heller, E. J. Bound-state eigenfunctions of classically chaotic hamiltonian systems: scars of periodic orbits. Phys. Rev. Lett. 53, 1515–1518 (1984).

    Article  MathSciNet  ADS  Google Scholar 

  12. Labuhn, H. et al. Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models. Nature 534, 667–670 (2016).

    Article  ADS  Google Scholar 

  13. Lesanovsky, I. & Katsura, H. Interacting Fibonacci anyons in a Rydberg gas. Phys. Rev. A 86, 041601 (2012).

    Article  ADS  Google Scholar 

  14. Sun, B. & Robicheaux, F. Numerical study of two-body correlation in a 1D lattice with perfect blockade. New J. Phys. 10, 045032 (2008).

    Article  ADS  Google Scholar 

  15. Olmos, B., Müller, M. & Lesanovsky, I. Thermalization of a strongly interacting 1D Rydberg lattice gas. New J. Phys. 12, 013024 (2010).

    Article  ADS  Google Scholar 

  16. Turner, C. J., Michailidis, A. A., Abanin, D. A., Serbyn, M. & Papić, Z. Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations. Phys. Rev. B 98, 155134 (2018b).

  17. Michailidis, A. A., Turner, C. J., Papić, Z., Abanin, D. A. & Serbyn, M. Stabilizing two-dimensional quantum scars by deformation and synchronization. Phys. Rev. Res. 2, 022065 (2020).

    Article  Google Scholar 

  18. Lin, C.-J., Calvera, V. & Hsieh, T. H. Quantum many-body scar states in two-dimensional Rydberg atom arrays. Phys. Rev. B 101, 220304 (2020).

    Article  ADS  Google Scholar 

  19. van Voorden, B., Minář, J. & Schoutens, K. Quantum many-body scars in transverse field Ising ladders and beyond. Phys. Rev. B 101, 220305 (2020).

    Article  ADS  Google Scholar 

  20. Sugiura, S., Kuwahara, T. & Saito, K. Many-body scar state intrinsic to periodically driven system. Phys. Rev. Res. 3, L012010 (2021).

    Article  Google Scholar 

  21. Mizuta, K., Takasan, K. & Kawakami, N. Exact Floquet quantum many-body scars under Rydberg blockade. Phys. Rev. Res. 2, 033284 (2020).

    Article  Google Scholar 

  22. Mukherjee, B., Nandy, S., Sen, A., Sen, D. & Sengupta, K. Collapse and revival of quantum many-body scars via Floquet engineering. Phys. Rev. B 101, 245107 (2020).

    Article  ADS  Google Scholar 

  23. Fendley, P., Sengupta, K. & Sachdev, S. Competing density-wave orders in a one-dimensional hard-boson model. Phys. Rev. B 69, 075106 (2004).

    Article  ADS  Google Scholar 

  24. Lesanovsky, I. Liquid ground state, gap, and excited states of a strongly correlated spin chain. Phys. Rev. Lett. 108, 105301 (2012).

    Article  ADS  Google Scholar 

  25. Mondragon-Shem, I., Vavilov, M. G. & Martin, I. The fate of quantum many-body scars in the presence of disorder. Preprint at https://arxiv.org/abs/2010.10535 (2020).

  26. Lin, C.-J., Chandran, A. & Motrunich, O. I. Slow thermalization of exact quantum many-body scar states under perturbations. Phys. Rev. Res. 2, 033044 (2020b).

  27. Lin, C.-J. & Motrunich, O. I. Exact quantum many-body scar states in the Rydberg-blockaded atom chain. Phys. Rev. Lett. 122, 173401 (2019).

    Article  ADS  Google Scholar 

  28. Iadecola, T., Schecter, M. & Xu, S. Quantum many-body scars from magnon condensation. Phys. Rev. B 100, 184312 (2019).

    Article  ADS  Google Scholar 

  29. Barut, A. O. et al. Dynamical Groups and Spectrum Generating Algebras Vol. 1 (World Scientific, 1988).

  30. Yang, C. N. η pairing and off-diagonal long-range order in a Hubbard model. Phys. Rev. Lett. 63, 2144–2147 (1989).

    Article  ADS  Google Scholar 

  31. Shoucheng, Z. Pseudospin symmetry and new collective modes of the Hubbard model. Phys. Rev. Lett. 65, 120–122 (1990).

    Article  Google Scholar 

  32. Moudgalya, S., Regnault, N. & Bernevig, B. A. Entanglement of exact excited states of Affleck–Kennedy–Lieb–Tasaki models: exact results, many-body scars, and violation of the strong eigenstate thermalization hypothesis. Phys. Rev. B 98, 235156 (2018).

    Article  ADS  Google Scholar 

  33. Arovas, D. P. Two exact excited states for the s = 1 AKLT chain. Phys. Lett. A 137, 431–433 (1989).

    Article  ADS  Google Scholar 

  34. Moudgalya, S., O'Brien, E., Bernevig, B. A., Fendley, P. & Regnault, N. Large classes of quantum scarred Hamiltonians from matrix product states. Phys. Rev. B 102, 085120 (2020).

    Article  ADS  Google Scholar 

  35. Mark, D. K., Lin, C.-J. & Motrunich, O. I. Unified structure for exact towers of scar states in the Affleck–Kennedy–Lieb–Tasaki and other models. Phys. Rev. B 101, 195131 (2020).

    Article  ADS  Google Scholar 

  36. Vafek, O., Regnault, N. & Bernevig, B. A. Entanglement of exact excited eigenstates of the Hubbard model in arbitrary dimension. SciPost Phys. 3, 043 (2017).

    Article  ADS  Google Scholar 

  37. Moudgalya, S., Regnault, N. & Bernevig, B. A. η-pairing in Hubbard models: from spectrum generating algebras to quantum many-body scars. Phys. Rev. B 102, 085140 (2020).

    Article  ADS  Google Scholar 

  38. Mark, D. K. & Motrunich, O. I. η-pairing states as true scars in an extended Hubbard model. Phys. Rev. B 102, 075132 (2020).

    Article  ADS  Google Scholar 

  39. Schecter, M. & Iadecola, T. Weak ergodicity breaking and quantum many-body scars in spin-1 XY magnets. Phys. Rev. Lett. 123, 147201 (2019).

    Article  ADS  Google Scholar 

  40. Chattopadhyay, S., Pichler, H., Lukin, M. D. & Ho, W. W. Quantum many-body scars from virtual entangled pairs. Phys. Rev. B 101, 174308 (2020).

    Article  ADS  Google Scholar 

  41. Iadecola, T. & Schecter, M. Quantum many-body scar states with emergent kinetic constraints and finite-entanglement revivals. Phys. Rev. B 101, 024306 (2020).

    Article  ADS  Google Scholar 

  42. Shibata, N., Yoshioka, N. & Katsura, H. Onsager’s scars in disordered spin chains. Phys. Rev. Lett. 124, 180604 (2020).

    Article  MathSciNet  ADS  Google Scholar 

  43. Lee, K., Melendrez, R., Pal, A. & Changlani, H. J. Exact three-colored quantum scars from geometric frustration. Phys. Rev. B 101, 241111 (2020).

    Article  ADS  Google Scholar 

  44. Pakrouski, K., Pallegar, P. N., Popov, F. K. & Klebanov, I. R. Many-body scars as a group invariant sector of Hilbert space. Phys. Rev. Lett. 125, 230602 (2020).

    Article  MathSciNet  ADS  Google Scholar 

  45. Ren, J., Liang, C. & Fang, C. Quasi-symmetry groups and many-body scar dynamics. Preprint at https://arXiv.org/abs/2007.10380 (2020).

  46. O'Dea, N., Burnell, F., Chandran, A. & Khemani, V. From tunnels to towers: quantum scars from Lie algebras and q-deformed Lie algebras. Phys. Rev. Res. 2, 043305 (2020).

    Article  Google Scholar 

  47. Buča, B., Tindall, J. & Jaksch, D. Non-stationary coherent quantum many-body dynamics through dissipation. Nat. Commun. 10, 1730 (2019).

    Article  ADS  Google Scholar 

  48. Tindall, J., Buča, B., Coulthard, J. R. & Jaksch, D. Heating-induced long-range η pairing in the Hubbard model. Phys. Rev. Lett. 123, 030603 (2019).

    Article  ADS  Google Scholar 

  49. Choi, S. et al. Emergent SU(2) dynamics and perfect quantum many-body scars. Phys. Rev. Lett. 122, 220603 (2019).

    Article  ADS  Google Scholar 

  50. Khemani, V., Laumann, C. R. & Chandran, A. Signatures of integrability in the dynamics of Rydberg-blockaded chains. Phys. Rev. B 99, 161101 (2019).

    Article  ADS  Google Scholar 

  51. Bull, K., Desaules, J.-Y. & Papić, Z. Quantum scars as embeddings of weakly broken Lie algebra representations. Phys. Rev. B 101, 165139 (2020).

    Article  ADS  Google Scholar 

  52. Turner, C. J., Desaules, J.-Y., Bull, K. & Papić, Z. Correspondence principle for many-body scars in ultracold Rydberg atoms. Phys. Rev. X 11, 021021 (2021).

    Google Scholar 

  53. Moudgalya, S., Prem, A., Nandkishore, R., Regnault, N. & Bernevig, B. A. Thermalization and its absence within Krylov subspaces of a constrained Hamiltonian. Preprint at https://arxiv.org/abs/1910.14048 (2019).

  54. Moudgalya, S., Bernevig, B. A. & Regnault, N. Quantum many-body scars in a Landau level on a thin torus. Phys. Rev. B 102, 195150 (2020).

    Article  ADS  Google Scholar 

  55. Hudomal, A., Vasić, I., Regnault, N. & Papić, Z. Quantum scars of bosons with correlated hopping. Commun. Phys. 3, 99 (2020).

    Article  Google Scholar 

  56. Zhao, H., Vovrosh, J., Mintert, F. & Knolle, J. Quantum many-body scars in optical lattices. Phys. Rev. Lett. 124, 160604 (2020).

    Article  ADS  Google Scholar 

  57. Sala, P., Rakovszky, T., Verresen, R., Knap, M. & Pollmann, F. Ergodicity breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians. Phys. Rev. X 10, 011047 (2020).

    Google Scholar 

  58. Pai, S. & Pretko, M. Dynamical scar states in driven fracton systems. Phys. Rev. Lett. 123, 136401 (2019).

    Article  ADS  Google Scholar 

  59. Khemani, V., Hermele, M. & Nandkishore, R. Localization from Hilbert space shattering: from theory to physical realizations. Phys. Rev. B 101, 174204 (2020).

    Article  ADS  Google Scholar 

  60. Shiraishi, N. & Mori, T. Systematic construction of counterexamples to the eigenstate thermalization hypothesis. Phys. Rev. Lett. 119, 030601 (2017).

    Article  ADS  Google Scholar 

  61. Surace, F. M., Giudici, G. & Dalmonte, M. Weak-ergodicity-breaking via lattice supersymmetry. Quantum 4, 339 (2020).

    Article  Google Scholar 

  62. Kuno, Y., Mizoguchi, T. & Hatsugai, Y. Flat band quantum scar. Phys. Rev. B 102, 241115 (2020).

    Article  ADS  Google Scholar 

  63. McClarty, P. A., Haque, M., Sen, A. & Richter, J. Disorder-free localization and many-body quantum scars from magnetic frustration. Phys. Rev. B 102, 224303 (2020).

    Article  ADS  Google Scholar 

  64. Wildeboer, J., Seidel, A., Srivatsa, N. S., Nielsen, A. E. B. & Erten, O. Topological quantum many-body scars in quantum dimer models on the kagome lattice. Preprint at https://arxiv.org/abs/2009.00022 (2020).

  65. Ok, S. et al. Topological many-body scar states in dimensions one, two, and three. Phys. Rev. Res. 1, 033144 (2019).

    Article  Google Scholar 

  66. Bull, K., Martin, I. & Papić, Z. Systematic construction of scarred many-body dynamics in 1D lattice models. Phys. Rev. Lett. 123, 030601 (2019).

    Article  ADS  Google Scholar 

  67. Shiraishi, N. Connection between quantum-many-body scars and the Affleck–Kennedy–Lieb–Tasaki model from the viewpoint of embedded Hamiltonians. J. Stat. Mech. Theory Exp. 2019, 083103 (2019).

    Article  MathSciNet  MATH  Google Scholar 

  68. Dirac, P. A. M. Note on exchange phenomena in the Thomas atom. Math. Proc. Cambridge Phil. Soc. 26, 376–385 (1930).

    Article  MATH  ADS  Google Scholar 

  69. Heller, E. J. Time dependent variational approach to semiclassical dynamics. J. Chem. Phys. 64, 63–73 (1976).

    Article  MathSciNet  ADS  Google Scholar 

  70. Haegeman, J. et al. Time-dependent variational principle for quantum lattices. Phys. Rev. Lett. 107, 070601 (2011).

    Article  ADS  Google Scholar 

  71. Green,A. G., Hooley, C. A., Keeling, J. & Simon, S. H. Feynman path integrals over entangled states. Preprint at https://arxiv.org/abs/1607.01778 (2016).

  72. Leviatan, E., Pollmann, F., Bardarson, J. H., Huse, D. A. & Altman, E. Quantum thermalization dynamics with matrix-product states. Preprint at https://arxiv.org/abs/1702.08894 (2017).

  73. Michailidis, A. A., Turner, C. J., Papić, Z., Abanin, D. A. & Serbyn, M. Slow quantum thermalization and many-body revivals from mixed phase space. Phys. Rev. X 10, 011055 (2020b).

    Google Scholar 

  74. Arnol’d, V. I. Mathematical Methods of Classical Mechanics Vol. 60 (Springer Science Business Media, 2013).

  75. Brandino, G. P., Caux, J.-S. & Konik, R. M. Glimmers of a quantum KAM theorem: insights from quantum quenches in one-dimensional Bose gases. Phys. Rev. X 5, 041043 (2015).

    Google Scholar 

  76. Nandkishore, R. M. & Sondhi, S. L. Many-body localization with long-range interactions. Phys. Rev. X 7, 041021 (2017).

    Google Scholar 

  77. Kormos, M., Collura, M., Takács, G. & Calabrese, P. Real-time confinement following a quantum quench to a non-integrable model. Nat. Phys. 13, 246–249 (2017).

    Article  Google Scholar 

  78. Robinson, N. J., James, A. J. A. & Konik, R. M. Signatures of rare states and thermalization in a theory with confinement. Phys. Rev. B 99, 195108 (2019).

    Article  ADS  Google Scholar 

  79. Yang, Z.-C., Liu, F., Gorshkov, A. V. & Iadecola, T. Hilbert-space fragmentation from strict confinement. Phys. Rev. Lett. 124, 207602a (2020).

    Article  ADS  Google Scholar 

  80. Castro-Alvaredo, O. A., Lencsés, M., Szécsényi, I. M. & Viti, J. Entanglement oscillations near a quantum critical point. Phys. Rev. Lett. 124, 230601 (2020).

    Article  MathSciNet  ADS  Google Scholar 

  81. Magnifico, G. et al. Real time dynamics and confinement in the \({{\mathbb{Z}}_{n}}\) Schwinger–Weyl lattice model for 1+1 QED. Quantum 4, 281 (2020).

    Article  Google Scholar 

  82. Chanda, T., Zakrzewski, J., Lewenstein, M. & Tagliacozzo, L. Confinement and lack of thermalization after quenches in the bosonic Schwinger model. Phys. Rev. Lett. 124, 180602 (2020).

    Article  ADS  Google Scholar 

  83. Borla, U., Verresen, R., Grusdt, F. & Moroz, S. Confined phases of one-dimensional spinless fermions coupled to Z2 gauge theory. Phys. Rev. Lett. 124, 120503 (2020).

    Article  MathSciNet  ADS  Google Scholar 

  84. Yang, B. et al. Observation of gauge invariance in a 71-site Bose-Hubbard quantum simulator. Nature 587, 392–396 (2020).

    Article  ADS  Google Scholar 

  85. Surace, F. M. et al. Lattice gauge theories and string dynamics in Rydberg atom quantum simulators. Phys. Rev. X 10, 021041 (2020b).

    Google Scholar 

  86. Celi, A. et al. Emerging two-dimensional gauge theories in Rydberg configurable arrays. Phys. Rev. X 10, 021057 (2020).

    Google Scholar 

  87. Pancotti, N., Giudice, G., Cirac, J. I., Garrahan, J. P. & Bañuls, M. C. Quantum East model: localization, nonthermal eigenstates, and slow dynamics. Phys. Rev. X 10, 021051 (2020).

    Google Scholar 

  88. Roy, S. & Lazarides, A. Strong ergodicity breaking due to local constraints in a quantum system. Phys. Rev. Res. 2, 023159 (2020).

    Article  Google Scholar 

  89. Lan, Z., van Horssen, M., Powell, S. & Garrahan, J. P. Quantum slow relaxation and metastability due to dynamical constraints. Phys. Rev. Lett. 121, 040603 (2018).

    Article  ADS  Google Scholar 

  90. Feldmeier, J., Pollmann, F. & Knap, M. Emergent glassy dynamics in a quantum dimer model. Phys. Rev. Lett. 123, 040601 (2019).

    Article  ADS  Google Scholar 

  91. Hart, O., De Tomasi, G. & Castelnovo, C. From compact localized states to many-body scars in the random quantum comb. Phys. Rev. Res. 2, 043267 (2020).

    Article  Google Scholar 

  92. Hallam, A., Morley, J. G. & Green, A. G. The Lyapunov spectra of quantum thermalisation. Nat. Commun. 10, 2708 (2019).

    Article  ADS  Google Scholar 

  93. Sachdev, S. & Ye, J. Gapless spin-fluid ground state in a random quantum Heisenberg magnet. Phys. Rev. Lett. 70, 3339–3342 (1993).

    Article  ADS  Google Scholar 

  94. Kitaev, A. A simple model of quantum holography. Talk at KITP. Univ. California Santa Barbara https://online.kitp.ucsb.edu/online/entangled15/kitaev/ (2015).

  95. Maldacena, J., Shenker, S. H. & Stanford, D. A bound on chaos. J. High Energy Phys. 2016, 106 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  96. Alhambra, Á. M., Anshu, A. & Wilming, H. Revivals imply quantum many-body scars. Phys. Rev. B 101, 205107 (2020).

    Article  ADS  Google Scholar 

  97. Omran, A. et al. Generation and manipulation of Schrödinger cat states in Rydberg atom arrays. Science 365, 570–574 (2019).

    Article  MathSciNet  ADS  Google Scholar 

  98. Bluvstein, D. et al. Controlling many-body dynamics with driven quantum scars in Rydberg atom arrays. Science https://doi.org/10.1126/science.abg2530 (2021).

  99. Kao, W., Li, K.-Y., Lin, K.-Y., Gopalakrishnan, S. & Lev, B. L. Creating quantum many-body scars through topological pumping of a 1D dipolar gas. Preprint at https://arxiv.org/abs/2002.10475 (2020).

  100. Scherg, S. et al. Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains. Preprint at http://arxiv.org/abs/2010.12965 (2020).

  101. Heller, E. J. in Chaos and Quantum Physics Vol. 52 (eds Giannoni, M. J. et al.) 547–661 (North-Holland, 1991).

  102. Berry, M. V. in Chaotic Behaviour of Deterministic Systems Vol. 36 (eds Chenciner, A. et al.) 171–271 (North-Holland, 1983).

  103. Sridhar, S. Experimental observation of scarred eigenfunctions of chaotic microwave cavities. Phys. Rev. Lett. 67, 785–788 (1991).

    Article  ADS  Google Scholar 

  104. Wilkinson, P. B. et al. Observation of “scarred” wavefunctions in a quantum well with chaotic electron dynamics. Nature 380, 608–610 (1996).

    Article  ADS  Google Scholar 

  105. Wintgen, D. & Hönig, A. Irregular wave functions of a hydrogen atom in a uniform magnetic field. Phys. Rev. Lett. 63, 1467–1470 (1989).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank our collaborators K. Bull, S. Choi, J.-Y. Desaules, W. W. Ho, A. Hudomal, M. Lukin, I. Martin, H. Pichler, N. Regnault, I. Vasić and in particular A. Michailidis and C. Turner, without whom this work would not have been possible. We also benefited from discussions with E. Altman, B. A. Bernevig, A. Chandran, P. Fendley, V. Khemani and L. Motrunich. M.S. was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 850899). D.A.A. was supported by the Swiss National Science Foundation and by the ERC under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 864597). Z.P. acknowledges support by the Leverhulme Trust Research Leadership Award RL-2019-015.

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  1. IST Austria, Klosterneuburg, Austria

    Maksym Serbyn

  2. Department of Theoretical Physics, University of Geneva, Geneva, Switzerland

    Dmitry A. Abanin

  3. School of Physics and Astronomy, University of Leeds, Leeds, UK

    Zlatko Papić

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Serbyn, M., Abanin, D.A. & Papić, Z. Quantum many-body scars and weak breaking of ergodicity. Nat. Phys. 17, 675–685 (2021). https://doi.org/10.1038/s41567-021-01230-2

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