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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.

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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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