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Weak ergodicity breaking from quantum many-body scars

Nature Physics volume 14, pages 745–749 (2018)Cite this article

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Abstract

The thermodynamic description of many-particle systems rests on the assumption of ergodicity, the ability of a system to explore all allowed configurations in the phase space. Recent studies on many-body localization have revealed the existence of systems that strongly violate ergodicity in the presence of quenched disorder. Here, we demonstrate that ergodicity can be weakly broken by a different mechanism, arising from the presence of special eigenstates in the many-body spectrum that are reminiscent of quantum scars in chaotic non-interacting systems. In the single-particle case, quantum scars correspond to wavefunctions that concentrate in the vicinity of unstable periodic classical trajectories. We show that many-body scars appear in the Fibonacci chain, a model with a constrained local Hilbert space that has recently been experimentally realized in a Rydberg-atom quantum simulator. The quantum scarred eigenstates are embedded throughout the otherwise thermalizing many-body spectrum but lead to direct experimental signatures, as we show for periodic recurrences that reproduce those observed in the experiment. Our results suggest that scarred many-body bands give rise to a new universality class of quantum dynamics, opening up opportunities for the creation of novel states with long-lived coherence in systems that are now experimentally realizable.

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Fig. 1: The Hilbert space graph of the Fibonacci chain with L = 6 sites.
Fig. 2: Periodic revivals in the dynamics of entanglement entropy and local correlation function.
Fig. 3: Scarred many-body states in the FSA approximation.
Fig. 4: Level statistics and zero modes in the Fibonacci chain.

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Acknowledgements

We acknowledge insightful discussions with M. Lukin and W.W. Ho. C.J.T., A.M. and Z.P. acknowledge support from EPSRC grants EP/P009409/1 and EP/M50807X/1, and Royal Society Research Grant RG160635. D.A. acknowledges support from the Swiss National Science Foundation. This work was initiated during ‘Conference on Many-Body-Localization: Advances in the Theory and Experimental Progress’ at ICTP Trieste.

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Authors and Affiliations

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

    C. J. Turner, A. A. Michailidis & Z. Papić

  2. IST Austria, Klosterneuburg, Austria

    A. A. Michailidis & M. Serbyn

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

    D. A. Abanin

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All authors contributed to developing the ideas, analysing the results and writing the manuscript. C.J.T., A.A.M. and M.S. performed the numerical simulations.

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Correspondence to Z. Papić.

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Turner, C.J., Michailidis, A.A., Abanin, D.A. et al. Weak ergodicity breaking from quantum many-body scars. Nature Phys 14, 745–749 (2018). https://doi.org/10.1038/s41567-018-0137-5

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