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Quantum critical behaviour at the many-body localization transition


Phase transitions are driven by collective fluctuations of a system’s constituents that emerge at a critical point1. This mechanism has been extensively explored for classical and quantum systems in equilibrium, whose critical behaviour is described by the general theory of phase transitions. Recently, however, fundamentally distinct phase transitions have been discovered for out-of-equilibrium quantum systems, which can exhibit critical behaviour that defies this description and is not well understood1. A paradigmatic example is the many-body localization (MBL) transition, which marks the breakdown of thermalization in an isolated quantum many-body system as its disorder increases beyond a critical value2,3,4,5,6,7,8,9,10,11. Characterizing quantum critical behaviour in an MBL system requires probing its entanglement over space and time4,5,7, which has proved experimentally challenging owing to stringent requirements on quantum state preparation and system isolation. Here we observe quantum critical behaviour at the MBL transition in a disordered Bose–Hubbard system and characterize its entanglement via its multi-point quantum correlations. We observe the emergence of strong correlations, accompanied by the onset of anomalous diffusive transport throughout the system, and verify their critical nature by measuring their dependence on the system size. The correlations extend to high orders in the quantum critical regime and appear to form via a sparse network of many-body resonances that spans the entire system12,13. Our results connect the macroscopic phenomenology of the transition to the system’s microscopic structure of quantum correlations, and they provide an essential step towards understanding criticality and universality in non-equilibrium systems1,7,13.

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Fig. 1: Microscopy of the many-body localization transition.
Fig. 2: Quantum critical dynamics at the MBL transition.
Fig. 3: Sparse network of resonances.
Fig. 4: Many-body correlations in the quantum critical regime.

Data availability

The data that support the findings of this study are available in the Dataverse repository at


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We acknowledge discussions with D. Abanin, E. Altman, H. Bernien, C. Chiu, S. Choi, E. Demler, A. Hébert, W. W. Ho, V. Kasper, V. Khemani, J. Kwan, L. Santos and J. Schmiedmayer. We were supported by grants from the National Science Foundation, the Gordon and Betty Moore Foundations EPiQS Initiative, an Air Force Office of Scientific Research MURI programme, an Army Research Office MURI programme and the NSF Graduate Research Fellowship Program. J.L. acknowledges support from the Swiss National Science Foundation.

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All authors contributed extensively to the construction of the experiment, the collection and analysis of the data, and the writing of the manuscript. M.G. supervised the work.

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Correspondence to Markus Greiner.

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Peer review information Nature thanks Maksym Serbyn and Jean-Philippe Brantut for their contribution to the peer review of this work.

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Supplementary Information

Supplementary Sections 1–9, including Supplementary Figs. 1–7 and Supplementary Table 1.

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Rispoli, M., Lukin, A., Schittko, R. et al. Quantum critical behaviour at the many-body localization transition. Nature 573, 385–389 (2019).

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