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Observation of energy-resolved many-body localization


Many-body localization (MBL) describes a quantum phase where an isolated interacting system subject to sufficient disorder displays non-ergodic behaviour, evading thermal equilibrium that occurs under its own dynamics. Previously, the thermalization–MBL transition has been largely characterized with the growth of disorder. Here, we explore a new axis, reporting on an energy-resolved MBL transition using a 19-qubit programmable superconducting processor, which enables precise control and flexibility of both disorder strength and initial state preparation. We observe that the onset of localization occurs at different disorder strengths, with distinguishable energy scales, by measuring time-evolved observables and quantities related to many-body wave functions. Our results open avenues for the experimental exploration of many-body mobility edges in MBL systems, whose existence is widely debated due to the finiteness of the system size, and where exact simulations in classical computers become unfeasible.

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Fig. 1: Energy-resolved MBL and its measurement scheme.
Fig. 2: Quantum processor and experimental pulse sequence.
Fig. 3: MBL phase diagram—experiment versus simulation.
Fig. 4: Real-time dynamics of imbalance—experiment versus simulation.
Fig. 5: Wave-function-related measurement and minimal entanglement quantification.

Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

Code availability

The codes used for the numerical simulation are available from the corresponding authors on reasonable request.


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We thank W. Liu, C. Song and K. Xu for technical support. R.M. thanks R. Fazio and M. Rigol for discussions. Devices were made at the Nanofabrication Facilities at Institute of Physics in Beijing and National Center for Nanoscience and Technology in Beijing. This research was supported by the National Natural Science Foundation of China (grant nos. 11674021, 11974039, 11851110757, 11725419 and 11904145), NSAF-U1930402, the National Key Research and Development Program of China (grant nos. 2016YFA0300600, 2017YFA0304300 and 2019YFA0308100), and the Zhejiang Province Key Research and Development Program (grant no. 2020C01019).

Author information




C.C. and R.M. proposed the idea. C.C. and Z.-H.S. performed the numerical simulation. Q.G. conducted the experiment. H.L. and D.Z. fabricated the device. R.M., C.C., Q.G., Z.-H.S., H.F. and H.W. co-wrote the manuscript, and all authors contributed to the experimental set-up, discussions of the results and development of the manuscript.

Corresponding authors

Correspondence to Rubem Mondaini or Heng Fan or H. Wang.

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The authors declare no competing interests.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–10, discussion and Table 1, nine sections and references.

Source data

Source Data Fig. 3

Including both experimental and numerical values.

Source Data Fig. 4

Including both experimental and numerical values.

Source Data Fig. 5

Including both experimental and numerical values.

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Guo, Q., Cheng, C., Sun, ZH. et al. Observation of energy-resolved many-body localization. Nat. Phys. 17, 234–239 (2021).

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