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Observation of many-body Fock space dynamics in two dimensions

Abstract

Quantum simulation provides platforms to study fundamental aspects of many-body physics in a controlled way, and to explore their implications for quantum technology. However, the dimension of the Hilbert space grows exponentially with the number of interacting particles, which means that investigations of strongly correlated problems such as quantum criticality and many-body localization in terms of few-body probes in real space are often insufficient. Here we demonstrate how to tackle such questions on a superconducting quantum processor from a Fock-space perspective. We map a many-body system onto an unconventional Anderson model on a network of many-body states, which allows the direct observation of wave-packet propagation in Fock space. We find a quantum-critical regime of anomalously enhanced wave-packet width and deduce a critical point from the maximum wave-packet fluctuations, which lends support to the two-dimensional many-body localization transition in finite-sized systems. Our results introduce an alternative picture for characterizing many-body dynamics and for exploring the controversial problems such as criticality and dimensionality. Moreover, the protocol is universal and scalable, and is therefore a promising strategy to solve a broader range of many-body problems on future quantum devices.

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Fig. 1: Quantum processor and schematic of many-body dynamics in Fock space.
Fig. 2: Many-body dynamics in Fock space.
Fig. 3: Dynamics of Bhattacharyya coefficient \({{{\mathcal{B}}}}{(t)}\).
Fig. 4: Signature of nonergodic transition in 2D system.

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Data availability

The data presented in the figures and that support the other findings of this study are available at https://doi.org/10.5281/zenodo.7733236.

Code availability

All the relevant source codes are available from the corresponding authors upon reasonable request.

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Acknowledgements

The device was fabricated at the Micro-Nano Fabrication Center of Zhejiang University. We acknowledge support from Zhejiang Province Key Research and Development Program (grant no. 2020C01019) and the National Natural Science Foundation of China (grants nos. 92065204, U20A2076, 12274368, U2230402, 12111530010, 12222401, 11974039, 12174167, 12047501 and 11934010). Q.G. is also supported by the Zhejiang Provincial Natural Science Foundation of China under grant no. LQ23A040006. L.Y. is also supported by the National Key R&D Program of China (grant no. 2022YFA1404203).

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Q.G. and L.Y. proposed the idea; Y.Y., L.X. and Z.B. conducted the experiment and analysed the data under the supervision of Q.G. and H.W.; Z.B., Z.G. and Y.-F.Y. performed the numerical simulation under the supervision of Q.G., C.C. and L.Y.; H.L. and J.C. fabricated the device under the supervision of H.W.; Q.G., L.Y., R.M. and H.W. co-wrote the manuscript; S.-Y.Z. supervised the whole project. All authors contributed to the experimental set-up, discussions of the results and development of the manuscript.

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Correspondence to Lei Ying or Qiujiang Guo.

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Supplementary sections 1–15, Figs. 1–21 and Table 1.

Supplementary Video 1

Wave-packet dynamics in Fock space.

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Yao, Y., Xiang, L., Guo, Z. et al. Observation of many-body Fock space dynamics in two dimensions. Nat. Phys. 19, 1459–1465 (2023). https://doi.org/10.1038/s41567-023-02133-0

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