Abstract
We construct a model of Pauli spin operators with all-to-all 4-local interactions by replacing Majorana fermions in the SYK model with spin operators. Equivalently, we replace fermions with hard-core bosons. We study this model numerically and compare the properties with those of the SYK model. We observe a striking quantitative coincidence between the spin model and the SYK model, which suggests that this spin model is strongly chaotic and, perhaps, can play some role in holography. We also discuss the path-integral approach with multi-local fields and the possibility of quantum simulations. This model may be an interesting target for quantum simulations because Pauli spins are easier to implement than fermions on qubit-based quantum devices.
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Acknowledgments
We would like to thank Brian Swingle for stimulating discussions at various stages, including the initial suggestion of replacing fermions with hard-core bosons. We thank Brian Swingle and Michael Winer for sharing their study on SpinXYq based on path integral. We also thank Tarek Anous, Budhaditya Bhattacharjee, Marcos Crichigno, Matthew DeCross, Michael Foss-Feig, Henry Lin, and Subir Sachdev. Part of the computations in this work has been done using the facilities of the Supercomputer Center, the Institute for Solid State Physics, the University of Tokyo. M. H. and E. R. thank the Royal Society International Exchanges award IEC/R3/213026. M. H. also thanks the STFC grants ST/R003599/1 and ST/X000656/1. A. J. and X. L. were supported by the U.S. Department of Energy under contract DE-SC0010010. M. T. was partially supported by the Japan Society for the Promotion of Science (JSPS) Grants-in-Aid for Scientific Research (KAKENHI) Grants No. JP20K03787 and JP21H05185.
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Hanada, M., Jevicki, A., Liu, X. et al. A model of randomly-coupled Pauli spins. J. High Energ. Phys. 2024, 280 (2024). https://doi.org/10.1007/JHEP05(2024)280
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DOI: https://doi.org/10.1007/JHEP05(2024)280