Abstract
In non-maximally quantum chaotic systems, the exponential behavior of out-of-time-ordered correlators (OTOCs) results from summing over exchanges of an infinite tower of higher “spin” operators. We construct an effective field theory (EFT) to capture these exchanges in (0 + 1) dimensions. The EFT generalizes the one for maximally chaotic systems, and reduces to it in the limit of maximal chaos. The theory predicts the general structure of OTOCs both at leading order in the 1/N expansion (N is the number of degrees of freedom), and after resuming over an infinite number of higher order 1/N corrections. These general results agree with those previously explicitly obtained in specific models. We also show that the general structure of the EFT can be extracted from the large q SYK model.
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Acknowledgments
We would like to thank Mark Mezei and Daniel Jafferis for stimulating and helpful discussions. PG is supported by the US Department of Defense (DOD) grant KK2014 and also by the Simons foundation as a member of the It from Qubit collaboration. HL is supported by the Office of High Energy Physics of U.S. Department of Energy under grant Contract Number DE-SC0012567 and DE-SC0020360 (MIT contract # 578218).
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Gao, P., Liu, H. An effective field theory for non-maximal quantum chaos. J. High Energ. Phys. 2023, 76 (2023). https://doi.org/10.1007/JHEP11(2023)076
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DOI: https://doi.org/10.1007/JHEP11(2023)076