Reaching Sachdev-Ye-Kitaev physics by shaking the Hubbard model

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Abstract
The Sachdev-Ye-Kitaev (SYK) model has attracted widespread attention due to its relevance to diverse areas of physics, such as high temperature superconductivity, black holes, and quantum chaos. The model is, however, extremely challenging to realize experimentally. In this work, we show how a particular form of Floquet engineering, termed ``kinetic driving'', effectively eliminates single-particle processes and creates quasi-random all-to-all interactions when applied to models of Hubbard type. For the specific case of the Bose-Hubbard model, we explicitly verify that the driven system indeed reproduces SYK physics by direct comparison of the spectral form factor and out-of-time ordered correlation functions (OTOCs). Our findings indicate that a cold-atom realization of kinetic driving -- achieved through modulation of hopping amplitudes in an optical lattice -- offers a practical and accurate platform for quantum simulation of the SYK model.
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