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We analyze a model of qubits that we argue has an emergent quantum gravitational description similar to the fermionic Sachdev-Ye-Kitaev (SYK) model. The model we consider is known as the quantum q-spin model because it features q-local interactions between qubits. It was previously studied as a model of a quantum spin glass, and while we find that the model is glassy for q=2, q=3, and likely q=4, we also find evidence for previously unexpected SYK-like behavior for the quenched free energy down to the lowest temperatures for q5. This SYK-like physics includes power-law correlation functions and an extensive low-temperature entropy, so we refer to the model as Spin SYK. The model is generic in that it includes all possible q-body couplings, lacks most symmetries, and has no spatial structure, so our results can be construed as establishing a certain ubiquity of quantum holography in systems dominated by many-body interactions. Furthermore, we discuss a generalized family of models that includes Spin SYK and which provably exhibit SYK-like physics in the solvable limit of large local Hilbert space dimension. We also comment on the implications of a bosonic system with SYK-like properties for the study of holography, Hamiltonian complexity, and related topics.
Swingle et al. (Thu,) studied this question.