Deterministic Hypergraph SYK: Melonic Dominance and Maximal Chaos Without Disorder Averaging

Abstract:We show that SYK-like melonic solvability and maximal chaos survive in a sparse deterministic model, without disorder averaging. Our deterministic hypergraph SYK model (hSYK) consists of $N$ Majorana fermions on a $q$-uniform, $d$-regular interaction hypergraph with only $O(dN)$ interaction terms and uniform positive couplings. Under explicit geometric and spectral expansion conditions, its two-point function satisfies the standard melonic Schwinger-Dyson equation up to $O(d^{-1})$ corrections, while the leading bilocal effective action coincides with that of ordinary SYK at the dominant large-$d$ saddle. Its connected four-point function factorizes into a temporal SYK ladder kernel and a line-graph random walk. A finite line-graph spectral gap controls the visibility of the maximally chaotic uniform mode in generic localized OTOCs and, by gapping non-uniform spatial modes in the bilocal spectrum, excludes additional light fluctuation modes beyond the Schwarzian. Exact diagonalization further shows melonic two-point scaling, single-instance Wigner-Dyson statistics, and the predicted graph-controlled spatial decay of OTOCs. The model therefore offers a disorder-free realization of the essential melonic and chaotic features of SYK, in a form more amenable to quantum simulation.

High Energy Physics - Theory (hep-th); Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)

arXiv:2609.19255 [hep-th]

(or arXiv:2609.19255v1 [hep-th] for this version)

https://doi.org/10.48550/arXiv.2609.19255 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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