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.
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BibTeX
@misc{prakash2026deterministic,
title = {{Deterministic Hypergraph SYK: Melonic Dominance and Maximal Chaos Without Disorder Averaging}},
author = {Shiroman Prakash},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19255},
eprint = {2609.19255},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19255},
}
RIS
TY - UNPB
TI - Deterministic Hypergraph SYK: Melonic Dominance and Maximal Chaos Without Disorder Averaging
AU - Shiroman Prakash
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19255
UR - https://arxiv.org/abs/2609.19255
AB - 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.
ER -