确定性超图SYK：无无序平均的Melonic主导性与最大混沌

中文摘要 AI 辅助

我们证明，在稀疏确定性模型中，SYK类的melonic可解性和最大混沌得以保留，无需无序平均。我们的确定性超图SYK模型（hSYK）由$N$个马约拉纳费米子组成，位于一个$q$-均匀、$d$-正则的相互作用超图上，仅包含$O(dN)$个相互作用项和均匀的正耦合常数。在明确的几何和谱展开条件下，其两点函数满足标准的melonic Schwinger-Dyson方程，修正项为$O(d^{-1})$，而前导双局域有效作用在主导的大$d$鞍点上与普通SYK一致。其连通四点函数分解为时间SYK阶梯核和线图随机游走。有限的线图谱间隙控制着最大混沌均匀模式在一般局域OTOC中的可见性，并且通过使双局域谱中的非均匀空间模式产生间隙，排除了Schwarzian之外额外的光涨落模式。精确对角化进一步显示了melonic两点标度、单实例Wigner-Dyson统计以及预测的图控制的OTOC空间衰减。因此，该模型提供了SYK基本melonic和混沌特征的无无序实现，其形式更适用于量子模拟。

英文摘要

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.

发表机构

• Department of Physics and Computer Science, Dayalbagh Educational Institute, Agra, India（戴阿尔巴格教育学院物理与计算机系）

机构由 AI 辅助整理，请以论文原文为准。

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28 pages, 8 figures