We study operator growth in a model of $N(N-1)/2$ interacting Majorana fermions, which live on the edges of a complete graph of $N$ vertices. Terms in the Hamiltonian are proportional to the product of $q$ fermions which live on the edges of cycles of length $q$. This model is a cartoon "matrix model": the interaction graph mimics that of a single-trace matrix model, which can be holographically dual to quantum gravity. We prove (non-perturbatively in $1/N$, and without averaging over any ensemble) that the scrambling time of this model is at least of order $\log N$, consistent with the fast scrambling conjecture. We comment on apparent similarities and differences between operator growth in our "matrix model" and in the melonic models.

中文翻译：

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卡通矩阵模型中的算子增长界限

我们研究了 $N(N-1)/2$ 相互作用的 Majorana 费米子模型中的算子增长，该模型位于 $N$ 顶点的完整图的边缘。哈密​​顿量中的项与 $q$ 费米子的乘积成正比，这些费米子位于长度为 $q$ 的循环的边缘。这个模型是一个卡通“矩阵模型”：交互图模仿了单迹矩阵模型的交互图，它可以全息对偶量子引力。我们证明（在 $1/N$ 中无扰动，并且没有对任何集合求平均）该模型的加扰时间至少为 $\log N$ 阶，与快速加扰猜想一致。我们评论了我们的“矩阵模型”和甜瓜模型中算子增长之间的明显异同。