论文标题
卡通矩阵模型中的操作员生长界限
Operator growth bounds in a cartoon matrix model
论文作者
论文摘要
我们以$ n（n-1）/2 $互动的Majorana fermions的模型来研究运营商的增长，该模型生存在$ n $顶点的完整图上。哈密顿式的术语与$ q $ fermions的产物成正比，该产品的长度$ q $的循环边缘。该模型是一个卡通“矩阵模型”：相互作用图模拟了单个跟踪矩阵模型的相互作用图，在量子重力上可以全息二。我们证明（非扰动以$ 1/n $，并且在没有任何合奏上平均）表明，该模型的争夺时间至少是订单$ \ log n $的，这与快速争夺的猜想一致。我们评论“矩阵模型”和旋速模型中操作员增长之间的明显相似性和差异。
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.
