Operator growth bounds in a cartoon matrix model | CU Experts

Overview

We study operator growth in a model of N(N − 1)/2 interacting Majorana fermions that live on the edges of a complete graph of N vertices. Terms in the Hamiltonian are proportional to the product of q fermions that 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.