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Quantum Simulation

Operator growth bounds in a cartoon matrix model

arXiv
Authors: Andrew Lucas, Andrew Osborne

Year

2020

Paper ID

22238

Status

Preprint

Abstract Read

~2 min

Abstract Words

122

Citations

N/A

Abstract

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.

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  • 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.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2007.07165 [2] arXiv https://arxiv.org/abs/2007.07165 [3] Publisher https://arxiv.org/abs/2007.07165

Local Citation Graph (Related-Paper Links)

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