An effective field theory for non-maximal quantum chaos

TL;DR

This paper develops an effective field theory to describe non-maximal quantum chaos, capturing the behavior of out-of-time-ordered correlators through higher spin exchanges, generalizing existing models for maximally chaotic systems.

Contribution

The authors construct a new EFT for non-maximal chaos in 0+1 dimensions, extending the maximally chaotic case and connecting it to the large q SYK model.

Findings

EFT predicts OTOC structure at leading order in 1/N

Resummation of higher order 1/N corrections aligns with model results

Large q SYK model analysis supports the EFT structure

Abstract

In non-maximally quantum chaotic systems, the exponential behavior of out-of-time-ordered correlators (OTOCs) results from summing over exchanges of an infinite tower of higher "spin" operators. We construct an effective field theory (EFT) to capture these exchanges in $(0+1)$ dimensions. The EFT generalizes the one for maximally chaotic systems, and reduces to it in the limit of maximal chaos. The theory predicts the general structure of OTOCs both at leading order in the $1/N$ expansion ($N$ is the number of degrees of freedom), and after resuming over an infinite number of higher order $1/N$ corrections. These general results agree with those previously explicitly obtained in specific models. We also show that the general structure of the EFT can be extracted from the large $q$ SYK model.