# A characterization of quantum chaos by two-point correlation functions

## TL;DR

This paper introduces a new way to characterize quantum many-body chaos using the spectral properties of two-point correlation matrices, especially useful for systems without exponential Lyapunov growth.

## Contribution

It proposes a novel spectral characterization of quantum chaos based on two-point correlations, applicable to locally interacting systems.

## Key findings

- Spectral properties of correlation matrices resemble those of random matrices.
- Numerical validation on SYK model confirms the approach.
- Application to XXZ spin chain demonstrates broader applicability.

## Abstract

We propose a characterization of quantum many-body chaos: given a collection of simple operators, the set of all possible pair-correlations between these operators can be organized into a matrix with random-matrix-like spectrum. This approach is particularly useful for locally interacting systems, which do not generically show exponential Lyapunov growth of out-of-time-ordered correlators. We demonstrate the validity of this characterization by numerically studying the Sachdev-Ye-Kitaev model and a one-dimensional spin chain with random magnetic field (XXZ model).