  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).
