  While the concepts of quantum many-body integrability and chaos are of
fundamental importance for the understanding of quantum matter, their precise
definition has so far remained an open question. In this work, we introduce an
alternative indicator for quantum many-body integrability and chaos, which is
based on the statistics of eigenstates by means of nearest-neighbor subsystem
trace distances. We show that this provides us with a faithful classification
through extensive numerical simulations for a large variety of paradigmatic
model systems including random matrix theories, free fermions, Bethe-ansatz
solvable systems, and models of many-body localization. While existing
indicators, such as those obtained from level-spacing statistics, have already
been utilized with great success, they also face limitations. This concerns for
instance the quantum many-body kicked top, which is exactly solvable but
classified as chaotic in certain regimes based on the level-spacing statistics,
while our introduced indicator signals the expected quantum many-body
integrability. We discuss the universal behaviors we observe for the
nearest-neighbor trace distances and point out that our indicator might be
useful also in other contexts such as for the many-body localization
transition.
