  Despite being fundamental to the understanding of solid-state electrolytes
(SSE), little is known on the degree of coordination between mobile ions in
diffusive events. Thus far, identification of concerted ionic hops mostly has
relied on the analysis of spatio-temporal pair correlation functions obtained
from atomistic molecular dynamics (MD) simulations. However, this type of
analysis neither allows for quantifying particle correlations beyond two body
nor determining concerted ionic hop mechanisms, thus hindering a detailed
comprehension and possible rational design of SSE. Here, we introduce an
unsupervised k-means clustering approach able to identify ion-hopping events
and correlations between many mobile ions, and apply it to a comprehensive ab
initio MD database comprising several families of inorganic SSE and millions of
ionic configurations. It is found that despite two-body interactions between
mobile ions are largest, higher-order $n$-ion ($2 < n$) correlations are most
frequent. Specifically, we prove an universal exponential decaying law for the
probability density function governing the number of concerted mobile ions. For
the particular case of Li-based SSE, it is shown that the average number of
correlated mobile ions amounts to $10 \pm 5$ and that this result is
practically independent of temperature. Interestingly, our data-driven analysis
reveals that fast-ion diffusion strongly and positively correlates with ample
hopping lengths and long hopping spans but not with high hopping frequencies
and short interstitial residence times. Finally, it is shown that neglection of
many-ion correlations generally leads to a modest overestimation of the hopping
frequency that roughly is proportional to the average number of correlated
mobile ions.
