  We investigate the effect of short-range correlations on the dynamical phase
diagram of quantum many-body systems with long-range interactions. Focusing on
Ising spin chains with power-law decaying interactions and accounting for
short-range correlations by a cluster mean field theory we show that
short-range correlations are responsible for the emergence of a chaotic
dynamical region. Analyzing the fine details of the phase diagram, we show that
the resulting chaotic dynamics bears close analogies with that of a tossed
coin.
