  The slow flow of amorphous solids exhibits striking heterogeneities: swift
localised particle rearrangements take place in the midst of a more or less
homogeneously deforming medium. Recently, experimental as well as numerical
work has revealed spatial correlations between these flow heterogeneities.
Here, we use molecular dynamics (MD) simulations to characterise the
rearrangements and systematically probe their correlations both in time and in
space. In particular, these correlations display a four-fold azimuthal symmetry
characteristic of shear stress redistribution in an elastic medium and we
unambiguously detect their increase in range with time. With increasing shear
rate, correlations become shorter-ranged and more isotropic. In addition, we
study a coarse-grained model motivated by the observed flow characteristics and
challenge its predictions directly with the MD simulations. While the model
captures both macroscopic and local properties rather satisfactorily, the
agreement with respect to the spatiotemporal correlations is at most
qualitative. The discrepancies provide important insight into relevant physics
that is missing in all related coarse-grained models that have been developed
for the flow of amorphous materials so far, namely the finite shear wave
velocity and the impact of elastic heterogeneities on stress redistribution.
