  We investigate the dynamics following a global parameter quench for two 1D
models with variable-range power-law interactions: a long-range transverse
Ising model, which has recently been realised in chains of trapped ions, and a
long-range lattice model for spinless fermions with long-range tunnelling. For
the transverse Ising model, the spreading of correlations and growth of
entanglement are computed using numerical matrix product state techniques, and
are compared with exact solutions for the fermionic tunnelling model. We
identify transitions between regimes with and without an apparent linear light
cone for correlations, which correspond closely between the two models. For
long-range interactions (in terms of separation distance r, decaying slower
than 1/r), we find that despite the lack of a light-cone, correlations grow
slowly as a power law at short times, and that -- depending on the structure of
the initial state -- the growth of entanglement can also be sublinear. These
results are understood through analytical calculations, and should be
measurable in experiments with trapped ions.
