  The phenomenon of many-body localisation received a lot of attention
recently, both for its implications in condensed-matter physics of allowing
systems to be an insulator even at non-zero temperature as well as in the
context of the foundations of quantum statistical mechanics, providing examples
of systems showing the absence of thermalisation following out-of-equilibrium
dynamics. In this work, we establish a novel link between dynamical properties
- the absence of a group velocity and transport - with entanglement properties
of individual eigenvectors. Using Lieb-Robinson bounds and filter functions, we
prove rigorously under simple assumptions on the spectrum that if a system
shows strong dynamical localisation, all of its many-body eigenvectors have
clustering correlations. In one dimension this implies directly an entanglement
area law, hence the eigenvectors can be approximated by matrix-product states.
We also show this statement for parts of the spectrum, allowing for the
existence of a mobility edge above which transport is possible.
