  We propose to define full many-body localization in terms of the recently
introduced integrals of motion[Chandran et al., arXiv:1407.8480], which
characterize the time-averaged response of the system to a local perturbation.
The quasi-locality of such integrals of motion implies an effective lightcone
that grows logarithmically in time. This subsequently implies that (i) the
average entanglement entropy can grow at most logarithmically in time for a
global quench from a product state, and (ii) with high probability, the time
evolution of a local operator for a time interval $|t|$ can be classically
simulated with a resource that scales polynomially in $|t|$.
