  We study the long-time evolution of the bipartite entanglement in
translationally invariant gapped harmonic lattice systems with finite-range
interactions. A lower bound for the von Neumann entropy is derived in terms of
the purity of the reduced density matrix. It is shown that starting from an
initially Gaussian state the entanglement entropy increases at least linearly
in time. This implies that the dynamics of gapped (non-critical) harmonic
lattice systems cannot be efficiently simulated by algorithms based on
matrix-product decompositions of the quantum state.
