  We study the multipartite entanglement of a quantum many-body system
undergoing a quantum quench. We quantify multipartite entanglement through the
quantum Fisher information (QFI) density and we are able to express it after a
quench in terms of a generalized response function. For pure state initial
conditions and in the thermodynamic limit, we can express the QFI as the
fluctuations of an observable computed in the so-called diagonal ensemble. We
apply the formalism to the dynamics of a quantum Ising chain after a quench in
the transverse field. In this model the asymptotic state is, in almost all
cases, more than two-partite entangled. Moreover, starting from the
ferromagnetic phase, we find a divergence of multipartite entanglement for
small quenches closely connected to a corresponding divergence of the
correlation length.
