  We conjecture that thermalization following a quantum quench in a strongly
correlated quantum system is closely connected to many-body delocalization in
the space of quasi-particles. This scenario is tested in the anisotropic
Heisenberg spin chain with different types of integrability-breaking terms. We
first quantify the deviations from integrability by analyzing the level spacing
statistics and the inverse participation ratio of the system's eigenstates. We
then focus on thermalization, by studying the dynamics after a sudden quench of
the anisotropy parameter. Our numerical simulations clearly support the
conjecture, as long as the integrability-breaking term acts homogeneously on
the quasiparticle space, in such a way as to induce ergodicity over all the
relevant Hilbert space.
