  We study how the proximity to an integrable point or to localization as one
approaches the atomic limit, as well as the mixing of symmetries in the chaotic
domain, may affect the onset of thermalization in finite one-dimensional
systems. We consider systems of hard-core bosons at half-filling with nearest
neighbor hopping and interaction, and next-nearest neighbor interaction. The
latter breaks integrability and induces a ground-state superfluid to insulator
transition. By full exact diagonalization, we study chaos indicators and
few-body observables. We show that when different symmetry sectors are mixed,
chaos indicators associated with the eigenvectors, contrary to those related to
the eigenvalues, capture the onset of chaos. The results for the complexity of
the eigenvectors and for the expectation values of few-body observables confirm
the validity of the eigenstate thermalization hypothesis in the chaotic regime,
and therefore the occurrence of thermalization. We also study the properties of
the off-diagonal matrix elements of few-body observables in relation to the
transition from integrability to chaos and from chaos to localization.
