  By means of full exact diagonalization, we study level statistics and the
structure of the eigenvectors of one-dimensional gapless bosonic and fermionic
systems across the transition from integrability to quantum chaos. These
systems are integrable in the presence of only nearest-neighbor terms, whereas
the addition of next-nearest neighbor hopping and interaction may lead to the
onset of chaos. We show that the strength of the next-nearest neighbor terms
required to observe clear signatures of nonintegrability is inversely
proportional to the system size. Interestingly, the transition to chaos is also
seen to depend on particle statistics, with bosons responding first to the
integrability breaking terms. In addition, we discuss the use of delocalization
measures as main indicators for the crossover from integrability to chaos and
the consequent viability of quantum thermalization in isolated systems.
