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By means of full exact diagonalization, we study level statistics and thestructure of the eigenvectors of one-dimensional gapless bosonic and fermionicsystems across the transition from integrability to quantum chaos. Thesesystems are integrable in the presence of only nearest-neighbor terms, whereasthe addition of next-nearest neighbor hopping and interaction may lead to theonset of chaos. We show that the strength of the next-nearest neighbor termsrequired to observe clear signatures of nonintegrability is inverselyproportional to the system size. Interestingly, the transition to chaos is alsoseen to depend on particle statistics, with bosons responding first to theintegrability breaking terms. In addition, we discuss the use of delocalizationmeasures as main indicators for the crossover from integrability to chaos andthe consequent viability of quantum thermalization in isolated systems.

Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization