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

Understand

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.