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

TL;DR

This paper investigates how one-dimensional bosonic and fermionic systems transition from integrability to quantum chaos, analyzing level statistics, eigenvector structure, and the implications for thermalization.

Contribution

It reveals the relationship between system size, particle statistics, and the onset of chaos, highlighting the role of next-nearest neighbor interactions and delocalization measures.

Findings

Chaos onset strength inversely proportional to system size

Bosons respond earlier to integrability breaking than fermions

Delocalization measures effectively indicate the integrability-chaos transition

Abstract

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.