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

2009/10/31 by Lea F. Santos, Marcos Rigol · 371 citations
Physics and Astronomy · #Boson #CHAOS (operating system) #Condensed matter physics #Crossover #Eigenvalues and eigenvectors #Gapless playback #Integrable system #Mathematical physics #Physics #Quantum #Quantum chaos #Quantum chaos and dynamical systems #Quantum dynamics #Quantum many-body systems #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Statistical physics #Thermalisation #cond-mat.quant-gas #cond-mat.stat-mech #cond-mat.str-el #k-nearest neighbors algorithm

paper · pdf · doi:10.1103/physreve.81.036206

published in Physical Review E 81(3), 036206 (American Physical Society) · 11 pages, 16 figures

openalex publication_date 2010/03/05 · arxiv created 2010/03/06 · arxiv updated 2010/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Random Matrix Theories in Quantum Physics: Common Concepts
• Level Statistics of XXZ Spin Chains with Discrete Symmetries: Analysis through Finite-size Effects
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Level repulsion in integrable and almost-integrable quantum spin models
• Chaos and Quantum Thermalization
• Random-matrix physics: spectrum and strength fluctuations
• Towards a statistical theory of finite Fermi systems and compound states: Random two-body interaction approach
• Interaction Quench in the Hubbard Model
• Quantum statistical mechanics in a closed system
• Random-matrix theory of quantum transport

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• Repulsively interacting fermions in a two-dimensional deformed trap with spin-orbit coupling
• Stationary entropies after a quench from excited states in the Ising chain
• Finding periodic orbits in projected quantum many-body dynamics
• Equilibration and GGE in interacting-to-free quantum quenches in dimensions d\gt 1
• Localized dynamics following a quantum quench in a non-integrable system: an example on the sawtooth ladder
• Symmetry breaking in chaotic many-body quantum systems at finite temperature