Universal power law in crossover from integrability to quantum chaos

Abstract

We study models of interacting fermions in one dimension to investigate the crossover from integrability to non-integrability, i.e., quantum chaos, as a function of system size. Using exact diagonalization of finite-sized systems, we study this crossover by obtaining the energy level statistics and Drude weight associated with transport. Our results reinforce the idea that for system size $L\to \infty$ non-integrability sets in for an arbitrarily small integrability-breaking perturbation. The crossover value of the perturbation scales as a power law $\sim L^{-3}$ when the integrable system is gapless and the scaling appears to be robust to microscopic details and the precise form of the perturbation. We conjecture that the exponent in the power law is characteristic of the random matrix ensemble describing the non-integrable system. For systems with a gap, the crossover scaling appears to be faster than a power law.

5 pages, 7 figures

References in corpus (7)

• Thermalization and its mechanism for generic isolated quantum systems
• Relaxation and Pre-thermalization in an Isolated Quantum System
• Heat Transport in low-dimensional systems
• Quench dynamics across quantum critical points
• Finite temperature dynamical DMRG and the Drude weight of spin-1/2 chains
• Finite-temperature Drude weight within the anisotropic Heisenberg chain
• Drude weight in systems with open boundary conditions

Cited by in corpus (29)

• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Quantum Many-Body Scars: A Quasiparticle Perspective
• Spectral statistics across the many-body localization transition
• Adiabatic eigenstate deformations as a sensitive probe for quantum chaos
• Universality in the onset of quantum chaos in many-body systems
• Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain
• Current operators in integrable models: A review
• Higher order spacing ratios in random matrix theory and complex quantum systems
• Operator growth in the transverse-field Ising spin chain with integrability-breaking longitudinal field
• Onset of many-body quantum chaos due to breaking integrability
• Integrals of motion for one-dimensional Anderson localized systems
• Distribution of the Ratio of Consecutive Level Spacings for Different Symmetries and Degrees of Chaos
• Many Body Localization Due to Correlated Disorder in Fock Space
• Dynamics of Fluctuations in Quantum Simple Exclusion Processes
• Criterion for the occurrence of many body localization in the presence of a single particle mobility edge
• Weak integrability breaking and level spacing distribution
• Homogeneous Floquet time crystal from weak ergodicity breaking
• Transport in the non-ergodic extended phase of interacting quasiperiodic systems
• Eigenstate thermalization hypothesis in two-dimensional XXZ model with or without SU(2) symmetry
• Chaotic spin chains in AdS/CFT
• Witnessing quantum chaos using observational entropy
• Spectral Crossovers and Universality in Quantum Spin-chains Coupled to Random Fields
• Adiabatic gauge potential and integrability breaking with free fermions
• Eigenstate thermalization and disappearance of quantum many-body scar states in interacting fermion systems
• Probing quantum phase transition via quantum speed limit
• Onset of Quantum Chaos and Ergodicity in Spin Systems with Highly Degenerate Hilbert Spaces
• Weak vs. strong breaking of integrability in interacting scalar quantum field theories
• On the difference between thermalization in open and isolated quantum systems: a case study
• Entanglement spectrum and block eigenvalue spacing distribution of correlated electron states