Universality in the onset of quantum chaos in many-body systems

Tyler Leblond, Dries Sels, Anatoli Polkovnikov, Marcos Rigol

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Abstract

We show that the onset of quantum chaos at infinite temperature in two many-body one-dimensional lattice models, the perturbed spin-1/2 XXZ and Anderson models, is characterized by universal behavior. Specifically, we show that the onset of quantum chaos is marked by maxima of the typical fidelity susceptibilities that scale with the square of the inverse average level spacing, saturating their upper bound, and that the strength of the integrability- or localization-breaking perturbation at these maxima decreases with increasing system size. We also show that the spectral function below the "Thouless"energy (in the quantum-chaotic regime) diverges when approaching those maxima. Our results suggest that, in the thermodynamic limit, arbitrarily small integrability- or localization-breaking perturbations result in quantum chaos in the many-body quantum systems studied here.

Original languageEnglish (US)
Article numberL201117
JournalPhysical Review B
Volume104
Issue number20
DOIs
StatePublished - Nov 15 2021

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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