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

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Authors
LeBlond, Tyler
Sels, Dries
Polkovnikov, Anatoli
Rigol, Marcos
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T. LeBlond, D. Sels, A. Polkovnikov, M. Rigol. "Universality in the onset of quantum chaos in many-body systems." Physical Review B, Volume 104, Issue 20, https://doi.org/10.1103/physrevb.104.l201117
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.
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