TY - JOUR
T1 - Universality in the onset of quantum chaos in many-body systems
AU - Leblond, Tyler
AU - Sels, Dries
AU - Polkovnikov, Anatoli
AU - Rigol, Marcos
N1 - Funding Information:
We acknowledge discussions with E. Altman, A. Dymarsky, S. Gopalakrishnan, D. Huse, M. Pandey, and L. Vidmar. This work was supported by the National Science Foundation under Grants No. PHY-2012145 (T.L. and M.R.), No. DMR-1813499 (A.P.), and No. DMR-2103658 (A.P.), and by the AFOSR under Grants No. FA9550-16-1-0334 (A.P.), No. FA9550-21-1-0342 (A.P.), and No. FA9550-21-1-0236 (D.S.). The computations were carried out in the Roar supercomputer in the Institute for Computational and Data Sciences (ICDS) at Penn State. The Flatiron Institute is a division of the Simons Foundation.
Publisher Copyright:
© 2021 American Physical Society.
PY - 2021/11/15
Y1 - 2021/11/15
N2 - 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.
AB - 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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U2 - 10.1103/PhysRevB.104.L201117
DO - 10.1103/PhysRevB.104.L201117
M3 - Article
AN - SCOPUS:85121097770
VL - 104
JO - Physical Review B-Condensed Matter
JF - Physical Review B-Condensed Matter
SN - 2469-9950
IS - 20
M1 - L201117
ER -