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

Tyler Leblond; Dries Sels; Anatoli Polkovnikov; Marcos Rigol

doi:10.1103/PhysRevB.104.L201117

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

Tyler Leblond
, Dries Sels
, Anatoli Polkovnikov
, Marcos Rigol

Quantum Computational Science

Research output: Contribution to journal › Article › peer-review

61 Scopus citations

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 language	English
Article number	L201117
Journal	Physical Review B
Volume	104
Issue number	20
DOIs	https://doi.org/10.1103/PhysRevB.104.L201117
State	Published - Nov 15 2021

Funding

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.

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10.1103/PhysRevB.104.L201117

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

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