Probing many-body quantum chaos with quantum simulators
Abstract
The spectral form factor (SFF), characterizing statistics of energy eigenvalues, is a key diagnostic of many-body quantum chaos. In addition, partial spectral form factors (PSFFs) can be defined which refer to subsystems of the many-body system. They provide unique insights into energy eigenstate statistics of many-body systems, as we show in an analysis on the basis of random matrix theory and of the eigenstate thermalization hypothesis. We propose a protocol that allows the measurement of the SFF and PSFFs in quantum many-body spin models, within the framework of randomized measurements. Aimed to probe dynamical properties of quantum many-body systems, our scheme employs statistical correlations of local random operations which are applied at different times in a single experiment. Our protocol provides a unified testbed to probe many-body quantum chaotic behavior, thermalization and many-body localization in closed quantum systems which we illustrate with numerical simulations for Hamiltonian and Floquet many-body spin-systems.
Cite
@article{arxiv.2106.15530,
title = {Probing many-body quantum chaos with quantum simulators},
author = {Lata Kh Joshi and Andreas Elben and Amit Vikram and Benoît Vermersch and Victor Galitski and Peter Zoller},
journal= {arXiv preprint arXiv:2106.15530},
year = {2022}
}
Comments
16+14 pages, 14 figures. The presentation throughout the paper is improved, without any change in the core content and results. New figure and appendix added. Matches with the published version