L. K. Joshi, A. Elben, A. Vikram, B. Vermersch, V. Galitski, P. Zoller Probing many-body quantum chaos with quantum simulators,
Phys. Rev. X (2022-01-27),
http://dx.doi.org/10.1103/PhysRevX.12.011018 doi:10.1103/PhysRevX.12.011018 (ID: 720665)
Toggle 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 which allows the measurement of 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 simulations for Hamiltonian and Floquet many-body spin-systems.