Probing Many-Body Quantum Chaos with Quantum Simulators

The spectral form factor (SFF), characterizing statistics of energy eigenvalues, is a key diagnostic many-body quantum chaos. In addition, partial factors (PSFFs) can be defined which refer to subsystems the system. They provide unique insights into eigenstate systems, as we show in an analysis on basis random matrix theory and thermalization hypothesis. We propose protocol that allows measurement SFF PSFFs spin models, within framework randomized measurements. Aimed probe dynamical properties our scheme employs statistical correlations local operations are applied at different times single experiment. Our provides unified testbed chaotic behavior, localization closed systems illustrate with numerical simulations for Hamiltonian Floquet spin-systems.