Many-body quantum chaos

The ergodicity and chaos are essential concepts for applying
equilibrium statistical mechanics techniques to any system. For quantum
systems, chaos is often identified through their level-spacing statistics.
It has been observed in numerics that quantum systems with integrable
(nonintegrable) classical counterparts have quantum levels showing
clustering or level crossing (level repulsion) when a parameter in the
Hamiltonian is varied. This leads to the Bohigas-Giannoni-Schmit
conjecture, which asserts that the spectral statistics of quantum systems
whose classical counterparts exhibit chaotic behavior are described by
random matrix theory (RMT). This conjecture is also regularly employed for
many-body quantum systems, where local degrees of freedom, e.g., fermions,
and qubits, have no classical limit. It remains a mystery for many years
why the RMT description successfully explains chaotic dynamics in such
many-body quantum systems. Only recently, a series of microscopic studies
have explored quantum chaos and spectral correlations in periodically
driven (Floquet) many-body systems to show the emergence of universal RMT
description of the spectral form factor characterizing spectral
fluctuations in these systems by going beyond the semiclassical
periodic-orbit approaches. I shall discuss our effort in this direction of
many-body quantum chaos during my presentation.