Spectral Statistics in Spatially Extended Chaotic Quantum Many-Body Systems

We study spectral statistics in spatially extended chaotic quantum many-body systems, using simple lattice Floquet models without time-reversal symmetry. Computing the spectral form factor Kotthorn analytically and numerically, we show that it follows random matrix theory (RMT) at times longer than a many-body Thouless time, t(Th). We obtain a striking dependence of t(Th) on the spatial dimension d and size of the system. Ford > 1, t(Th) is finite in the thermodynamic limit and set by the intersite coupling strength. By contrast, in one dimension t(Th) diverges with system size, and for large systems there is a wide window in which spectral correlations are not of RMT form. Lastly, our Floquet model exhibits a many-body localization transition, and we discuss the behavior of the spectral form factor in the localized phase.