Scrambling and thermalization behavior of a diffusive system

Dynamical correlation functions give valuable insights into the thermalization behavior of a many-body system. We investigate different dynamical correlation functions in the non-integrable one-dimensional Bose-Hubbard model by means of density matrix renormalization group schemes. At high temperatures, well defined quasi-particles cease to exist and the time-ordered Green’s function exhibits rapidly decaying excitations. Out-of-time ordered (OTO) correlators on the other hand have recently been proposed to describe the spread of quantum information, which is not necessarily coupled to the propagation of quasi-particles. Despite the high temperatures, we indeed observe that the OTO correlators display a pronounced linear light-cone. Our numerical analysis moreover reveals that the scrambling of information does not account for the slowest timescale in the thermalization behavior of the system. Instead, conserved quantities cause hydrodynamic long-time tails which decelerate the full thermalization. We furthermore propose two different interferometric schemes to approach the challenge of measuring time-ordered as well as out-of-time ordered dynamical correlation functions in real space in cold atom experiments.