Evolution of two-time correlations in strongly correlated dissipative systems: aging and hierarchical dynamics*

In recent years, considerable experimental efforts have been devoted
to dynamically generate complex states and monitor their evolution. Despite
remarkable advances, the theoretical principles behind the
non-equilibrium dynamics of strongly correlated quantum matter are
still far from being fully understood. In particular, very few studies
have sought to clarify the influence of environmental couplings on the
propagation of correlations. We attempt here to fill this gap. To do so, we extend quasi-exact time-dependent matrix product state techniques
to simulate the evolution of two-time correlations in the XXZ spin-1/2 model in
contact with an environment causing local dephasing on all sites.
We find this system to display hierarchical and aging dynamics. The latter dynamical regime is
characterized by a breakdown of time-translation invariance, a slow
non-exponential relaxation of two-time correlations and the presence
of dynamical scaling.