We advance perturbative approaches for out-of-equilibrium quantum many-body systems by applying unitary perturbation theory to the real-time evolution of the weakly interacting Hubbard model in d > 1 dimensions. We derive general expressions for the fermionic operators that allow us to perturbatively calculate the time evolution of observables to second-order expansion in the interaction strength. We find that the results are stable up to and including the prethermalization regime. We apply our findings to the nonequilibrium build-up of density-density correlations after a weak interaction quench and compare the prethermalization values to equilibrium correlations. Furthermore, we analyze the light-cone-like structure of the density-density susceptibility and the equal-time correlation function in the context of the Lieb-Robinson bounds.
We investigate the quantum quench dynamics of the interacting Hatano-Nelson model with open boundary conditions using both Abelian bosonization and numerical methods. Specifically, we follow the evolution of the particle density and current profile in real space over time by turning the imaginary vector potential on or off in the presence of weak interactions. Our results reveal spatiotemporal Friedel oscillations in the system with light cones propagating ballistically from the open ends, accompanied by local currents of equal magnitude for both switch-off and -on protocols. Remarkably, the bosonization method accurately accounts for the density and current patterns with a single overall fitting parameter. The continuity equation is satisfied by the long-wavelength part of the density and current, despite the nonunitary time evolution when the Hatano-Nelson term is switched on.
We explore the time evolution of correlations in a homogeneous gas of lattice bosons with filling factor
n0, following a sudden reduction in the lattice depth to a regime where the interactions are weak. In the limit of vanishing interactions, we find a simple closed-form expression for the static structure factor. The corresponding real-space density-density correlation function shows multiple spatial oscillations which disperse linearly in time. By perturbatively including the effect of interactions, we study the evolution of boson quasimomentum distribution following the quench. In one dimension, the quasimomentum distribution develops peaks at finite momentum which disperse towards $q=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$. In two dimensions, the momentum occupation rapidly approaches a steady-state distribution characterized by a broad peak at
q=0. Quasi-long-range order is never found at finite time. Our studies provide insight into the dynamics of isolated quantum systems.