Bauer, JohannesBabadi, MehrtashDemler, Eugene2019-09-262015Bauer, Johannes, Mehrtash Babadi, and Eugene Demler. 2015. “Dynamical Instabilities and Transient Short-Range Order in the Fermionic Hubbard Model.” Physical Review B 92 (2). https://doi.org/10.1103/physrevb.92.024305.1098-01211550-235Xhttp://nrs.harvard.edu/urn-3:HUL.InstRepos:41412151We study the dynamics of magnetic correlations in the half-filled fermionic Hubbard model following a fast ramp of the repulsive interaction. We use Schwinger-Keldysh self-consistent second-order perturbation theory to investigate the evolution of single-particle Green's functions and solve the nonequilibrium Bethe-Salpeter equation to study the dynamics of magnetic correlations. This approach gives us new insights into the interplay between single-particle relaxation dynamics and the growth of antiferromagnetic correlations. Depending on the ramping time and the final value of the interaction, we find different dynamical behavior which we illustrate using a dynamical phase diagram. Of particular interest is the emergence of a transient short-range ordered regime characterized by the strong initial growth of antiferromagnetic correlations followed by a decay of correlations upon thermalization. The discussed phenomena can be probed in experiments with ultracold atoms in optical lattices.en-USJournal Article2019-09-2610.1103/PhysRevB.92.024305