Interplay of charge and spin dynamics after an interaction quench in the Hubbard model

We investigate the unitary dynamics following a sudden increase Delta U > 0 of repulsion in the paramagnetic sector of the half-filled Hubbard model on a Bethe lattice, by means of a variational approach that combines a Gutzwiller wave function with a partial Schrieffer-Wolff transformation, both defined through time-dependent variational parameters. Besides recovering at Delta U-c the known dynamical transition linked to the equilibrium Mott transition, we find a pronounced dynamical anomaly at larger Delta U-* > Delta U-c manifested in a singular behavior of the long-time average of double occupancy. Although the real-time dynamics of the variational parameters at Delta U-* strongly resembles the one at Delta U-c, a careful frequency spectrum analysis suggests a dynamical crossover, instead of a dynamical transition, separating regions of a different behavior of the spin exchange.