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

We investigate the unitary dynamics following a sudden increase $\mathrm{\Delta }U>0$ 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 wavefunction 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 pronounced dynamical anomaly at larger $\mathrm{\Delta }{U}_{\ast }>\mathrm{\Delta }{U}_c$ manifested in a singular behaviour of the long-time average of double occupancy. Although the real-time dynamics of the variational parameters at $\mathrm{\Delta }{U}_{\ast }$ strongly resembles the one at $\mathrm{\Delta }{U}_c$, careful frequency spectrum analysis suggests a dynamical crossover, instead of a dynamical transition, separating regions of a different behaviour of the spin-exchange.