Back-reaction and correlation effects on pre-thermalization in Mott-Hubbard systems

For the Fermi-Hubbard model in the strongly interacting Mott insulator state, we study the pre-thermalization dynamics after a quench. To this end, we employ the method of the hierarchy of correlations and compare different levels of accuracy. To leading order, the usual free quasi-particle dynamics (as encoded in the two-point correlation functions) yields the standard picture of pre-thermalization. Taking into account the back-reaction of these quasi-particle fluctuations onto the mean-field background as the first next-to-leading order effect, we observe a strong degradation of pre-thermalization, especially in low dimensions. In contrast, the inclusion of three-point correlations enhances pre-thermalization.