Quantum Dynamics of the Hubbard-Holstein Model in Equilibrium and   Non-Equilibrium: Application to Pump-Probe Phenomena
  The spectral response and physical features of the 2D Hubbard-Holstein model are calculated both in equilibrium at zero and low chemical dopings, and after an ultra short powerful light pulse, in undoped systems. At equilibrium and at strong charge-lattice couplings, the optical conductivity reveals a 3-peak structure in agreement with experimental observations. After an ultra short pulse and at nonzero electron-phonon interaction, phonon and spin subsystems oscillate with the phonon period $T_{ph} \approx 80$ fs. The decay time of the phonon oscillations is about 150-200 fs, similar to the relaxation time of the charge system. We propose a criterion for observing these oscillations in high $T_c$ compounds: the time span of the pump light pulse $\tau_{pump}$ has to be shorter than the phonon oscillation period $T_{ph}$. 
G. De Filippis, V. Cataudella, E. A. Nowadnick, T. P. Devereaux, A. S.   Mishchenko and N. Nagaosa
cond-mat.str-el