Quantum Dynamics of the Hubbard-Holstein Model in Equilibrium and Nonequilibrium: 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 ultrashort powerful light pulse, in undoped systems. At equilibrium and at strong charge-lattice couplings, the optical conductivity reveals a three-peak structure in agreement with experimental observations. After an ultrashort pulse and at nonzero electron-phonon interaction, phonon and spin subsystems oscillate with the phonon period T-ph approximate to 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.