Kadanoff-Baym-Keldysh-Ehrenfest dynamics of correlated materials responding to ultrafast laser pulses

In our many earlier simulations of the response of materials and molecules to laser pulses, one-electron states were determined by the time-dependent Schr\"{o}dinger equation with an instantaneous one-electron Hamiltonian. These states were then used with Ehrenfest's theorem in a semiclassical treatment of the coupled dynamics of electrons and nuclear coordinates. For strongly-correlated materials, however, true nonequilibrium self-energies are required. Here we describe a practical numerical procedure for employing the Kadanoff-Baym/Keldysh equations together with Ehrenfest's theorem. In preliminary work we treat the simplest possible model of a system in which there is the potential for both a Peierls structural transition (involving doubling of the unit cell) and a Mott-Hubbard electronic transition (involving electron correlations). These calculations are relevant to understanding the dynamics of insulator-metal phase transitions in VO$_{2}$, which has been studied in ultrafast pump-probe measurements [1-3] and nanoscale imaging [4]. \\[4pt] [1] C. K\"{u}bler, Phys. Rev. Lett. 99, 116401 (2007).\\[0pt] [2] M. van Veenendaal, Phys. Rev. (in press).\\[0pt] [3] A. Cavalleri et al., Phys. Rev. B 70, 161102(R) (2004).\\[0pt] [4] M. M. Qazilbash et al., Phys. Rev. B 83, 165108 (2011).