Photoinduced phase transitions in narrow-gap Mott insulators: the case of VO$_2$

We study the nonequilibrium dynamics of photoexcited electrons in the narrow-gap Mott insulator VO$_2$. The initial stages of relaxation are treated using a quantum Boltzmann equation methodology, which reveals a rapid ($\sim$ femtosecond time scale) relaxation to a pseudothermal state characterized by a few parameters that vary slowly in time. The long-time limit is then studied by a Hartree-Fock methodology, which reveals the possibility of nonequilibrium excitation to a new metastable $M_1$ metal phase that is qualitatively consistent with a recent experiment. The general physical picture of photoexcitation driving a correlated electron system to a new state that is not accessible in equilibrium may be applicable in similar materials.