Analytical nonadiabatic exchange-correlation potentials for nonequilibrium studies of strongly correlated materials

The quest for a microscopic understanding of the ultrafast processes in strongly correlated materials hinges on the fact that it captures the role of electron correlations. To accomplish this challenging task, a way forward is through derivation of appropriate exchange-correlation (XC) potentials for implementation in time-dependent density-functional theory (TDDFT). We present here analytical expressions for such (nonadiabatic) potentials in the limits of strong and weak electron correlations, obtained by using the Sham-Schlueter equation approach. The XC potentials are obtained from the local-in-space electron self-energy in the one-band Hubbard model. To test the potentials, we employ them in TDDFT calculations for the one-band Hubbard model and compare the results with the nonequilibrium dynamical mean-field theory solution which shows good agreement. We discuss strategies for formulation of a universal XC potential valid also for intermediate strengths of electron correlations. The net outcome is a reliable and computationally efficient XC potential that takes into account both memory and correlation effects and can be applied to examine ultrafast properties of materials at any strength of the perturbing field.