Time Dependent Density Functional Theory and Strongly Correlated Systems: Insight From Numerical Studies

We illustrate the potential of Time Dependent Density Functional Theory (TDDFT) for describing the nonequilibrium behavior of strongly correlated (lattice) models. Starting from an exact time-evolution of the many-body wavefunction, we determine, via reverse engineering, the exact exchange correlation (xc) potential $v_{xc}$ for small Hubbard chains of different lengths and electron fillings and exposed to time-dependent perturbations. We compare some of the exact results to those of adiabatic-like treatments, in order to extract some of the properties that approximate xc potentials should have. Finally, we provide details of work in progress and future directions.