We illustrate the scope of time-dependent density-functional theory for strongly correlated (lattice) models out of equilibrium. Using the exact many-body time evolution, we reverse engineer the exact exchange correlation (xc) potential $v_{\mathrm{xc}}$ for small Hubbard chains exposed to time-dependent fields. We introduce an adiabatic local density approximation to $v_{\mathrm{xc}}$ for the 1D Hubbard model and compare it to exact results, to gain insight about approximate xc potentials. Finally, we provide some remarks on the $v$-representability for the 1D Hubbard model.

• Received 11 December 2007

DOI:https://doi.org/10.1103/PhysRevLett.101.166401