We obtain the exact Kohn-Sham potentials VKS of time-dependent density-functional theory for one-dimensional Hubbard chains, driven by a dc external field, using the time-dependent electron density and current density obtained from exact many-body time evolution. The exact Vxc is compared to the adiabatically exact Vxcad and the "instantaneous ground state" Vxcigs. The latter is shown to work effectively in some cases when the former fails. Approximations for the exchange-correlation potential Vxc and its gradient, based on the local density and on the local current density, are also considered and both physical quantities are observed to be far outside the reach of any possible local approximation. Insight into the respective roles of ground-state and excited-state correlation in the time-dependent system, as reflected in the potentials, is provided by the pair correlation function.
|Journal||Physical Review B: Condensed Matter and Materials Physics|
|Publication status||Published - 9 May 2014|