We present a density functional theory (DFT) for lattice models with local
electron-electron (e-e) and electron-phonon (e-ph) interactions.
Exchange-correlation potentials are derived via dynamical mean field theory for
the infinite-dimensional Bethe lattice, and analytically for an isolated
Hubbard-Holstein site. These potentials exhibit discontinuities as a function
of the density, which depend on the relative strength of the e-e and e-ph
interactions. By comparing to exact benchmarks, we show that the DFT formalism
gives a good description of the linear conductance and real-time dynamics.Comment: 5 pages, 3 figures, supplemental material provided as pd
