  Site-occupation embedding theory (SOET) is an alternative formulation of
density-functional theory (DFT) for model Hamiltonians where the
fully-interacting Hubbard problem is mapped, in principle exactly, onto an
impurity-interacting (rather than a non-interacting) one. It provides a
rigorous framework for combining wavefunction (or Green function) based methods
with DFT. In this work, exact expressions for the per-site energy and double
occupation of the uniform Hubbard model are derived in the context of SOET. As
readily seen from these derivations, the so-called bath contribution to the
per-site correlation energy is, in addition to the latter, the key density
functional quantity to model in SOET. Various approximations based on Bethe
ansatz and perturbative solutions to the Hubbard and single impurity Anderson
models are constructed and tested on a one-dimensional ring. The
self-consistent calculation of the embedded impurity wavefunction has been
performed with the density matrix renormalization group method. It has been
shown that promising results are obtained in specific regimes of correlation
and density. Possible further developments have been proposed in order to
provide reliable embedding functionals and potentials.
