  We present detailed benchmark ground-state calculations of the one- and
two-dimensional Hubbard model utilizing the cluster extensions of the
rotationally invariant slave-boson (RISB) mean-field theory and the density
matrix embedding theory (DMET). Our analysis shows that the overall accuracy
and the performance of these two methods are very similar. Furthermore, we
propose a unified computational framework that allows us to implement both of
these techniques on the same footing. This provides us with a new line of
interpretation and paves the ways for developing systematically new
generalizations of these complementary approaches.
