  We compare the accuracy of the ghost-rotationally-invariant slave-boson
(g-RISB) theory and dynamical mean-field theory (DMFT) on the single-band
Hubbard model, as a function of the number of bath sites in the embedding
impurity Hamiltonian. Our benchmark calculations confirm that the accuracy of
g-RISB can be systematically improved by increasing the number of bath sites,
similar to DMFT. With a few bath sites, we observe that g-RISB is
systematically more accurate than DMFT for the ground-state observables. On the
other hand, the relative accuracy of these methods is generally comparable for
the quasiparticle weight and the spectral function. As expected, we observe
that g-RISB satisfies the variational principle in infinite dimensions, as the
total energy decreases monotonically towards the exact value as a function of
the number of bath sites, suggesting that the g-RISB wavefunction may approach
the exact ground state in infinite dimensions. Our results suggest that the
g-RISB is a promising method for first principle simulations of strongly
correlated matter, which can capture the behavior of both static and dynamical
observables, at a relatively low computational cost.
