Accuracy of ghost-rotationally-invariant slave-boson and dynamical mean field theory as a function of the impurity-model bath size

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.