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 mean-field theory and the density matrix embedding theory. 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 different line of interpretation and paves the ways for developing systematically distinct generalizations of these complementary approaches.
We assess the accuracy of ghost-rotationally-invariant slave-boson (g-RISB) theory in multiorbital systems by applying it to both the three-orbital degenerate Hubbard model and a realistic
Sr2RuO4 model extracted from first-principle simulations and comparing the results to those obtained using dynamical mean-field theory (DMFT). Our findings indicate that g-RISB's accuracy can be systematically improved toward the exact DMFT limit in infinite-dimensional multiorbital models by increasing the number of ghost orbitals. This allows for a more precise description of aspects of Hund metal physics and Mott physics compared with the original RISB approach. We also demonstrate that g-RISB reliably captures the quasiparticle weights, Fermi surface, and low-energy spectral function for the realistic
Sr2RuO4 model compared with DMFT. Moreover, we showcase the potential of using the density matrix renormalization group method as an impurity solver within the g-RISB framework to study systems with a larger number of ghost orbitals. These results show the potential of g-RISB as a reliable tool for simulating correlated materials. The connection between the g-RISB and DMFT self-energy is also discussed.