Convergence behavior of ghost rotationally-invariant slave-boson theory at small bath size: a comparative study with dynamical mean-field theory

We study the convergence behavior of the ghost-rotationally-invariant slave-boson (gRISB) theory with increasing bath orbitals and compare it to the dynamical mean-field theory (DMFT) on the single-band Hubbard model. We show that the accuracy of gRISB can be systematically improved by increasing the number of ghost-orbitals in the bath of the embedded impurity model, similar to DMFT. Moreover, we demonstrate that gRISB generally produces more accurate static physical quantities than DMFT at small bath size, where the total energy and double occupancy in gRISB converge rapidly with bath size Nb = 3 while DMFT requires Nb = 5 to reach the same level of convergence. In addition, gRISB also captures reliable spectral functions compared to DMFT. Our results demonstrate that gRISB is a promising method that requires a few bath orbitals to reach convergence.