Bath parameterization in multi-band cluster Dynamical Mean-Field Theory

Abstract

Accurate and reliable algorithms to solve complex impurity problems are instrumental to a routine use of quantum embedding methods for material discovery. In this context, we employ an efficient selected configuration interaction impurity solver to investigate the role of bath discretization, specifically, bath size and parameterization, in Hamiltonian-based cluster dynamical mean field theory (CDMFT) for the one- and two-orbital Hubbard models. We consider two- and four-site clusters for the single-orbital model and a two-site cluster for the two-orbital model. Our results demonstrate that, for small bath sizes, the choice of parameterization can significantly influence the solution, highlighting the importance of systematic convergence checks. Comparing different bath parameterizations not only reveals the robustness of a given solution but can also provide insights into the nature of different solutions and potential instabilities of the paramagnetic state. We present an extensive analysis of the zero-temperature Mott transition of the paramagnetic half-filled single-band Hubbard model, benchmarking our findings against previous literature. We find that for the single-band model the dependence on parameterization is weak for the largest bath sizes accessible with ASCI, while a tendency towards a nematic solution can be seen when the bath size is small. Building on this, we extend our study to the multi-band regime, where we present the first systematic analysis at zero temperature for two orbitals and a two-site cluster. This setup allows us to assess the effect of nearest-neighbor dynamical correlations on the multi-orbital Mott transition. In this case, some quantitative dependence on the parameterization is retained for the two-orbital model, for instance in the value of the critical interaction for a Mott transition.