Efficient hybridization fitting for dynamical mean-field theory via semi-definite relaxation

We introduce a nested optimization procedure using semi-definite relaxation for the fitting step in Hamiltonian-based cluster dynamical mean-field theory (DMFT) methodologies. We show that the proposed method is more efficient and flexible than state-of-the-art fitting schemes, which allows us to treat as large a number of bath sites as the impurity solver at hand allows. We characterize its robustness to initial conditions and symmetry constraints, thus providing conclusive evidence that in the presence of a large bath, our semi-definite relaxation approach can find the correct set of bath parameters without needing to include \emph{a priori} knowledge of the properties that are to be described. We believe this method will be of great use for Hamiltonian-based calculations, simplifying and improving one of the key steps in cluster dynamical mean-field theory calculations.