Efficient hybridization fitting for dynamical mean-field theory via semi-definite relaxation
Carlos Mejuto-Zaera, Leonardo Zepeda-Núñez, Michael Lindsey, Norm M. Tubman, Birgitta Whaley, Lin Lin
Abstract
We introduce a nested optimization procedure using semidefinite relaxation for the fitting step in Hamiltonian-based cluster dynamical mean-field theory 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 semidefinite relaxation approach can find the correct set of bath parameters without needing to include 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.