Dynamical renormalization of interactions in downfolded Hamiltonians with the stochastic cRPA

The model downfolded Hamiltonians facilitate the electronic structure calculations by reducing the computational load, however, several methodological issues can compromise the accuracy of this approach. Among them is an accurate inclusion of the environment dynamics that translates into the frequency dependence of one- and two-body interaction terms, which is often overlooked.

In this work, we develop and test the stochastic methods to efficiently downfold many-body interactions in large-scale systems. We next discuss the importance of including the dynamical renormalization of the downfolded Hamiltonian, in particular, for models in a minimal basis. We demonstrate the efficiency of the proposed methodology on predicting optical excitations in the negatively charged NV center defect in diamond.