Dynamical Downfolding and Construction of Effective Hamiltonians for Correlated Systems*

There is longstanding interest in reducing the computational cost for electronic structure calculations of correlated systems. Recently, Romanova et. al have developed a method of dynamical downfolding to map a large correlated problem onto a small (treatable) subspace [Romanova et al., npj  Computational Materials 9 (1), 126, 2023]. The method entails the construction of an effective correlated quasiparticle Hamiltonian, which requires solving auxiliary one- and two-body propagator problems. This work succeeded in finding quantitative agreement with the experimental spectrum of an NV center. The limitations of this approach have, however, yet to be explored. Using a solvable model system, we investigate how the renormalization of one-body and two-body terms arises in the downfolded Hamiltonian and the correspondence to the aforementioned dynamical downfolding procedure.  Further, we explore the effectiveness of the downfolding procedure as the coupling between the correlated subspace and the rest space is increased.