Dynamical configuration interaction: Quantum embedding that combines wave functions and Green's functions

Abstract

We present the concept, derivation, and implementation of dynamical configuration interaction, a quantum embedding theory that combines Green's function methodology with the many-body wave function. In a strongly-correlated active space, we use full configuration interaction (CI) to describe static correlation exactly. We add energy dependent corrections to the CI Hamiltonian which, in principle, include all remaining correlation derived from the bath space surrounding the active space. Next, we replace the exact Hamiltonian in the bath with one of excitations defined over a correlated ground state. This transformation is naturally suited to the methodology of manybody Green's functions. In this space, we use a modified GW /Bethe-Salpeter equation procedure to calculate excitation energies. Combined with an estimate of the ground state energy in the bath, we can efficiently compute the energy dependent corrections, which correlate the full set of orbitals, for very low computational cost. We present dimer dissociation curves for H2 and N2 in good agreement with exact results. Additionally, excited states of N2 and C2 are in excellent agreement with benchmark theory and experiment. By combining the strengths of two disciplines, we achieve a balanced description of static and dynamic correlation in a fully ab-initio, systematically improvable framework.

The GW Compendium: A Practical Guide to Theoretical Photoemission Spectroscopy

“…Other routes to combine GW with quantum chemistry are an emerging field. A newly developed method combines GW with configuration interaction by embedding a wave function calculation inside of a Green's function calculation (Dvorak et al, 2018; Dvorak and Rinke, 2019). These developments offer valuable insight to merge these disciplines in the future.…”

Quantum simulations of materials on near-term quantum computers

“…For instance, density functional embedding theory has been developed to improve the accuracy and scalability of DFT calculations [53][54][55][56][57] . Density matrix embedding theory (DMET) [58][59][60] and various Green's function based approaches 61,62 , e.g., DMFT, have been developed to describe systems with strongly-correlated electronic states. At present, ab initio calculations of materials using DMET and DMFT have been limited to relatively small unit cells (a few tens of atoms) of pristine crystals, due to their high computational cost 63,64 .…”

Site-occupation Green's function embedding theory: A density functional approach to dynamical impurity solvers

“…An appealing extension of Green's function techniques to quantum chemical problems is self-energy embedding theory (SEET) [22][23][24][25] where local and non-local electronic correlations are modelled by the combination of wave function-based methods with many-body perturbation theory. A mixture of configuration interaction with Green's functions has also been recently proposed by Dvorak and Rinke [26].…”