Diatomic molecule as a testbed for combining DMFT with electronic structure methods such as $GW$ and DFT

TL;DR

This study evaluates various combinations of DMFT with $GW$ and DFT methods on the H$_2$ molecule, revealing limitations and strengths of each approach in strongly correlated regimes and proposing improved schemes.

Contribution

The paper introduces and compares fully self-consistent, one-shot, and quasiparticle self-consistent $GW$+DMFT methods, highlighting their performance and limitations on a diatomic molecule.

Findings

Most $GW$+DMFT flavors break down in strongly correlated regimes due to causality issues.

Only self-consistent quasiparticle $GW$+DMFT with static and causal double-counting recover the atomic limit.

LDA+DMFT provides the most accurate total energy predictions with known static double-counting.

Abstract

We implemented combination of DMFT and $GW$ in its fully self-consistent way, one shot $GW$ approximation, and quasiparticle self-consistent scheme, and studied how well these combined methods perform on H$_2$ molecule as compared to more established methods such as LDA+DMFT. We found that most flavors of $GW$+DMFT break down in strongly correlated regime due to causality violation. Among $GW$+DMFT methods, only the self-consistent quasiparticle $GW$+DMFT with static double-counting, and a new method with causal double-counting, correctly recover the atomic limit at large H-atom separation. While some flavors of $GW$+DMFT improve the single-electron spectra as compared to LDA+DMFT, the total energy is best predicted by LDA+DMFT, for which the exact double-counting is known, and is static.