A regularized second-order correlation method from Green's function theory

TL;DR

This paper introduces QPMP2, a scalable Green's function-based method that accurately captures electronic correlation in molecules and materials, effectively handling strong correlation and avoiding divergences of traditional methods.

Contribution

The paper develops a size-extensive, Green's function-based perturbation theory called QPMP2 that improves upon MP2 and coupled cluster methods for strongly correlated systems.

Findings

QPMP2 reproduces exact ground state energies of the Hubbard dimer.

It qualitatively captures the metal-insulator transition in Hubbard models.

QPMP2 provides an efficient, size-consistent regularization for strongly correlated molecules.

Abstract

We present a scalable single-particle framework to treat electronic correlation in molecules and materials motivated by Green's function theory. We derive a size-extensive Brillouin-Wigner perturbation theory from the single-particle Green's function by introducing the Goldstone self-energy. This new ground state correlation energy, referred to as Quasi-Particle MP2 theory (QPMP2), avoids the characteristic divergences present in both second-order M{\o}ller-Plesset perturbation theory and Coupled Cluster Singles and Doubles within the strongly correlated regime. We show that the exact ground state energy and properties of the Hubbard dimer are reproduced by QPMP2 and demonstrate the advantages of the approach for the six-, eight- and ten-site Hubbard models where the metal-to-insulator transition is qualitatively reproduced, contrasting with the complete failure of traditional methods. We apply this formalism to characteristic strongly correlated molecular systems and show that QPMP2 provides an efficient, size-consistent regularization of MP2.