The description of strong correlation within self-consistent Green's function second-order perturbation theory

TL;DR

This paper presents an implementation of self-consistent Green's function second-order perturbation theory (GF2) for molecular systems, effectively describing strong correlation effects such as metal-insulator transitions without spin-symmetry breaking.

Contribution

The paper introduces a practical GF2 implementation for strongly correlated systems, demonstrating its ability to handle multireference ground states and phase transitions.

Findings

GF2 accurately describes metal-insulator transitions.

The method captures multireference electronic ground states.

GF2 remains computationally feasible for complex systems.

Abstract

We report an implementation of self-consistent Green's function many-body theory within a second-order approximation (GF2) for application with molecular systems. This is done by iterative solution of the Dyson equation expressed in matrix form in an atomic orbital basis, where the Green's function and self-energy are built on the imaginary frequency and imaginary time domain respectively, and fast Fourier transform is used to efficiently transform these quantities as needed. We apply this method to several archetypical examples of strong correlation, such as a H$_{32}$ finite lattice that displays a highly multireference electronic ground state even at equilibrium lattice spacing. In all cases GF2 gives a physically meaningful description of the metal to insulator transition in these systems, without resorting to spin-symmetry breaking. Our results show that self-consistent Green's function many-body theory offers a viable route to describing strong correlations while remaining within a computationally tractable single-particle formalism.