Self-consistent Green's function approaches

TL;DR

This paper reviews Green's function methods for many-body fermion systems, focusing on their fundamental equations, implementation, and inclusion of complex interactions, emphasizing self-consistency for thermodynamic accuracy.

Contribution

It introduces a comprehensive derivation of Green's function techniques, including Algebraic Diagrammatic Construction and self-consistent formalisms at finite temperature, with applications to nuclear matter.

Findings

Implementation of Green's function methods for nuclear systems

Comparison of models with other approaches in the book

Validation of self-consistent formalism for thermodynamic properties

Abstract

We present the fundamental techniques and working equations of many-body Green's function theory for calculating ground state properties and the spectral strength. Green's function methods closely relate to other polynomial scaling approaches discussed in chapters 8 and 10. However, here we aim directly at a global view of the many-fermion structure. We derive the working equations for calculating many-body propagators, using both the Algebraic Diagrammatic Construction technique and the self-consistent formalism at finite temperature. Their implementation is discussed, as well as the inclusion of three-nucleon interactions. The self-consistency feature is essential to guarantee thermodynamic consistency. The pairing and neutron matter models introduced in previous chapters are solved and compared with the other methods in this book.