Nambu-Covariant Many-Body Theory II: Self-Consistent Approximations

TL;DR

This paper reformulates the Self-Consistent Green's Function theory in a Nambu-covariant framework for symmetry-broken phases, developing a self-consistent ladder approximation applicable to many-body systems at finite temperature.

Contribution

It extends Nambu-covariant perturbation theory to non-perturbative self-consistent schemes and formulates a ladder approximation suitable for symmetry-broken phases.

Findings

Derived spectral function-based equations in Nambu tensors.

Proved stability conditions for HFB self-energy.

Enabled application to infinite nuclear matter.

Abstract

The theory of Self-Consistent Green's Function (SCGF) is reformulated in an explicit Nambu-covariant fashion for applications to many-body systems at non-zero temperature in symmetry-broken phases. This is achieved by extending the Nambu-covariant formulation of perturbation theory, presented in the first part of this work, to non-perturbative schemes based on self-consistently dressed propagators and vertices. We work out in detail the self-consistent ladder approximation, motivated by a trade-off between numerical complexity and many-body phenomenology. Taking a complex general Hartree-Fock-Bogoliubov (HFB) propagator as a starting point, we also formulate and prove a sufficient condition on the stability of the HFB self-energy to ensure the convergence of the initial series of ladders at any energy. The self-consistent ladder approximation is written purely in terms of spectral functions and the resulting set of equations, when expressed in terms of Nambu tensors, are remarkably similar to those in the symmetry-conserving case. This puts the application of the self-consistent ladder approximation to symmetry-broken phases of infinite nuclear matter within reach.