Nambu-Covariant Many-Body Theory I: Perturbative Approximations

TL;DR

This paper develops a covariant many-body perturbation theory framework for symmetry-breaking phases, utilizing Nambu tensors to simplify diagrammatic calculations at finite temperature.

Contribution

It introduces a Nambu tensor-based covariant formulation of many-body perturbation theory that simplifies symmetry-breaking approximation design.

Findings

Derives a factorisation of Feynman diagrams valid for general Hamiltonians.

Provides a covariant formulation respecting symmetry-breaking transformations.

Simplifies the construction of many-body approximations in symmetry-breaking phases.

Abstract

Symmetry-breaking considerations play an important role in allowing reliable and accurate predictions of complex systems in quantum many-body simulations. The general theory of perturbations in symmetry-breaking phases is nonetheless intrinsically more involved than in the unbroken phase due to non-vanishing anomalous Green's functions or anomalous quasiparticle interactions. In the present paper, we develop a formulation of many-body theory at non-zero temperature which is explicitly covariant with respect to a group containing Bogoliubov transformations. Based on the concept of Nambu tensors, we derive a factorisation of standard Feynman diagrams that is valid for a general Hamiltonian. The resulting factorised amplitudes are indexed over the set of un-oriented Feynman diagrams with fully antisymmetric vertices. We argue that, within this framework, the design of symmetry-breaking many-body approximations is simplified.