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arXiv · 2107.09759

Nambu-Covariant Many-Body Theory I: Perturbative Approximations

M. Drissi·A. Rios·C. Barbieri
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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.

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M. Drissi, A. Rios, C. Barbieri. 2021-07-20. Nambu-Covariant Many-Body Theory I: Perturbative Approximations. https://doi.org/10.1016/j.aop.2024.169729

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