A1 Journal article (refereed)
Cutting rules and positivity in finite temperature many-body theory (2022)

Hyrkäs, M., Karlsson, D., & van Leeuwen, R. (2022). Cutting rules and positivity in finite temperature many-body theory. Journal of Physics A : Mathematical and Theoretical, 55(33), Article 335301. https://doi.org/10.1088/1751-8121/ac802d

JYU authors or editors

Publication details

All authors or editors: Hyrkäs, Markku; Karlsson, Daniel; van Leeuwen, Robert

Journal or series: Journal of Physics A : Mathematical and Theoretical

ISSN: 1751-8113

eISSN: 1751-8121

Publication year: 2022

Publication date: 11/07/2022

Volume: 55

Issue number: 33

Article number: 335301

Publisher: IOP Publishing

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1088/1751-8121/ac802d

Publication open access: Not open

Publication channel open access: 

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/82804

Publication is parallel published: https://arxiv.org/abs/2203.11083

Abstract

For a given diagrammatic approximation in many-body perturbation theory it is not guaranteed that positive observables, such as the density or the spectral function, retain their positivity. For zero-temperature systems we developed a method [Phys.Rev.B{\bf 90},115134 (2014)] based on so-called cutting rules for Feynman diagrams that enforces these properties diagrammatically, thus solving the problem of negative spectral densities observed for various vertex approximations. In this work we extend this method to systems at finite temperature by formulating the cutting rules in terms of retarded $N$-point functions, thereby simplifying earlier approaches and simultaneously solving the issue of non-vanishing vacuum diagrams that has plagued finite temperature expansions. Our approach is moreover valid for nonequilibrium systems in initial equilibrium and allows us to show that important commonly used approximations, namely the $GW$, second Born and $T$-matrix approximation, retain positive spectral functions at finite temperature. Finally we derive an analytic continuation relation between the spectral forms of retarded $N$-point functions and their Matsubara counterparts and a set of Feynman rules to evaluate them.

Free keywords: diagrammatic perturbation theory; non-equilibrium Green’s functions; quantum many-body theory; spectral properties

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Ministry reporting: Yes

VIRTA submission year: 2022

JUFO rating: 2