Cutting rules and positivity in finite temperature many-body theory
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
Julkaistu sarjassa
Journal of Physics A : Mathematical and TheoreticalPäivämäärä
2022Tekijänoikeudet
© 2022 IOP Publishing Ltd
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.
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Julkaisija
IOP PublishingISSN Hae Julkaisufoorumista
1751-8113Asiasanat
Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/148946372
Metadata
Näytä kaikki kuvailutiedotKokoelmat
Rahoittaja(t)
Suomen AkatemiaRahoitusohjelmat(t)
Tutkijatohtori, SA; Akatemiahanke, SALisätietoja rahoituksesta
D.K. acknowledges the academy of Finland for funding under Project No. 308697. M.H. thanks the Finnish Cultural Foundation for support. R.v.L. acknowledges the academy of Finland for funding under Project No. 317139Lisenssi
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