Regensburg 2025 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 17: Correlated Electrons: Method Development

TT 17.13: Vortrag

Dienstag, 18. März 2025, 12:45–13:00, H33

How to stay on the physical branch of self-consistent many-electron schemes — •Herbert Eßl, Matthias Reitner, and Alessandro Toschi — TU Wien

We precisely determine the mathematical condition under which the physical solution of the many-electron problem, obtained by self-consistent resummations becomes unstable by increasing interaction strength. The evaluation of the proposed criterion only requires the calculation of two-particle correlation functions. The validity of our predictions has been explicitly verified by performing self-consistent calculations of basic interacting models. Our findings eventually unveil the precise connection linking the misleading convergence of the self-consistent schemes to the multivaluedness of the Luttinger-Ward functionals and to the divergences of the irreducible vertex functions. Further, our analysis explains how the misleading convergence occurs even in parameter regions without vertex divergences. More importantly, it allows us to define a general scheme for stabilizing the physical solution, when it is unstable in conventional self-consistent schemes.

Keywords: many-body pertubation theory; self-consistent schemes; non-perturbative effects; two-particle correlation functions; Luttinger Ward functional