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Origin of Misleading Convergence in Self-Consistent Many-Electron Theories: Fundamental Aspects and Practical Implications

Herbert Eßl1,*, Matthias Reitner1, Evgeny Kozik2, and Alessandro Toschi1

  • *Contact author: herbert.essl@tuwien.ac.at
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Phys. Rev. Lett. 137, 016502 – Published 1 July, 2026

DOI: https://doi.org/10.1103/zjy7-4jqd

Abstract

Self-consistent approaches in many-electron problems typically converge to an unphysical solution in strongly correlated regimes. By deriving the mathematical condition for the stability of the physical solution, we unveil the precise relation between two distinct issues previously considered equivalent: the misleading convergence in self-consistent schemes and the multivaluedness of the Luttinger-Ward functional. Although these problems are fundamentally linked through the divergences of the irreducible vertex function, we show that misleading convergence can occur even in the absence of such divergences. Eventually, a systematic procedure for stabilizing the physical solution is proposed.

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Phys. Rev. Lett. 137, 016502– Published 1 July, 2026
  • Received 1 March 2025
  • Accepted 19 May 2026
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