How to stay on the physical branch in self-consistent many-electron approaches

2025/02/03 by Eßl, Herbert, Reitner, Matthias, Kozik, Evgeny +1 · 1 citation
#FOS: Physical sciences #Strongly Correlated Electrons (cond-mat.str-el)

paper · doi:10.48550/arxiv.2502.01420

Abstract

We derive the mathematical condition under which the physical solution of the many-electron problem, obtained by self-consistent approaches, becomes unstable upon increasing interaction strength. The validity of our criterion is explicitly verified by performing self-consistent calculations of basic interacting models. In this context, we eventually unveiled the precise connection linking the misleading convergence of self-consistent schemes to the multivaluedness of the Luttinger-Ward functional as well as to the divergences of the irreducible vertex function. Our analysis also explains how a misleading convergence of self-consistent approximations can occur even in parameter regions without vertex divergences. Even more importantly, it allows us to define a general procedure for stabilizing the physical solution, when it is unstable in conventional self-consistent schemes.

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• Diagrammatic bosonisation, aspects of criticality, and the Hohenberg-Mermin-Wagner Theorem in parquet approaches

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