Derives an explicit stability criterion for parquet fixed-point iterations showing convergence issues arise independently of vertex divergences and demonstrates a controlled stabilization method that reaches the physical solution across multiple divergence lines.
Generating functional for the full parquet approximation
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abstract
Parquet diagrams sum self-consistently Feynman graphs for the vertex function with all two-particle multiple scatterings. We show how the complete parquet equations for the Hubbard-like models can be integrated to a generating functional from which all thermodynamic quantities are derived via (functional) derivatives. An explicit Luttinger-Ward functional $\Phi[G;\Lambda,{\cal K};U]$ is constructed containing only the renormalized one-particle, $G$, irreducible, $\Lambda$, and reducible, ${\cal K}$, two-particle propagators as independent variational functions. The parquet approximation is proven to be a thermodynamically consistent, $\Phi$-derivable theory obeying the necessary conservation laws.
fields
cond-mat.str-el 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Stabilizing the parquet problem
Derives an explicit stability criterion for parquet fixed-point iterations showing convergence issues arise independently of vertex divergences and demonstrates a controlled stabilization method that reaches the physical solution across multiple divergence lines.