Generating functional for the full parquet approximation

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 $\Phi [G;\Lambda ,\mathcal{K};U]$ is constructed containing only the renormalized one-particle, $G$, irreducible, $\Lambda$, and reducible, $\mathcal{K}$, 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.

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