Eckhardt, C., Kappl, P., Kauch, A., & Held, K. (2023). A functional-analysis derivation of the parquet equation. SciPost Physics, 15(5), Article 203. https://doi.org/10.21468/SciPostPhys.15.5.203
strongly related electron systems; parquet equation
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Abstract:
The parquet equation is an exact field-theoretic equation known since the 60s that underlies numerous approximations to solve strongly correlated Fermion systems. Its derivation previously relied on combinatorial arguments classifying all diagrams of the two-particle Green’s function in terms of their (ir)reducibility properties. In this work we provide a derivation of the parquet equation solely employing techniques of functional analysis namely functional Legendre transformations and functional derivatives. The advantage of a derivation in terms of a straightforward calculation is twofold: (i) the quantities appearing in the calculation have a clear mathematical definition and interpretation as derivatives of the Luttinger–Ward functional; (ii) analogous calculations to the ones that lead to the parquet equation may be performed for higher-order Green’s functions potentially leading to a classification of these in terms of their (ir)reducible components.
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Project title:
elektronische Korrelationen auf dem 3-Teilchen-Niveau: P 32044-N32 (FWF - Österr. Wissenschaftsfonds)