A functionalanalysis derivation of the parquet equation
Abstract
The parquet equation is an exact fieldtheoretic 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 twoparticle 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 LuttingerWard functional; (ii) analogous calculations to the ones that lead to the parquet equation may be performed for higherorder Green's functions potentially leading to a classification of these in terms of their (ir)reducible components.
 Publication:

SciPost Physics
 Pub Date:
 November 2023
 DOI:
 10.21468/SciPostPhys.15.5.203
 arXiv:
 arXiv:2305.16050
 Bibcode:
 2023ScPP...15..203E
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics
 EPrint:
 Submission to SciPost