TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.5.203
TI  - A functional-analysis derivation of the parquet equation
PY  - 2023/11/24
UR  - https://www.scipost.org/SciPostPhys.15.5.203
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 5
SP  - 203
A1  - Eckhardt, Christian J.
AU  - Kappl, Patrick
AU  - Kauch, Anna
AU  - Held, Karsten
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.15.5.203,
	title={{A functional-analysis derivation of the parquet equation}},
	author={Christian J. Eckhardt and Patrick Kappl and Anna Kauch and Karsten Held},
	journal={SciPost Phys.},
	volume={15},
	pages={203},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.5.203},
	url={https://scipost.org/10.21468/SciPostPhys.15.5.203},
}