Report on 2305.16050v1
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.
Authors 4
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TU Wien · Max Planck Institute for the Structure and Dynamics of Matter · RWTH Aachen University
Affiliation as printed
Institute for Theoretical Solid State Physics, RWTH Aachen University, 52074 Aachen, Germany
Institute of Solid State Physics, TU Wien, 1040 Vienna, Austria
Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany
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Affiliation as printed
Institute of Solid State Physics , TU Wien , 1040 Vienna , Austria
Institute of Solid State Physics, TU Wien, 1040 Vienna, Austria
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Affiliation as printed
Institute of Solid State Physics , TU Wien , 1040 Vienna , Austria
Institute of Solid State Physics, TU Wien, 1040 Vienna, Austria
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Affiliation as printed
Institute of Solid State Physics , TU Wien , 1040 Vienna , Austria
Institute of Solid State Physics, TU Wien, 1040 Vienna, Austria
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