Derivation of exact flow equations from the self-consistent parquet relations

We exploit the parquet formalism to derive exact flow equations for the two-particle-reducible four-point vertices, the self-energy, and typical response functions, circumventing the reliance on higher-point vertices. This includes a concise, algebraic derivation of the multiloop flow equations, whi...

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Bibliographic Details
Published in:New journal of physics 2018-12, Vol.20 (12), p.123029
Main Authors: Kugler, Fabian B, Delft, Jan von
Format: Article
Language:English
Subjects:
Apexes
conservation laws
Derivation
Differential equations
Energy conservation
exact flow equations
Flow equations
functional renormalization group
Mathematical analysis
parquet equations
Physics
Response functions
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Summary:We exploit the parquet formalism to derive exact flow equations for the two-particle-reducible four-point vertices, the self-energy, and typical response functions, circumventing the reliance on higher-point vertices. This includes a concise, algebraic derivation of the multiloop flow equations, which have previously been obtained by diagrammatic considerations. Integrating the multiloop flow for a given input of the totally irreducible vertex is equivalent to solving the parquet equations with that input. Hence, one can tune systems from solvable limits to complicated situations by variation of one-particle parameters, staying at the fully self-consistent solution of the parquet equations throughout the flow. Furthermore, we use the resulting differential form of the Schwinger-Dyson equation for the self-energy to demonstrate one-particle conservation of the parquet approximation and to construct a conserving two-particle vertex via functional differentiation of the parquet self-energy. Our analysis gives a unified picture of the various many-body relations and exact renormalization group equations.
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/aaf65f