Shifted-Action Expansion and Applicability of Dressed Diagrammatic Schemes

Abstract

While bare diagrammatic series are merely Taylor expansions in powers of interaction strength, dressed diagrammatic series, built on fully or partially dressed lines and vertices, are usually constructed by reordering the bare diagrams, which is an a priori unjustified manipulation, and can even lead to convergence to an unphysical result [Kozik, Ferrero and Georges, PRL 114, 156402 (2015)]. Here we show that for a broad class of partially dressed diagrammatic schemes, there exists an action $S^{(\xi )}$ depending analytically on an auxiliary complex parameter $\xi$, such that the Taylor expansion in $\xi$ of correlation functions reproduces the original diagrammatic series. The resulting applicability conditions are similar to the bare case. For fully dressed skeleton diagrammatics, analyticity of $S^{(\xi )}$ is not granted, and we formulate a sufficient condition for converging to the correct result.

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References in corpus (6)

• Color superconductivity in dense quark matter
• Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
• Emergent BCS regime of the two-dimensional fermionic Hubbard model: ground-state phase diagram
• Diagrammatic Monte Carlo method for many-polaron problems
• Bold Diagrammatic Monte Carlo Method Applied to Fermionized Frustrated Spins
• Skeleton series and multivaluedness of the self-energy functional in zero space-time dimensions

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