Legendre Transformation of the Luttinger-Ward Functional from the Bare Interaction Vertex to the Renormalized One

Takafumi Kita

doi:10.7566/jpsj.91.114002

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arXiv · 2210.08660

Legendre Transformation of the Luttinger-Ward Functional from the Bare Interaction Vertex to the Renormalized One

Takafumi Kita

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Abstract

On the basis of the Luttinger-Ward functional for interacting many-body systems given in terms of full Green's function $G$ and the bare interaction vertex $Γ^{(0)}$, we develop a novel Legendre transformation to express the grand thermodynamic potential $Ω$ as a functional of $G$ and the renormalized interaction vertex $Γ$ so that (i) $G$ and $Γ$ obey the stationarity conditions $δΩ/δG=0$ and $δΩ/δΓ=0$ and (ii) $Γ$ reduces to $Γ^{(0)}$ in the weak-coupling limit. The formalism enables us to perform microscopic studies of thermodynamic, single-particle, and two-particle properties in a unified self-consistent conserving framework.

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Takafumi Kita. 2022-10-16. Legendre Transformation of the Luttinger-Ward Functional from the Bare Interaction Vertex to the Renormalized One. https://doi.org/10.7566/jpsj.91.114002

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