The Luttinger–Ward functional has no direct physical meaning, but it is useful in proving conservation laws. The functional is closely related to the Baym–Kadanoff functional constructed independently by Gordon Baym and Leo Kadanoff in 1961. See more In solid state physics, the Luttinger–Ward functional, proposed by Joaquin Mazdak Luttinger and John Clive Ward in 1960, is a scalar functional of the bare electron-electron interaction and the renormalized one-particle propagator See more Diagrammatically, the Luttinger–Ward functional is the sum of all closed, bold, two-particle irreducible Feynman diagrams (also known as “skeleton” diagrams): The diagrams are … See more Given a system characterized by the action $${\displaystyle S[c,{\bar {c}}]}$$ in terms of Grassmann fields $${\displaystyle c_{i},{\bar {c}}_{i}}$$, the partition function can be expressed as the path integral: where See more • Luttinger's theorem • Ward identity See more WebThe failure stems from the nonexistence of the Luttinger-Ward functional for a system in which the self-energy diverges. Since it is the existence of the Luttinger-Ward functional that is the basis for Luttinger's theorem which relates the charge density to sign changes of the single-particle Green function, no such theorem exists.

Free Energy from Stationary Implementation of the DFT …

WebFeb 28, 2013 · The failure stems from the nonexistence of the Luttinger-Ward functional for a system in which the self-energy diverges. Since it is the existence of the Luttinger-Ward functional that is the basis for Luttinger’s theorem which relates the charge density to sign changes of the single-particle Green function, no such theorem exists. WebLuttinger-Ward functional Ji Feng1, 1International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, Chinay (Dated: November 22, 2024) I. GREEN’S FUNCTION In the interaction picture an operator is given by A I(t) = eiH 0t=~Ae iH 0t=~: (1) The Wick’s rotation paxton hood

Luttinger-Ward functional approach in the Eliashberg framework:

Web72 Luttinger-Ward functional 72.3 The Luttinger-Ward functional and the Legendre transform of T lnZ 77 The self-energy functional approach and DMFT 77.... WebDiagrammatically, the Luttinger–Ward functional is the sum of all closed, bold, two-particle irreducible Feynman diagrams (also known as “skeleton” diagrams): The diagrams are … Webof the Luttinger-Ward functional, which strongly suggests that Eq. (1) gives nonstationary total energies. The Luttinger-Ward functional of DFTþDMFT has been well known for several years [17], but it has never been successfully implemented to compute the free energy of solids. It has the following form: Γ½G¼ TrlogG−Tr½ðG−1 0 −G− ... paxtonia softball