Nonexistence of the Luttinger-Ward Functional and Misleading Convergence of Skeleton Diagrammatic Series for Hubbard-Like Models - Département de physique
Article Dans Une Revue Physical Review Letters Année : 2015

Nonexistence of the Luttinger-Ward Functional and Misleading Convergence of Skeleton Diagrammatic Series for Hubbard-Like Models

Résumé

The Luttinger-Ward functional Φ[G], which expresses the thermodynamic grand potential in terms of the interacting single-particle Green’s function G, is found to be ill-defined for fermionic models with the Hubbard on-site interaction. In particular, we show that the self-energy Σ[G] ∝ δΦ[G]/δG is not a single-valued functional of G: in addition to the physical solution for Σ[G], there exists at least one qualitatively distinct unphysical branch. This result is demonstrated for several models: the Hubbard atom, the Anderson impurity model, and the full two-dimensional Hubbard model. Despite this pathology, the skeleton Feynman diagrammatic series for Σ in terms of G is found to converge at least for moderately low temperatures. However, at strong interactions, its convergence is to the unphysical branch. This reveals a new scenario of breaking down of diagrammatic expansions. In contrast, the bare series in terms of the non-interacting Green’s function G0 converges to the correct physical branch of Σ in all cases currently accessible by diagrammatic Monte Carlo. Besides their conceptual importance, these observations have important implications for techniques based on the explicit summation of diagrammatic series.
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Dates et versions

hal-02363983 , version 1 (08-01-2025)

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Evgeny Kozik, Michel Ferrero, Antoine Georges. Nonexistence of the Luttinger-Ward Functional and Misleading Convergence of Skeleton Diagrammatic Series for Hubbard-Like Models. Physical Review Letters, 2015, 114 (15), pp.156402. ⟨10.1103/PhysRevLett.114.156402⟩. ⟨hal-02363983⟩
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